On the Ytterbium Valence and the Physical Properties in Selected Intermetallic Phases

Abstract

The present review summarizes important aspects of the crystal chemistry of ytterbium-based intermetallic compounds along with a selection of their outstanding physical properties. These originate in many cases from the ytterbium valence. Different valence states are possible here, divalent (4f¹⁴), intermediate-valent, or trivalent (4f¹³) ytterbium, resulting in simple diamagnetic, Pauli or Curie–Weiss paramagnetic, or valence fluctuating behavior. Especially, some of the Yb³⁺ intermetallics have gained deep interest due to their Kondo or heavy Fermion ground states. We have summarized their property investigations using magnetic and transport measurements, specific heat data, NMR, ESR, and Mössbauer spectroscopy, elastic and inelastic neutron scattering, and XAS data as well as detailed thermoelectric measurements.

Ytterbium is one of the few rare earth elements that is prone to valence instabilities in intermetallic compounds. In the rare earth series, many examples are known for cerium, where the interplay between the 4f¹ configuration for Ce³⁺ and the empty f shell for tetravalent cerium led to a huge number of compounds with broadly varying magnetic and electrical properties, such as long-range magnetic ordering (antiferro-, ferro-, or ferrimagnetism), Kondo-type behavior, heavy Fermion behavior as well as static or dynamic intermediate cerium valence. These many facets of structure–property relationships of cerium intermetallics have been summarized in review articles.¹⁻⁶ While only a few examples are known for divalent samarium (the trivalent state is usually observed),⁷ many europium compounds have been studied with respect to their valence behavior.⁸⁻¹⁰ Most of these compounds exhibit the stable half-filled f shell (4f⁷ configuration), and consequently, divalent europium is the usual case for intermetallics along with paramagnetism and long-range magnetic ordering, sometimes at comparatively high ordering temperatures. The scarce case of trivalent europium in intermetallic phases has recently been reviewed.¹⁰

The present review focuses on intermetallic ytterbium compounds. Here, the configurations 4f¹⁴ (filled f shell; divalent ytterbium; diamagnetic) and 4f¹³ (paramagnetic trivalent ytterbium) are the edge states, and static and dynamic ytterbium valence states are observed in-between. Especially, the trivalent ytterbium compounds have attracted high attention in solid-state chemistry and physics, since the 4f¹³ configuration is the 4f hole analogue to Ce³⁺. Thus, the ground state properties of these ytterbium-based phases are highly sensitive to the amount of 4f electron (hole)–conduction electron hybridization (Kondo effect).¹¹⁻¹⁴ This influences the Ruderman–Kittel–Kasuya–Yosida (RKKY) exchange interactions and consequently the magnetic ordering. The broad analogy to cerium intermetallics is especially interesting with respect to intermediate-valence and potential heavy Fermion materials.¹⁵⁻¹⁷

Materials science can only work with an excellent interplay of solid-state physics and solid-state chemistry, whereby detailed phase analyses and high-quality sample preparation along with precise structure determination are the indispensable prerequisites for reliable property measurements. Herein we review these features for the field of intermetallic ytterbium compounds with a strong emphasis on the ytterbium valence behavior.

The review is written from a solid-state chemist’s point of view. Bearing the enormous number of compounds¹⁸ and property measurements in mind, it is simply not possible to include all known intermetallic ytterbium compounds and all references into such an overview (e.g., > 350 references for YbRh₂Si₂ in SciFinder¹⁹). Herein we mainly concentrate on the role of the ytterbium valence in intermetallics and underpin these peculiarities with selected examples. Any missing compound or reference is unintentional.

SYNTHESES AND CRYSTAL GROWTH

The peculiar electronic structure of ytterbium has drastic effects on its physical properties, when compared with the neighboring rare earth elements. Its divalent nature already in the elemental state leads to drastically reduced melting (1097 K) and boiling (1466 K) points.²⁰ Arc-melting is a broadly used synthesis technique for intermetallic samples;²¹ however, drastic evaporation losses can occur in the cases of ytterbium-based synthesis, when reacting ytterbium with the high-melting noble metals, e.g., platinum (mp 2025 K) or iridium (mp 2683 K). To give an example, during an arc-melting synthesis of YbRh₂Si₂,²² the ytterbium would largely evaporate before the rhodium melts. Thus, only a few ytterbium intermetallics were prepared by arc melting. Representative examples are YbNiAl₄²³ or Yb₃Rh₉Si₂Sn₃.²⁴ For the precise reaction conditions, we refer to the individual publications. In the present chapter, we summarize the different techniques that find application.

Broader phase analytical studies were conducted by simple, direct reaction of the elements in sealed evacuated fused silica ampules. This is possible for almost all Yb_xT_yX_z samples with X = elements of the group 13, 14, or 15. The inner surface of the silica ampules can be graphitized (thermal decomposition of acetone) for passivation, or alumina crucibles can be used as inert container material. The reactions and annealing sequences are usually carried out in tube or muffle furnaces. These reactions are not that far from the classical ceramic method²⁵ for the preparation of solids. Often the samples are still multiphase after the first annealing cycle. Thus, repeated grinding, pressing of pellets, and reannealing is necessary in order to obtain samples that are at least phase-pure on the level of powder X-ray diffraction. A critical feature is the repeated grinding, since the increasing surface area might lead to surface oxidation and thus Yb₂O₃ contamination (vide infra). This ceramic technique was frequently used for the synthesis of ytterbium-based ternary phosphides and arsenides.²⁶ The best way to avoid these Yb₂O₃ contaminations is the use of distilled ytterbium and working under purified inert gas.

For physical property measurements, high sample purity is required. Nowadays, the intermetallic ytterbium phases are prepared in sealed (arc-welded²⁷ under argon or helium atmosphere) high-melting metal tubes, usually niobium or tantalum, but molybdenum can also find application. This ensures largely inert crucible conditions and prevents evaporation losses of ytterbium. For the reaction, the metal tubes can be sealed in silica tubes (oxidation protection), and the annealing sequence can be run in a tube or muffle furnace. Much better results are obtained through induction melting and subsequent annealing.^28,29 Good quantities of X-ray pure polycrystalline samples are available by this technique.

Direction-dependent property measurements can only be performed on high-quality single crystals. This deserves sophisticated crystal growth conditions. The flux growth technique³⁰⁻³³ is meanwhile well established in the field of crystal growth of intermetallic phases. Usually the low-melting p block elements aluminum, gallium, indium, tin, and bismuth find application as flux medium. Two strategies for crystal growth are possible. The easy way is the self-flux technique (the so-called reactive flux), where the low-melting p element is a component of the product and flux medium at the same time. Otherwise, one can use an inert flux (the so-called nonreactive flux), which does not enter the product crystals. There are some prerequisites for targeted crystal growth: (i) the flux medium should be inert toward the crucible material and (ii) the excess flux should easily be separable from the product crystals.

Typical examples for flux-grown crystals are YbRh₂Si₂ and YbIr₂Si₂,³⁴ or Yb₂CuGe₆ and Yb₃Cu₄Ge₄,³⁵ which form in liquid indium. Also, Yb₂AuGe₃ crystals can be grown from liquid indium with up to 2 mm edge size.³⁶ The excess flux can be dissolved in diluted hydrochloric acid. Similar flux growth experiments are feasible with aluminum and gallium as the flux medium.³⁷ A interesting example for a nonreactive flux is the growth of YbRh₆P₄ crystals in liquid bismuth.³⁸ Besides dissolution of the flux after successful crystal growth, the liquid flux can also be separated by centrifugation at elevated temperatures. Here are two possible ways: (i) a second crucible filled with quartz wool or a quartz wool plug can be placed (reversed) on top of the one containing the starting materials³⁰ or (ii) a frit-disc crucible set (“Canfield crucible set”) can be utilized.³⁹

Finally, we turn back to the classical textbook examples for crystal growth. Due to the high vapor pressure of molten ytterbium, the Czochralski technique cannot be used. The Bridgman technique (where again sealed tubes are used) was successfully applied for crystal growth of the copper-rich ytterbium compounds YbCu_4.25 and YbCu_4.4.⁴⁰ Tantalum was used as container materials, and the crucible lowering speed at the high-frequency coil was 3 mm h^–1. Crystals for diffraction experiments were finally separated from different slices that were prepared from the bulk crystal via spark erosion. Further examples for the Bridgman crystal growth are the germanides Yb₂Ru₃Ge₄,⁴¹ YbPdGe, and YbPtGe.⁴²

CRYSTAL CHEMICAL PRINCIPLES

The present review has a higher focus on the physical properties of ytterbium intermetallics, and we therefore only give a short and concise overview on some of the basic crystal chemical principles that are important for the family of Yb_xT_yX_z intermetallics. The structural chemistry is mostly driven by the ytterbium valence. As discussed above, the filled 4f shell of Yb(II) might be considered as a diamagnetic core–electron shell, and consequently, we observe a crystal chemical behavior of an alkaline earth element. This is readily understandable when comparing the ionic radii for coordination number 6 for Ca²⁺ (100 pm) and Yb²⁺ (102 pm).⁴³ We thus observe a close structural relationship of the divalent ytterbium intermetallics with their respective calcium analogues. Typical examples are the binary Zintl phases Ca₂Ge⁴⁴ and Yb₂Ge⁴⁵ as well as the ternary Zintl phases CaZnSn⁴⁶ and YbZnSn⁴⁷ with many more pairs of isotypic compounds than for Yb²⁺/Ca²⁺.⁴⁸

A similar close relationship is known for Eu²⁺ (117 pm) and Sr²⁺ (118 pm).⁴³ Some examples are EuAl₂Pt and SrAl₂Pt (MgCuAl₂ type, space group Cmcm),⁴⁹ EuAl₅Pt₃⁵⁰ and SrAl₅Pt₃⁵¹ (YNi₅Si₃ type, space group Pnma), SrAu₃Al₂⁵² and EuAu₃Al₂⁵³ (RbAu₃Ga₂ type, space group Pnma), EuAu₂Al₂⁵⁴ and SrAu₂Al₂^54,55 (CaBe₂Ge₂ type, space group P4/nmm), Eu₂T₂In⁵⁶ and Sr₂T₂In⁵⁷ (T = Pd, Pt; Ca₂Ir₂Si type, space group C2/c), EuRh₂In₈⁵⁸ and SrRh₂In₈⁵⁹ (CeFe₂Al₈ type, space group Pbam), EuPtSi and SrPtSi (LaIrSi type, space group Pnma),⁶⁰ or finally EuPt₂Si₂ and SrPt₂Si₂ (ThCr₂Si₂ type, space group I4/mmm).⁶¹ Besides the direct comparisons Sr²⁺/Eu²⁺ and Ca²⁺/Yb²⁺, it is not always possible to directly compare an Eu(II) example and an Yb(II) example within one series of compounds, since (i) the structure type is not formed with both cations or (ii) the given ytterbium is trivalent. And even if both compounds are known and adopt the same structure type, the physical properties are significantly different due to Yb(II) being a diamagnetic cation while Eu(II) exhibits a half-filled 4f shell (4f⁷).

In the case of trivalent ytterbium intermetallics, the ytterbium compound usually adopts the crystal structure of the neighboring compounds existing with thulium or lutetium. A first fast hint for the ytterbium valence can be gathered from the plot of the unit cell volumes of a given series of rare earth compounds, a so-called Iandelli plot. As examples, we present the series of REPdZn⁶²⁻⁶⁴ and RE₂Pt₂Pb^47,65 phases in Figure 1. Since divalent ytterbium has a distinctly larger radius than trivalent ytterbium, positive deviations in the Iandelli plot (this is the case for the REPdZn series) indicate divalent ytterbium. If the unit cell volume fits smoothly into the plot, then ytterbium is trivalent (this is the case for the RE₂Pt₂Pb series). Nevertheless, one important observation needs to be mentioned at this point. Although the physical property measurements (vide infra) show stable trivalent ytterbium in Yb₂Pt₂Pb, the Iandelli plot shows a very small positive deviation. Such an anomaly is frequently observed for rare earth series with trivalent ytterbium. Another striking series with such a weak positive deviation is the one of REAl₃C₃.⁶⁶ Many more examples for both cases can be found when checking structural databases like the Pearson database.¹⁸

Figure 1.

Plot of the unit cell volumes for the series REPdZn (per formula unit) and RE₂Pt₂Pb (subcell volumes). Data was taken from the Pearson database.¹⁸

Compounds that exhibit temperature- or pressure-dependent valence phase transitions show a discontinuity in their lattice parameters. YbPd₂Al₃ (YNi₂Al₃ type, space group P6/mmm), for example, exhibits a mixed valent state (Yb^II and Yb^III) at room temperature which transitions into an almost fully divalent state below T_trans = 110 K. The temperature dependence of the lattice parameters is shown in Figure 2. Here, a clear increase of the c lattice parameter is visible (+3 pm, 0.7%). Due to the relatively high transition temperature, single crystal studies were possible, that confirmed the thermal behavior of the lattice parameters and clearly indicated that no structural phase transition takes place. However, significant distortions in the respective Yb coordination polyhedra are observed.⁶⁷

Figure 2.

Lattice parameters of YbPd₂Al₃ obtained from temperature-dependent powder X-ray diffraction experiments upon cooling from 300 to 10 K and from single-crystal X-ray diffraction experiments. Reprinted with permission from ref (67).

Finally, a very recent study of Yb₂Pd₂Cd should be mentioned. Here, a structural phase transition at ∼150 K was observed. The high-temperature modification adopts the Mo₂B₂Fe type (space group P4/mbm) while below the phase transition temperature, LT-Yb₂Pd₂Cd is found in a new structure type (space group P4/mbm) with a doubled c axis. The striking structural feature concerns the ytterbium–palladium coordination. The average Yb–Pd distances distort, forming a smaller and a larger coordination environment and enabling a charge separation for Yb²⁺ and Yb³⁺.⁶⁸

SELECTED CRYSTAL STRUCTURES

In the present chapter, we want to selectively focus on some structural principles and refer to extended crystal chemical review articles for further reading. Some of the Yb_xT_yX_z phases crystallize with their individual structure type which have all been thoroughly described in the original articles.

Many of the intermetallic ytterbium compounds belong to the so-called equiatomic phases YbTX (T = (transition) metal; X = element of group 13, 14, or 15). The most frequent structure types that occur for these phases are TiNiSi (space group Pnma), ZrNiAl (space group P62m), MgAgAs (space group F43m), PbFCl (space group P4/nmm), and other AlB₂ (space group P6/mmm) derived superstructures. Their crystal chemistry has been reviewed in the Handbook on the Physics and Chemistry of Rare Earths.¹³ These structure types allow for a certain structural flexibility. To give an example, for the orthorhombic TiNiSi type, a manifold of ytterbium-based phases YbTX (T = Mg, Ni, Cu, Rh, Pd, Pt, Au; X = Al, Si, P, Ga, Ge, Sn, Sb) have been synthesized.^13,18 Apart from the overview on the equiatomic YbTX phases, the crystal chemistry of these versatile structure types has repeatedly been discussed in various other review articles.^{3−6,8,69−72} We refer to these overviews for further reading.

A huge number of property studies has been conducted for the binary aluminides YbAl₂ (MgCu₂ type, cubic Laves phase, space group Fd3m)⁷³ and YbAl₃ (Cu₃Au type; ordered cubic closest packing, space group Pm3m).^74,75 Both compounds crystallize with well-known basic structure types. In this context it is interesting to note that ternary ones have also been reported with the structure types of the cubic and hexagonal Laves phases. In the case of the MgCu₂ type phases, especially the solid solution members Yb_1–xIn_xCu₂ have been studied, where the ytterbium substructure has been magnetically diluted through indium substitution. YbCu₄In⁷⁶ shows 1:1 Yb/In ordering and crystallizes with the noncentrosymmetric MgCu₄Sn type (space group F43m). The crystal chemical details of Laves phase superstructures have recently been reviewed.⁷⁷ Several aluminides were reported as equiatomic compounds, and the MgZn₂ type (space group P6₃/mmc) was assigned.¹³ Meanwhile, it is known that an equiatomic composition with complete atom ordering is not possible. The superstructure formation leads to a small deviation. The correct model was solved for Yb₆Ir₅Ga₇ (space group P6₃/mcm) and the series of gallides RE₆Ir₅Ga₇.^78,79 Shortly later, also the aluminum containing RE₆T₅Al₇ phases (RE = Sc, Y, Ce–Nd, Sm, Gd–Lu; T = Ru, Ir)⁸⁰ have been structurally characterized. With respect to the physical properties, one must differentiate between the fully ordered 6–5–7 phases and solid solutions where mixed occupied sites occur. Often, disorder destroys magnetic ordering or drastically reduces the magnetic ordering temperature.

We now discuss the crystal chemistry of some selected examples. One of the striking ternary ytterbium intermetallics is YbRh₂Si₂ (ThCr₂Si₂ type, space group I4/mmm) originally reported in 1979 by Rossi et al.²² Due to its outstanding physical properties (vide infra), meanwhile >350 publications are listed in SciFinder.¹⁹ The YbRh₂Si₂ unit cell is presented in Figure 3. The rhodium atoms have a tetrahedral silicon coordination with Rh–Si distances of 235 pm. These [RhSi₄] tetrahedra are condensed via edge-sharing, building a dense layer in the ab plane. Adjacent layers are connected via Si–Si bonds (246 pm). The resulting network provides large cages for the ytterbium atoms which have a coordination number of 18, i.e., Yb@Si₁₀Rh₈. Due to the large cages, the shortest Yb–Yb distances are 401 pm, corresponding to the a lattice parameter. The ThCr₂Si₂ family of compounds is one of the largest among all intermetallic compounds with more than 4000 entries in the Pearson database.¹⁸ The crystal chemical details for these materials are summarized in diverse overviews.^1,69,81,82

Figure 3.

Crystal structures of YbRh₂Si₂²² and YbIrIn₅.⁸³ Ytterbium, rhodium (iridium), and silicon (indium) atoms are drawn as medium gray, blue, and magenta circles, respectively. The network of edge-sharing [RhSi₄] tetrahedra for YbRh₂Si₂ and the characteristic polyhedra for YbIrIn₅ are emphasized.

Another, smaller series of tetragonal compounds concerns those with HoCoGa₅ type structure⁸⁴ (space group P4/mmm). This type has been observed for YbCoGa₅ and the indides YbTIn₅ (T = Co, Rh, Ir).^83,85 The YbIrIn₅ unit cell⁸³ is also presented in Figure 3. The YbIrIn₅ structure is composed of two striking building units. The ytterbium atoms have slightly tetragonally distorted cuboctahedral indium coordination (8 × 320 and 4 × 327 pm Yb–In), which can be considered as a cutout of an ordered closest fcc related packing (given the comparable size of ytterbium and indium). These cuboctahedra condense to layers via four common rectangular faces. These layers alternate with layers of condensed Ir@In₈ square prisms (275 pm Ir–In). Similar to YbRh₂Si₂ discussed above, the ytterbium atoms in YbIrIn₅ are also well separated from each other. The shortest Yb–Yb distance of 462 pm again corresponds to the lattice parameter a.

Yb₂Pt₂Pb⁴³ is one of the few ytterbium intermetallics that belong to the family of U₃Si₂ derived phases. Due to a puckering effect, one observes superstructure formation for Yb₂Pt₂Pb (space group P4₂/mnm) with a small distortion of the ytterbium trigonal and square prisms. For better visibility, only one layer is presented in Figure 4. A more detailed crystal chemical discussion is given in references (86 and 87). The striking feature of this plumbide is the Shastry–Sutherland-like substructure of the ytterbium atoms, which gives rise to magnetic frustration (discussed in detail in the magnetic part, vide infra). Several years after the discovery of the compound,⁴⁷ this has motivated many detailed property studies, which are addressed below.

Figure 4.

Cutout of the Yb₂Pt₂Pb⁴⁷ structure. Ytterbium, platinum, and lead atoms are drawn as medium gray, blue, and magenta circles, respectively. The CsCl and AlB₂ related slabs and the two crystallographically independent ytterbium sites are emphasized. Only one layer is shown for better visibility.

A complex cubic structure occurs for the aluminum- and zinc-rich compounds YbT₂Al₂₀ (T = Ti, V, Cr) and YbT₂Zn₂₀ (T = Co, Rh, Ir).¹⁸ They crystallize with the CeCr₂Al₂₀ type, space group Fd3m with 184 atoms per unit cell. The main interest in these ytterbium compounds concerned their heavy-Fermion type behavior. The many facets of their physical properties have recently been summarized.⁸⁸ As an example we present the YbCo₂Zn₂₀ structure⁸⁹ in Figure 5. Although the structure seems complex at first sight, it can easily be constructed from two basic building units. The ytterbium and cobalt atoms of YbCo₂Zn₂₀ form a substructure that is isopointal with the cubic Laves phase MgCu₂, i.e., has the same space group symmetry. The zinc atoms now surround the ytterbium and cobalt atoms, leading to Yb@Zn₁₆ and Co@Zn₁₂ polyhedra which condense in a tetrahedral motif. Again, the ytterbium atoms are well separated from each other and show no bonding contacts. This “highly diluted” rare earth substructure is prone for basic property studies.

Figure 5.

Cutout of the YbCo₂Zn₂₀⁸⁹ structure. Cobalt and zinc atoms are drawn as medium blue and magenta circles, respectively. The connectivity pattern of the Yb@Zn₁₆ and Co@Zn₁₂ polyhedra is emphasized. For details see text.

In Figure 6, we now turn to a series of ytterbium compounds with complex extended polyanionic networks which exhibit multiple ytterbium sites. Exemplarily, we present the structures of Yb₃Pd₄Ge₄,⁹⁰ Yb₂Pt₃Sn₅,²⁹ and Yb₂Au₃In₅.⁹¹ The common structural feature concerns the dense condensation of the transition metal and p element atoms within the polyanionic networks [Pd₄Ge₄], [Pt₃Sn₅], and [Au₃In₅]. The latter are stabilized through Pd–Ge, Pt–Sn, Au–In as well as Ge–Ge, Sn–Sn, and In–In bonding interactions. The networks then leave cavities of different sizes which are filled by the ytterbium atoms. This leads to the coordination polyhedra Yb1@Ge₆Pd₆ and Yb2@Ge₆Pd₈ for Yb₃Pd₄Ge₄, Yb1@Sn₆Pt₂ and Yb2@Pt₅Sn₈ for Yb₂Pt₃Sn₅ as well as Yb1@Au₄In₁₀ and Yb2@Au₅In₈ for Yb₂Au₃In₅. The three compounds tend to exhibit mixed ytterbium valences. From a crystal chemical point of view, the smaller cavities are filled by trivalent ytterbium (static mixed valency). For Yb₂Pt₃Sn₅, this feature was tested also from a synthetic point of view. Given the comparable size of Yb²⁺ and Ca²⁺ it was possible to synthesize the stannides CaErPt₃Sn₅, CaTmPt₃Sn₅, CaYbPt₃Sn₅, and CaLuPt₃Sn₅ with calcium site preference on the “divalent” place.⁹²

Figure 6.

View of the Yb₃Pd₄Ge₄,⁹⁰ Yb₂Pt₃Sn₅,²⁹ and Yb₂Au₃In₅⁹¹ structures along the short unit cell axis. Ytterbium, palladium (platinum, gold), and germanium (tin, indium) atoms are drawn as medium gray, blue, and magenta circles, respectively. The [Pd₄Ge₄], [Pt₃Sn₅], and [Au₃In₅] networks and the crystallographically independent ytterbium sites are emphasized.

The last crystal chemical example concerns ytterbium aluminum borides. Figure 7 shows projections of the α- and β-YbAlB₄⁹³ and Yb₂AlB₆⁹⁴ structures along the short unit cell axis. The boron atoms build up planar layers with different tessellations, which are stacked in a ...AA... sequence. Between the layers, pentagonal prisms for the smaller aluminum atoms and hexagonal, respectively, heptagonal ones for the larger ytterbium atoms are formed. The two modifications of YbAlB₄ show ytterbium exclusively in the heptagonal prisms, while two prism types occur in Yb₂AlB₆. The YbAlB₄ modifications gained high interest in recent years since they exhibit heavy Fermion ground state and superconductivity at low temperatures (vide infra). Already more than 120 publications appeared for this composition.¹⁹

Figure 7.

View of the α-YbAlB₄,⁹³ β-YbAlB₄⁹³ and Yb₂AlB₆⁹⁴ structures along the short unit cell axis. Ytterbium, aluminum, and boron atoms are drawn as medium gray, blue, and magenta circles, respectively. The boron nets and the crystallographically independent ytterbium sites are emphasized.

PHYSICAL PROPERTIES AND SPECTROSCOPY

Given the large number of known phases and the fact that some of them have only been characterized with respect to their structure, the review focuses on the ytterbium valence and selected physical properties that arise from these. Thus, selected compounds with a divalent or trivalent ytterbium state are discussed to outline these properties.

Most compounds have routinely been studied with respect to their magnetic behavior in order to get a first hint for the ytterbium valence. A significantly smaller section of these studies is additionally accompanied by resistivity and specific heat measurements; however, these measurements are usually not routinely conducted. Therefore, magnetic, resistivity, and specific heat investigations are, where applicable, discussed together in the following chapter. Subsequently, separate chapters summarize the data on more sophisticated investigation techniques such as (i) inelastic neutron scattering, (ii) XANES/XAS, (iii) X-ray photoelectron spectroscopy (XPS), (iv) nuclear magnetic and electron resonance spectroscopy (NMR and ESR), (v) ¹⁷¹Yb Mössbauer spectroscopy, and (vi) thermoelectric measurements.

Within each property chapter, the data has been summarized with respect to composition (binary or ternary) as well as structure types or structural families (e.g., Zintl phases), facilitating the comparability with respect to the valence electron count, etc.

MAGNETISM, RESISTIVITY AND SPECIFIC HEAT

Before starting with a broader discussion on the magnetic properties of intermetallic ytterbium compounds, we need to comment on ytterbium sesquioxide, Yb₂O₃, the most inconvenient byproduct occurring during the synthesis of Yb intermetallics. Yb₂O₃ exhibits paramagnetism (4f¹³ configuration; T_N = 2.3 K⁹⁵) and can dominate the susceptibility in the low-temperature regime,⁹⁶ especially in the case of intermediate-valent or almost divalent ytterbium intermetallics. In those cases, a clear quantification of the Yb₂O₃ content is necessary along with a correction procedure.⁹⁷ If this feature is not taken into account, the interpretation of the magnetic data remains ambiguous. Since many of the ytterbium intermetallics order magnetically at very low temperature, the Yb₂O₃ impurity might overlay the intrinsic magnetism of the sample.

Divalent Ytterbium Compounds

Purely divalent ytterbium compounds have the valence electron configuration 4f¹⁴, which exhibits high stability. This filled 4f shell can be considered as a core-electron shell; therefore, no magnetic moment is observed. Such ytterbium intermetallics behave either as diamagnets or as Pauli paramagnets. Since most of these phases are metallic conductors, the observed susceptibility usually arises from an overcompensation of the intrinsic core diamagnetism by the Pauli susceptibility caused by the conduction electrons.

Exemplarily, the temperature dependences of the magnetic susceptibility of Yb₅Cu₂Zn and Yb₃Ag₄Mg₁₂ are given in Figure 8. Above 100 K, the susceptibilities are very weak and almost temperature-independent. The room temperature value of 7.2 × 10^–6 emu mol^–1 for Yb₅Cu₂Zn indicates Pauli paramagnetism.⁹⁸ In contrast, in Yb₃Ag₄Mg₁₂ the intrinsic diamagnetism is not as strongly overcompensated by the Pauli contribution, leading to a room temperature value of −4.61 × 10^–4 emu mol^–1.⁹⁹ The susceptibility increases in the low-temperature regimes (the so-called Curie tails), which originates from traces of paramagnetic impurities. Further examples of room temperature susceptibilities are given in Table 1. In these compounds, the ytterbium atoms are divalent and therefore carry no magnetic moment.

Figure 8.

Temperature dependence of the magnetic susceptibility χ of Yb₃Ag₄Mg₁₂⁹⁹ and Yb₅Cu₂Zn,⁹⁸ measured at 10 kOe.

Table 1. Magnetic Susceptibilities of Selected Ytterbium Intermetallics at Room Temperature^a.

Compound	χ/emu mol–1	Reference
YbAgMg	+1.2(1) × 10–4	(100)
YbAuMg	+2.4 × 10–4	(101)
Yb3Ag4Mg12	–4.61 × 10–4	(99)
Yb5Cu2Zn	+7.2 × 10–6	(98)
YbAgCd	+4.8 × 10–5	(102)
YbAuCd	+5.8 × 10–5	(101)
YbPdIn2	–4.9(2) × 10–4	(103)
YbCuSn	+4.22 × 10–4	(104)
YbAgSn	–1.37 × 10–5	(104)
YbAuSn	–2.62 × 10–5	(104)
YbZnSn	+2.0(1) × 10–4	(47)
YbCuSb	+1.38 × 10–4	(104)
YbAgSb	–7.69 × 10–5	(104)
YbAuSb	–8.47 × 10–5	(104)

^aStandard deviations are given in parentheses, where available.

Trivalent Ytterbium Compounds

Trivalent ytterbium cations have a 4f¹³ valence electron configuration. The g value of 8/7 and the total angular momentum of J = 7/2 lead to a magnetic moment of μ = = 4.54 μ_B per Yb³⁺.¹⁰⁵ The f electrons may play an important role in bonding/hybridization of intermetallic ytterbium compounds, leading to interesting properties, such as heavy Fermion behavior, Kondo behavior, intermediate valence, or complex magnetic structures. These properties can be influenced by different parameters, like the chemical environment, the magnetic field, temperature, or pressure.¹⁰⁶

Characteristic for heavy Fermion behavior is the large electronic specific heat coefficient γ at low temperatures, 2 or 3 orders of magnitude larger (arbitrary value of 400 mJ mol^–1 K^–2 according to ref (107)) than that of copper (∼1 mJ mol^–1 K^–2).¹⁰⁸ In addition, heavy Fermion compounds typically have large Pauli susceptibilities at low temperatures, due to the large density of states.¹⁰⁹ It is very difficult to establish the heavy Fermion behavior of ytterbium compounds, due to the challenging distinction between magnetic, crystal field, and Kondo energy scales. Thus, many compounds show both, magnetic and heavy Fermion character.¹¹⁰

The common way to fit the dependence of the magnetic susceptibility is using the Curie–Weiss law. Within the modified Curie–Weiss law, contributions of the conduction electrons are also taken into account. This makes it possible to adjust even slight curvatures of the reciprocal susceptibility. However, both laws do not consider the temperature dependency of the effective magnetic moment, which marks the only way to explain decrease of the χ^–1 value. The ICF model (interconfiguration fluctuation model),¹¹¹ developed by Sales and Wohlleben, addresses a possible mixed-valent behavior of rare earth atoms (like Yb or Ce) and is represented by

with T_sf as the spin fluctuation temperature and v(T) as the temperature-dependent mean occupation of the ground state given by

where E_ex is the energy gap between the ground and the excited state. In most cases, the experimental χ(T) data can be described by

consisting in part of the ICF model (χ_ICF), the Curie–Weiss impurity (χ_CW), and χ₀, the latter being a sum of temperature-independent contributions.^111,112

In the following paragraph, some striking examples will be briefly discussed. The magnetic properties and specific heat coefficients of these and further compounds were summarized in Table 2.

Table 2. Magnetic Properties of Selected Ytterbium Compounds^a.

Compound	TC/K	TN/K	μeff/μB	γ/mJ mol–1 K–2	Reference
YbAlB4				125	(204,222)
YbAl3C3			4.66		(177)
YbFe2Zn20			Near 4.53	520	(88,183−186)
YbCo2Zn20			Near 4.53	7900	(88,183−186)
YbNiAl4			2.9	16	(23,215,216)
YbNi3Al9	–	3.4	4.37	110	(223)
YbNi4Si			4.15	25	(224)
YbNiGa		1.7, 1.9	4.4	450	(126)
YbNiSn	5.65	–	4.3	300	(121−123,125)
YbCuAl			4.32	260	(146,147,225)
YbCu2Si2			4.19	135	(226)
YbPdCu4	–	0.8	4.33	200	(227)
YbInCu4			4.37	50–400	(228,229)
YbRh2Si2	–	0.07	2 × 10–3		(155,161)
YbRhSn	–	1.4, 1.85	4.3–4.5	1200(200)	(110,126−128)
YbRhSb	2.7	–	1.4	370	(129−131)
Yb4Rh7Ge6			4.55–4.65	0.184	(230)
YbPdBi	1	–	4.11(5)	1200(100)	(110,127)
Yb4Ir7Ge6			4.8	0.281	(230)
YbPtGe	5.4	–	4.48	209	(231)
YbPtIn		1.4, 3.4	4.21–4.4	400	(126,232)
YbPtSn	3.5(4)	–	4.27(2)		(127)
Yb2Pt2Pb	–	2.07	4.42–4.54	30	(173,233)
YbPtBi	–	0.4		8000	(135−139)

^aMagnetic properties include Néel temperature, T_N; Curie temperature, T_C; effective magnetic moment, μ_eff; and specific heat capacity (Sommerfeld) coefficient (γ). Standard deviations are given in parentheses, where available.

Binary Compounds

During the last 50 years, YbAl₂ (MgCu₂ type, space group Fd3m) and YbAl₃ (Cu₃Au type, space group Pm3m) have been extensively examined regarding their physical properties. Both compounds show Curie–Weiss behavior above 100 K, with a broad maximum of the susceptibility around 850 K for YbAl₂. The detected characteristic spin fluctuation temperatures are T_sf = 200 K for YbAl₂ and T_sf = 125 K in case of YbAl₃.^13,114 In a hard X-ray photoemission spectroscopy study for YbAl₂, below 300 K, a ytterbium valence of ca. +2.2 was determined.^115,116 The Kondo temperature suggested from the magnetic measurements is very high (T_K > 2000 K).^97,117 The valence of YbAl₃ (+2.75) results in a ground state with 4f occupancy of 0.75.^118,119 In contrast, photoemission experiments revealed a valence of +2.73, whereas the determined Kondo temperature is in an order of 500–600 K, and the specific heat coefficient is γ = 40 mJ/mol K². Below the Fermi-liquid temperature T_fl = 50 K, a quadratic temperature dependence of the resistivity was found.^118−120

Equiatomic Ternary Compounds

Weak ferromagnetism is reported for the equiatomic compound YbNiSn (TiNiSi type, space group Pnma). The dense Kondo compound has a Curie-temperature of T_C = 5.65 K, and the magnetic moment lies along the c axis. A value of μ_eff = 4.3 μ_B was determined as an effective magnetic moment close to the value of a free Yb³⁺ ion (4.54 μ_B). The maximum detected magnetization is 0.85 μ_B per Yb atom. Kondo fluctuations with a Kondo temperature T_K = 2 K lead to the reduction of the ferromagnetism.^121−124 Further investigations by Mössbauer spectroscopy, neutron diffraction, and resistivity measurements confirm these results.^121−125

The susceptibility of YbRhSn with ZrNiAl type structure (space group P62m) follows the Curie–Weiss law at high temperatures, with a trivalent state of the Yb ions. The deduced effective magnetic moment was in a range of 4.4–4.5 μ_B, and a negative Weiss constant was observed.^126−128 Two different magnetic transitions at T = 1.85 and 1.4 K were reported via heat capacity data, which shift to lower temperatures with applied magnetic fields as expected for antiferromagnetic ordering. In addition, the heat capacity data indicate a possible heavy Fermion ground state. The resistivity of YbRhSn is Kondo-like and decreases almost linearly down to 20 K, followed by a rapid decrease at 1.8 K. Below 1 K it has a Fermi-liquid-like temperature variation.^126−128

YbRhSb was first synthesized by Muro et al. in 2004 and crystallizes with the TiNiSi type structure. It reveals a ferromagnetic transition at T_C = 2.7 K. For an applied magnetic field parallel to the crystallographic b axis, a spontaneous moment of only ∼3.0 × 10^–3 μ_B per Yb atom was observed, although the magnetic easy axis is the a axis. At around 2 T a metamagnetic transition occurs, and at 15 T the magnetization reaches 1.4 μ_B/Yb for the B∥a axis, somewhat reduced when compared with the theoretical saturation magnetization of 4 μ_B.¹⁰⁵ The specific heat coefficient was determined to be γ ∼ 370 mJ mol^–1 K^–2 in the ferromagnetically ordered state.¹²⁹ Instead of typical ferromagnets, the Curie temperature furthermore decreases with higher applied magnetic fields. Thus, the weak ferromagnetism of YbRhSb is possibly the result of a canted antiferromagnetic structure. Resistivity measurements and investigations in a p/T phase diagram revealed a minimum for T_M(p) at p_C = 1.7 GPa. For p ≥ 2 GPa, the canted antiferromagnetic structure changes to a ferromagnetic structure and a moment of 0.4 μ_B/Yb within the bc plane.^130−133

YbBiPt crystallizes in the cubic MgAgAs type structure with space group F43m.¹³⁴ Antiferromagnetic ordering was detected at T_N = 0.4 K, while the determined Weiss constant is Θ_P = 0.4 K.^135−137 Heat capacity data (Figure 9) revealed an extremely large low-temperature specific heat coefficient of γ = 8 J mol^–1 K^–2,^135−137 and the also determined Kondo temperature was measured to be T_K = 1 K.^134,136 Further experiments showed that the antiferromagnetism is very sensitive to magnetic field, pressure, and strain.^137−140 In addition, below T_N very broad magnetic neutron-diffraction peaks were observed.^141,142

Figure 9.

Low-temperature specific heat C_p(T) of YbBiPt between 0.09 and 0.85 K. Inset: Same data as C_p/T vs T. Reprinted with permission from ref (136).

YbCuAl crystallizes with a ZrNiAl type structure^143−145 (space group P62m), was first discovered by Dwight et al. in 1968¹⁴⁴ and shows mixed-valent character for Yb in this compound.^146,147 Down to T = 30 K, the susceptibility follows the Curie–Weiss law, while at the lowest temperatures it is marked by a saturation at a high level. The observed intermediate valence is close to 3, and YbCuAl can be described as a heavy Fermion compound with a high value of its specific heat coefficient (γ = 260 mJ mol^–1 K^–2).^148,149 For more details, we refer to the review of Bonville in 1988, who summarized the results of the different physical experiments on YbCuAl together with other ytterbium compounds.¹⁴⁹

Further Ternary Compounds

One of the most intensively studied ytterbium compounds is YbRh₂Si₂. Over the last 20 years, more than 350 publications have been published on this silicide. It was first described by Rossi et al. in 1979,²² adopts the tetragonal ThCr₂Si₂ type structure (space group I4/mmm), and has a (theoretically) three-dimensional Fermi surface.^150−154 Antiferromagnetic ordering was detected at very low temperatures, with the Néel temperature being T_N = 70 mK. Yet, the nature of this order is still not clear and was further examined with different techniques such as neutron scattering,¹⁵⁵ static susceptibility,¹⁵⁶²⁹Si NMR,¹⁵⁷ or ESR^158−160 (vide infra). Ferromagnetic fluctuations cause incommensurate antiferromagnetic correlations, which were detected by these investigations above 70 mK.

YbRh₂Si₂ exhibits a non-Fermi-liquid behavior. The ordered Yb³⁺ moment is very small, with only 2 × 10^–3 μ_B/Yb atom (Figure 10). The characteristic Kondo-temperature is T_K = 25 K.¹⁶¹ A quantum critical point is suggested for the suppression of T_N at ambient pressure by a magnetic field of only B_c = 60 mT.¹⁶² The substitution of Si by Ge shifts the quantum critical point to lower fields,^156,163 whereas Co substitution leads to ferromagnetism.^164,165 In addition, superconductivity was reported for YbRh₂Si₂, thus leading to the assumption of a strong coupling of electronic and nuclear magnetism.^166,167 Reasons for this superconductivity as well as the mentioned nature of ordering and the quantum critical point itself remain unclear and are the subject of further research.¹⁶⁸

Figure 10.

Temperature dependence of the magnetic and inverse magnetic susceptibility of YbRh₂Si₂ measured parallel to the a and c axis with different applied fields. Reprinted with permission from ref (169).

One of the remarkable trivalent ytterbium compounds is the Shastry–Sutherland^170−172 phase Yb₂Pt₂Pb, originally reported in 1999.⁴⁷ Yb₂Pt₂Pb adopts the Er₂Au₂Sn type structure (space group P4₂/mnm). Later property studies were performed on single crystals which were grown from lead flux (Yb:Pt:Pb = 5:4:40 starting composition).¹⁷³ Orientation-dependent magnetic susceptibility measurements showed a high anisotropy with an about 30 times larger value for χ₍₁₀₀₎ as compared to χ₍₀₀₁₎ (Figure 11).¹⁷⁴ The Néel temperature of Yb₂Pt₂Pb is T_N = 2.07 K.¹⁷³

Figure 11.

Temperature dependence of the magnetic and inverse magnetic susceptibility of Yb₂Pt₂Pb measured parallel (100) and (001). Reprinted with permission from ref (174).

Besides, Yb₂Pt₂Pb was studied by specific heat and resistivity measurements and with respect to its crystal field parameters obtained by inelastic neutron scattering data. All these property studies were supported by quantum chemical calculations for a better understanding of the structure–property relationships. The complete property data of Yb₂Pt₂Pb has recently been reviewed,⁸⁷ and we refer to this broad overview for more details.

Magnetization data support the anisotropic behavior observed in the orientation-dependent susceptibility measurements. Yb₂Pt₂Pb shows multiple metamagnetic steps in both the (100) and (110) directions.¹⁷⁵ The maximum magnetization observed in (100) at 5 T is around 2.4 μ_B per ytterbium atom, significantly reduced when compared with the theoretical value of 4 μB (g × J). The magnetic structure of Yb₂Pt₂Pb was studied from powder and single crystal neutron diffraction data.¹⁷⁶ The ordered ytterbium magnetic moments were described in a 5 × 5 × 1 magnetic supercell.

YbAl₃C₃ is another example of isotropic exchange interaction and crystallizes with the hexagonal ScAl₃C₃ type structure (space group P6₃/mmc). The ytterbium atoms form a triangular lattice, then a structural phase transition to an orthorhombic phase (own structure type) occurs at T_S = 80 K.^177−179 Above this temperature, Curie–Weiss behavior with an effective magnetic moment of μ_eff = 4.66 μ_B was observed, underlining the trivalent state of the ytterbium atoms. The calculated Weiss constant of Θ_P = −120 K indicates antiferromagnetic interactions in the paramagnetic regime.^177,178 Below T_S, no long-range magnetic order was visible by measurements of the magnetization or specific heat. It has been proposed that the anisotropic Kramers doublet of YbAl₃C₃ forms an antiferromagnetic dimer ground state with a single-triplet energy gap of about 15 K in a relatively narrow field and the 4f electrons are expected to behave as a S = 1/2 spin system at low temperatures, thus suggesting only weaker interdimer interaction in the ytterbium triangles.^{177,178,180−182}

YbCo₂Zn₂₀ is a member of the CeCr₂Al₂₀ type family (space group Fd3m). The high temperature susceptibility follows the Curie–Weiss law with an effective magnetic moment near the value of a free Yb³⁺ ion (μ_eff = 4.54 μ_B). No magnetic ordering down to 20 mK was observed, while the recorded magnetization isotherms at low temperatures indicate a metamagnetic transition. At lowest temperatures, the magnetic ground state is enhanced by the Pauli susceptibility. By heat capacity measurements, a large Sommerfeld coefficient of γ = 7.9 J^–1 mol^–1K^–2 was observed. Kondo interactions were confirmed via the T² resistivity, resulting from the A coefficient (A = 165 μΩ K^–2). This classifies YbCo₂Zn₂₀ as a superheavy electron metal. For further detail, we refer to the literature and reviews.^88,183−186

Stoichiometric YbInCu₄ adopts the MgCuSn₄ type structure^187,188 (cubic C15B, space group F43m);¹⁸⁹ however, the disordered structure (solid solution) Yb_1–xIn_xCu₂ (C15, MgCu₂ type, space group Fd3m) has also been observed.^190,191 It is one of the few Yb compounds (YbPd₂Al₃ is another one⁶⁷) that exhibits a first-order isostructural valence transition (VT) with the transition temperature T_trans = 42 K.^189−191 In the high-temperature regime, the Yb valence has been reported to be +2.9 and suddenly drops to +2.74 when cooling below T_trans.¹⁹² At the same time, the magnetic ground state undergoes a transition from a local moment susceptibility of 4.5 μ_B to temperature-independent Pauli paramagnetism below T_trans.¹⁹³ No change in the structure is observed during the transition, although the unit cell volume increases by ∼0.5%.^194,195

Furthermore, the transition was confirmed by synchrotron radiation X-ray absorption, X-ray emission spectroscopy, inelastic neutron scattering (vide infra),^196−200 and abrupt changes in other physical properties like electrical resistivity, specific heat capacity, and nuclear spin-relaxation rate (vide infra).^198,201,202 The transition is also accompanied by a drastic change of the Kondo temperature (T_K) from 20 to ∼400 K in the low-temperature phase.^199,203

In Yb-based heavy Fermion systems, β-YbAlB₄ was the first discovered superconductor with the transition temperature T_C = 80 mK.^204,205 The results of transport and thermodynamic properties suggest non-Fermi liquid behavior in the normal β-YbAlB₄ state.^205,206 It adopts the orthorhombic ThMoB₄ type structure (space group Cmmm) with the Yb and Al atoms being in the ab plane between two B layers of hepta- and hexagonal boron rings (vide ultra).⁹³ This structural environment and the strong observed valence fluctuations²⁰⁷ are essential for understanding the properties of β-YbAlB₄. Within the ab plane, the Kondo hybridization was discussed to be isotropic, in contrast to the anisotropy between the crystal c axis and the ab plane.²⁰⁸ This may explain the observed T/B scaling of the magnetic susceptibility and the intrinsic quantum criticality.^209−214

Another example of an intermediate valence ytterbium compound is YbNiAl₄, which adopts the YNiAl₄ type structure (space group Cmcm). The temperature dependence of the magnetic susceptibility is compatible with the ICF model. At T = 4.2 K the determined valence of the Yb atoms is +2.1, in contrast to +3 at T = 1000 K. Resistivity measurements reveled a Fermi-liquid behavior, due to the observed AT² variation below 60 K. At room temperature, it shows a metallic-like behavior. The heat capacity measurements gave no hints for any magnetic ordering down to 1.9 K. For the electronic specific heat capacity, a value of γ = 16 mJ mol^–1 K^–2 was determined, so that a heavy Fermion state can be excluded.^23,215 In addition, various transport measurements (thermal and electrical) were analyzed.²¹⁶ In-situ high-pressure studies show an increase of the ytterbium valence with increasing pressure for YbNiGa₄ and YbNiIn₄.²¹⁷

Also, the complex structure of Yb₄Ga₂₄Pt₉, a platinide, shows intermediate ytterbium valence. Hard X-ray photoelectron spectra and magnetic susceptibility measurements point to an ytterbium valence of ∼2.5.²¹⁸ The stannide YbRhSn₂²¹⁹ and the solid solution YbIn_1–xAu_1+x (x = 0–0.3)²²⁰ show comparable behavior.

An intermediate ytterbium valence can also be induced by isovalent substitution. The phosphide Yb₂Ni₁₂P₇ exhibits a heavy-Fermion paramagnetic ground state and switches to intermediate valence in Yb₂Ni₁₂As₇.²²¹

INELASTIC NEUTRON SCATTERING

Inelastic neutron scattering is often used to probe crystal field excitations which allow drawbacks on the crystal electric field (CEF) splitting for a certain atom and magnetic phase transitions. In contrast to elastic scattering, in this case, the energy difference of the scattered neutrons is detected. Therefore, it is a useful tool to obtain information about the ground state and the magnetic exchange interactions of, in this case, the Yb atoms.²³⁴

Binary Compounds

One of the first compounds that has been studied by inelastic neutron scattering was YbBe₁₃ (NaZn₁₃ type, space group Fm3c).²³⁵ The spectra were recorded on a polycrystalline sample between 1.2 and 300 K. Since YbBe₁₃ undergoes antiferromagnetic ordering at T_N = 1.28 K,²³⁶ the single line observed at 1.2 K was interpreted as a magnon. The spin fluctuations associated with the magnetic ordering, however, persist for quite a large temperature range and are still observable at 10 K. At 39 K, the CEF splitting can be observed with Γ₇ being the ground state and Γ₈ (3.20 meV) and Γ₆ (4.39 meV) being the next excited states. These observations contradict the results from the literature where a different sequence was reported; however, all agree on the Γ₇ ground state.^236,237

For YbPd (CsCl type, space group Pm3m) and Yb₃Pd₄ (Pu₃Pd₄ type, space group R3), inelastic neutron scattering has been used to probe the proposed magnetic transitions in these intermediate valent compounds and to determine the CEF splitting to gain information about the ground state. For YbPd, Γ₈ was determined to be the ground state with Γ₇ being 4.75 meV and Γ₆ being 12.3 meV higher in energy. This scheme is in line with trivalent Yb in a cubic environment. At 1.3 K, an additional contribution with magnetic origin is observed for YbPd. For Yb₃Pd₄, the first excitation was shifted to lower energy (4.08 meV) and is more distinct compared to the one in YbPd. It is interesting to note that despite Yb₃Pd₄ being trigonal (26 independent CF parameters are expected–note, the referenced paper states that Yb₃Pd₄ is triclinic; this statement has been corrected) the observed transitions still can be interpreted by a cubic site symmetry. Finally, measurements between 1.3 and 6 K revealed a strong inelastic line at low temperatures that softens toward the proposed magnetic phase transition near 3 K. An abrupt change of the line width at T = 3.1 K indicates that this excitation can be attributed to a magnon in the magnetically ordered state.²³⁸

Ternary Compounds

To understand the valence fluctuating behavior of YbInAu₂ (MnCu₂Al type, space group Fm3m), neutron scattering experiments were conducted and compared to the results of YbAl₃ (Cu₃Au type, space group Pm3m) which exhibits similar physical properties. The data obtained at temperatures near the susceptibility maxima (∼80 K for YbInAu₂ and ∼120 K for YbAl₃) could be fitted with a single spectral function. At 5 K, however, the data of YbAl₃ needs more components while the data of YbInAu₂ still can be fitted with a single function. The differences are also visible in the phonon scattering (high angle data). Here, a well-defined phonon mode is visible for YbAl₃ in contrast to YbInAu₂.²³⁹

As mentioned before, Yb_1–xIn_xCu₂ (MgCu₂ type, space group Fd3m) shows a temperature-dependent valence phase transition. It changes from a nearly trivalent state at high temperatures to a mixed-valent Pauli paramagnetic state at low temperatures. A sample with x = 0.5 was investigated at T = 30 and 60 K, above and below the transition temperature of T = 40 K. The spin dynamics in the mixed-valent phase (T = 30 K) can be modeled with a Lorentzian power spectrum with the center at E = 40 meV.²⁴⁰

Also, different YbT₂X₂ compounds were investigated by inelastic neutron scattering. Among the first investigations was the work on YbT₂Si₂ for T = Fe, Co, and Ni (ThCr₂Si₂ type, space group I4/mmm).²⁴¹ The performed experiments showed that YbCo₂Si₂ exhibits three excited states at ∼4, 12.5, and 30.5 meV above the ground state, while for YbNi₂Si₂, two clear transitions at ∼7.5 and 13.5 meV are visible alongside a shoulder at lower energy of the 7.5 meV peak. For YbFe₂Si₂, no clear inelastic signals are observed.²⁴¹ Taking the experimentally determined energies for YbCo₂Si₂ into account, the CF level scheme could be derived, indicating Γ₇ to be the ground state.²⁴² YbMn₂Si₂ (ThCr₂Si₂ type, space group I4/mmm) has the peculiarity that it shows two antiferromagnetic transitions at T_N,1 = 526 and T_N,2 = 30 K originating from the Mn atoms.²⁴³ Determination of the magnetic structure showed that, below T_N,1, the Mn atoms show a + – + – sequence, while below T_N,2, a + – – + magnetic substructure arises, which leads to a doubling of c in the magnetic unit cell. At 1.5 K also the Yb atoms are antiferromagnetically ordered, however, with their spins orthogonal to the Mn spins.²⁴⁴ Above 30 K, only one Yb site is present which exhibits a doublet ground state as well as three excited states at 4.65, 11.89, and 15.05 meV. Below 30 K, however, a second Yb site emerges due to the antiferromagnetically ordered Yb atoms. This leads to two additional signals in the inelastic neutron spectrum of YbMn₂Si₂ at 2.5 K. These transitions can be associated with a different CEF scheme for the Yb2 site with energy levels at 7.24, 8.76, and 16.4 meV.^245,246 For the heavy Fermion compound YbRh₂Si₂ (ThCr₂Si₂ type, space group I4/mmm), inelastic neutron scattering experiments conducted at 1.5 K are also dominated by the CEF excitations of the Yb³⁺ ion. Besides a ground state doublet, three excited state doublets were observed at higher energies of 17, 25, and 43 meV, in line with the CF theory for a tetragonal system.²⁴⁷ Subsequent calculations showed that the ground state is a Γ₆ Kramers doublet.²⁴⁸ For YbIr₂Si₂, both modifications (CaBe₂Ge₂ type, P4/nmm, and ThCr₂Si₂ type, I4/mmm) were investigated by inelastic neutron scattering experiments at 1.5 K. As for YbRh₂Si₂, a doublet ground state and three excited doublet states are expected. For the body-centered polymorph, energies of 0, 18, 25, and 36 meV were observed, while for the primitive polymorph they are slightly lower in energy at 0, 15, 22, and 33 meV.²⁴⁹ These values are in good agreement with the calculated values for both YbRh₂Si₂ and YbIr₂Si₂.²⁵⁰

XANES/XAS

X-ray absorption spectroscopy (XAS) describes the overall measurement of the absorption spectrum of electrons, which interact with polychromatic X-ray photons and absorbs characteristic wavelengths. The XA spectrum can be separated into two parts. First, the area at higher photon energy than the absorption, called extended X-ray absorption fine structure (EXAFS) which contains information about the local environment of the absorbing atom. The second area is at the absorption energy, the X-ray absorption near edge structure (XANES) or near edge X-ray absorption fine structure (NEXAFS), which gives insight into the electronic properties, e.g., the oxidation state of the absorbing atom. In the following chapter, examples of classical intermetallic Yb-compounds as well as Zintl phases will be addressed with regards to their respective valence in the XAS and XANES measurements.

Binary Compounds

The binary compounds YbAl₂ (MgCu₂ type, space group Fd3m) and YbAl₃ (Cu₃Au type, space group Pm3m) are among the most investigated intermetallics. Both have one crystallographic Yb position in the crystal structure. One of the earliest X-ray absorption measurements of YbAl₂ was done by Beaurepaire, Kappler, and Krill in 1986.²⁵¹ In their work, YbAl₂ was measured at room temperature under pressures of 10 and 30 kbar. At room temperature, YbAl₂ has a valence of +2.3, whereas under pressure the valence rises to +2.6 at 30 kbar (pressure-induced oxidation). Due to the width of the 2p core hole of 4.6 eV, the Yb²⁺ and Yb³⁺L_III edges could not be resolved, but the two contributions are separated by about 6 eV.²⁵¹ Dallera et al. measured the pressure dependence of the Yb L_III edge in YbAl₂ up to 385 kbar using the partial fluorescence yield mode of the X-ray absorption (PFY-XAS), giving a higher resolution of the spectra compared to the conventional measurement mode. The absorption spectra show the valence shift from a valence in YbAl₂ of +2.25 at ambient pressure to a valence of +2.9 at 385 kbar. At pressures of 170 and 385 kbar, the spectra of YbAl₂ become similar to Yb_1–xIn_xCu₂, which has a stated valence of +2.96, indicating a valence close to +3.²⁵²

XA spectra of YbAl₃ were measured at 10 and 300 K, showing the Yb 3d → 4f transition and indicating an open 4f shell in the ground state. A decrease in the intensity of 11% at 10 K compared to 300 K is additionally reported by Tjeng et al., suggesting a decrease in the valence of the Yb atom, which is also shown in the photoemission spectroscopy.²⁵³ The pressure-induced valence change of YbAl₃ was measured by PFY-XAS starting at ambient pressure and the valence of +2.75 for YbAl₃, which subsequently rises alongside the increasing pressure. At 9 GPa, the valence is +2.82, then +2.86 at 20 GPa, and finally +2.93 at an applied pressure of 38 GPa. The incident energy for Yb²⁺ is 8.942 keV, Yb³⁺ resonates at a slightly higher energy of 8.950 keV.²⁵⁴ By changing from bulk materials to nanoparticles, the valence of YbAl₃ changes from +2.86 to +2.70 after mechanical milling in a planetary high-energy ball milling system for 120 h. The reference Yb₂O₃ indicates the Yb³⁺ peak at 8946.5 eV, and the spectra of the milled YbAl₃ shows an increase of the Yb²⁺ contribution at 8941 eV. The valences for 20 and 70 h milling time are +2.74 and +2.70, respectively. A cause of the valence change is the size effect stated. The milled YbAl₃ particles possess two types of Yb atoms, the trivalent in the bulk of the sample and the ones near the surface having a variation of their coordination number, leading to divalent Yb. Another reason is the disorder introduced in the ball milling process, which is particularly visible in the X-ray diffraction data.²⁵⁵

YbGa₂ crystallizes at ambient pressure in the hexagonal CaIn₂ type structure (P6₃/mmc), at higher pressures above 22 GPa a phase transition into the UHg₂ type (P6/mmm) occurs. XANES measurements of the Yb L_III-edge show a valence increase from Yb²⁺ at ambient pressure to Yb³⁺ in the high-pressure structure. At low pressures, two peaks are visible, wherein the peak at higher energy represents the Yb³⁺ and is within 1 eV to the reference Yb₂O₃, and the second peak is 7 eV lower, corresponding to Yb²⁺. Measurements were taken at 0.6, 4.7, and 28.8 GPa, showing a continuous increase in the intensity of Yb³⁺ and decrease of the Yb²⁺ white line until the phase transition occurs and only Yb³⁺ is present (Figure 12). In the high-pressure modification, YbGa₂ possesses a two-dimensional polyanion, compared to the Ga network found in the normal pressure phase. The two-dimensional arrangement can then be supported with the additional electrons from the Yb atoms.²⁵⁶

Figure 12.

Yb L_III XANES spectra of YbGa₂ at different pressures. The white lines at low energies are attributed to Yb²⁺, and the lines at higher energies are attributed to Yb³⁺. Figure reproduced with permission from ref (256). Copyright 2001 John Wiley & Sons, Inc.

The hexagonal phase Yb₅Si₃ crystallizes in the Mn₅Si₃ type structure (P6₃/mcm) and possesses two distinct crystallographic Yb positions (4d and 6g). Alongside XANES, Mössbauer spectroscopic investigations and magnetic measurements were also conducted. The magnetic measurements indicated that only trivalent Yb is present, in contrast to the Mössbauer spectrum proposing 60% of Yb³⁺. XANES measurements were performed at 10 and 300 K; these show two white lines at 8943 and 8935 eV corresponding to Yb³⁺ and Yb²⁺, respectively. The calculated valence from the spectra is +2.88, which is higher than the expected value of +2.6 if the Yb atoms on the 6d site were purely trivalent and the ones on the 4g site divalent. The authors suggested that a hybridization of the 4f electrons is occurring, whose strength is different for the two different crystallographic sites. The Yb atoms on the 4d site are more strongly influenced than the Yb atoms on 6g.²⁵⁷

Yb₅Ge₄ (Sm₅Ge₄ type, space group Pnma) is reported to be a mixed valence compound with a valence of +2.42, showing the white band at 8948 eV and a big shoulder at 8941 eV, indicating Yb³⁺ and Yb²⁺, respectively.²⁵⁸

Equiatomic Ternary Compounds

The heavy Fermion compound YbCuAl (ZrNiAl type, space group P62m) is described with a Yb valence of nearly +3. With increasing pressure, the valence of Yb can be increased, and with lowering the temperature, the Yb becomes more divalent as shown by XES measurements.²²⁵ YbAuIn also crystallizes in the hexagonal ZrNiAl type structure with one crystallographic Yb position. X-ray absorption measurements of YbAuIn were taken at 15–18 and 300 K at ambient pressure, resulting in an intensive white line at 8941 eV corresponding to a divalent Yb, but also a weak shoulder at 8949 eV showing a small amount of trivalent Yb. By fitting the spectra and excluding Yb₂O₃ impurities, a valence of +2.17 was determined.²⁵⁹ YbGaGe possesses two crystallographically different Yb positions and crystallizes in the hexagonal YPtAs type structure (P6₃/mmc). The compound shows a white band at around 8940 eV and a small shoulder around 8950 eV, indicating a divalent system with oxidic impurities, which is in line with the magnetic measurements.²⁶⁰

Further Ternary Compounds

YbRh₂Si₂ (ThCr₂Si₂ type, space group I4/mmm) has a temperature- and magnetic-field-dependent Yb valence, which is decreasing with lower temperature and increasing alongside higher magnetic fields. To measure the influence of the two parameters, XAS measurements were conducted by Nakai et al. The Yb L_III absorption spectra show a shoulder at 8940 eV appearing at decreasing temperature and an intensive white line at 8946 eV, indicating the trivalent Yb, whose intensity decreases with lower temperatures. Above 200 K, the valence was determined to be +2.96, while below 25 K, a valence of +2.92 was reported. In contrast, the valence change of Yb was measured by increasing magnetic field at 2 K. At 0 T, the valence is +2.92, and it rises to +2.93 monotonically with stronger magnetic fields up to 33 T.²⁶¹

X-ray absorption spectra of YbCu₂Si₂, YbCu₂Ge₂ (ThCr₂Si₂ type, space group I4/mmm), and YbPt₂ (MgCu₂ type, space group Fd3m) were measured at 300 K, showing a pure trivalent Yb in YbPt₂, divalent Yb in YbCu₂Ge₂, and a mixed valence occurring in YbCu₂Si₂ with a higher amount of Yb³⁺ than Yb²⁺. It was also stated that the Yb valence in YbCu₂Si₂ does not show any signs of a temperature dependency.²⁶² Similar to YbCu₂Ge₂, YbAl₂Ga₂ possesses a white line at 8936 eV and a resulting valence of Yb²⁺.²⁶³ YbMn₂Ge₂ (ThCr₂Si₂ type, space group I4/mmm) is also described as a mixed valent compound with a Yb valence of +2.40 at 300 K. This compound shows not only a negative thermal expansion, but also a temperature dependence of the Yb valence. With the increase of the temperature, the white line at 8943 eV decreases while the one at 8949 eV increases, corresponding to the Yb²⁺ and Yb³⁺ respectively, leading to a valence of +2.82 at 700 K. Also, the valence of Yb can be influenced by applying pressure; e.g., at a pressure of 1.4 GPa, the Yb valence is +2.82.²⁶⁴

The YbT₂X₂₀ compounds with T = Cr, Ti, V, Co, Fe, Ir, Rh and X = Al, Zn all crystallize in the cubic CeCr₂Al₂₀ type structure (space group Fd3m). These structures are heavy Fermion compounds and can possess a particularly high specific heat coefficient. XAS measurements were taken of YbRh₂Zn₂₀ and YbIr₂Al₂₀ at 2, 250, and 290 K, respectively, with additional measurements at 2 K with an applied external field of 10 T. The absorption spectra of YbRh₂Zn₂₀ have two peaks, the white line at 8950 eV indicating Yb³⁺ and a shoulder at 8940 eV originating from Yb²⁺. The valence at 250 K is stated as +2.89 and is decreasing with decreasing temperature, especially below 100 K, reaching a valence of +2.87 at 20 K. The same trend is visible for YbIr₂Al₂₀, also having a decreasing Yb valence with decreasing temperatures below 90 K; above 100 K, the valence is nearly constant. As for the measurements under an applied field, only changes in the valence are present below 80 K.²⁶⁵ In contrast, YbCo₂Zn₂₀ was investigated by XAS measurements, showing no indication of temperature or magnetic field dependency.²⁶⁶ YbFe₂Zn₂₀ and Cd-substituted YbFe₂Zn_20–xCd_x with x = 0–1.4 were analyzed by Fahl et al. Their XANES studies of the Yb L_III absorption show only the white line at 8946 eV corresponding to Yb³⁺ and no additional shoulder, making all compounds formally trivalent.²⁶⁷

For the valence transition compounds Yb_1–xIn_xCu₂ (x = 0.5), the valence transition temperature is stated to be T_trans = 42 K where the valence changes from +2.98 to +2.85, as calculated from the XANES measurements at 300 and 7 K, respectively.²⁶⁸ Another study on Yb_0.5In_0.5Cu₂ by Yamaoka et al. focused on the pressure-induced valence transition. In their work, X-ray absorption spectra of Yb_0.5In_0.5Cu₂ were taken at 300 and 13 K under pressure. At 300 K, Yb_0.5In_0.5Cu₂ shows no pressure dependent valence; at 13 K on the other hand, it presents an increase of valence at pressures of 3.1 GPa and above.²⁶⁹ The XAS spectra of YbAgCu₄ (MgCu₄Sn type, space group F43m) measured at 10 and 300 K by Lawrence et al. show the white line at 8947 eV and a shoulder at 8940 eV, corresponding to Yb³⁺ and Yb²⁺, respectively. Also, they are stating that the valence of YbAgCu₄ is nearly +3 and changes continuously with temperature.²⁷⁰ Sarrao et al. investigated the Yb valence in the YbTCu₄ series (MgCu₄Sn type, space group F43m) with T = Mg, Ag, Au, Zn, Cd, Tl by XAS of the Yb L_III line between 20 and 300 K, showing the Mg compound with the lowest Yb valence of +2.64 at 20 K and +2.69 at 300 K, followed by YbTlCu₄ with +2.75 to +2.82, YbCdCu₄ +2.76 to +2.82, YbZnCu₄ +2.84 to +2.88, YbAgCu₄ +2.86 to +2.93, and finally YbAuCu₄ with a valence of +2.95 at 20 K and +2.96 at 300 K.²⁴⁰ XANES studies of YbPtIn₄ and YbPdIn₄ (YNiAl₄ type, space group Cmcm) were reported, stating both compounds containing mixed valent Yb.²⁷¹

Zintl Phases

The Zintl compounds Yb₁₄TSb₁₁ (T = Zn, Mn, Mg; Ca₁₄AlSb₁₁ type, space group I4₁/acd) exhibit besides intriguing magnetic also highly important thermoelectric properties (see thermoelectric properties). Using the Zintl counting rules, the Mn-containing compounds only have Yb²⁺ cations, while the Zn and Mg compound should also contain one Yb³⁺. To verify the valence of the Yb atoms in these compounds, XANES measurements were taken by He et al. The absorption spectra of all three compounds indicate the presence of both Yb²⁺ and Yb³⁺, but the overall valence is close to Yb²⁺. Additionally, it is visible that the Mg and Mn compounds have a constant amount of Yb³⁺, but in the Zn compound, the valence is highly temperature-dependent. The formation of Yb³⁺ is explained by introducing disorder in the structure of Yb₁₄TSb₁₁.²⁷²

X-RAY PHOTOELECTRON SPECTROSCOPY (XPS)

X-ray photoelectron spectroscopy (XPS) describes the analysis of a (solid) material, using the photoelectric effect, meaning the emission of an electron due to absorption of X-ray radiation. Typically, Al Kα is used as an X-ray source with a photon energy around 1486 eV. Due to the nature of the interaction between condensed matter and electrons, especially the short inelastic mean free path of, e.g., 1–2 nm for metallic systems, makes this analysis a rather surface-sensitive method.

Binary Compounds

YbAl₂ (MgCu₂ type, space group Fd3m) was measured by XPS in 1985 by Oh et al. at 120, 460, and 750 K. The spectra at the two lower temperatures show the peaks of both Yb²⁺ and Yb³⁺, with the 4f¹⁴ → 4f¹³ and 4f¹³ → 4f¹² bands, respectively. At higher temperatures, the intensity of the peak originating from the divalent Yb atoms is reduced, while the trivalent one increases, leading to valences of +2.32 at 120 K, + 2.40 at 460 K, and finally +2.53 at 750 K.²⁷³ In 2012, the valence of Yb in YbAl₂ was analyzed by HAXPES using hard X-ray radiation of 7.94 keV for excitation at 20 K, allowing the Yb 3d core levels to be shown. In the spectrum recorded at 20 K, the Yb 3d core-levels can be seen at 1515–1540 eV (3d_5/2) and 1560–1585 eV (3d_3/2). The spectra at 20 and 300 K both show Yb²⁺ and Yb³⁺ species, leading to a mean valence of +2.20, staying nearly unchanged below 300 K.¹¹⁶

The valence of YbAl₃ (Cu₃Au type, space group Pm3m) was analyzed using XPS by Buschow et al. in 1977. The Yb 4f spectra show a peak multiplet extending from 5 to 10 eV, corresponding to Yb³⁺. Also, a spin doublet is visible from 0 to 3 eV, indicating divalent Yb, but no mean valence of the compound could be calculated from the measured spectra.²⁷⁴ Later, in 1996, YbAl₃ was measured by XPS, with a well-resolved doublet of divalent Yb and the multiplet of trivalent Yb. The mean valence of YbAl₃ was determined to be +2.63 based on the recorded XPS spectra.²⁷⁵ The nearly same results were reported by Joyce et al. in 2001, measuring YbAl₃ around 20 K showing both Yb valence species in the spectra with a mean valence around +2.6.²⁷⁶

YbCu₂ and YbAg₂ (both KHg₂ type, space group Imma), YbAu₂ (MoSi₂ type, space group I4/mmm), and YbNi₅ (CaCu₅ type, space group P6/mmm) were measured by XPS to determine the valence states of ytterbium in these compounds. The measured spectra show the 4f and the 5p levels. As expected, the trivalent Yb compound YbNi₅ has peaks only in the region of Yb³⁺ while YbCu₂, which is purely divalent, shows the two peaks corresponding to Yb²⁺. YbAg₂ on the other hand, exhibits a small trivalent signal due to oxidic impurities. According to the unit cell volume, YbAu₂ should possess a trivalent Yb state, but the XPS measurements showed not only the Yb³⁺ peaks, but also the more intensive peaks of divalent Yb in the spectra, indicating YbAu₂ to rather be an intermediate valence system, compared to YbCu₂.²⁷⁷

The valence fluctuating compound YbB₁₂ (UB₁₂ type, space group Fm3m) was investigated at room temperature, showing the Yb²⁺ doublet at 0–3 eV and the Yb³⁺ multiplet between 5 and 12 eV. The mean valence of Yb was determined to be +2.9.²⁷⁸

Finally, Yb₄As₃, Yb₄Sb₃, and Yb₄SbBi₃ (all Th₃P₄ type, space group I43d) are also known to be valence fluctuating compounds. The XPS spectra, measured at room temperature, all show the peaks for divalent and trivalent Yb, although the Yb³⁺ peak in Yb₄Bi₃ is of low intensity. After analyzing the Yb 4f spectra, the mean Yb valences were calculated to be +2.32, +2.34, and +2.10 for Yb₄As₃, Yb₄Sb₃, and Yb₄Bi₃, respectively.²⁷⁹

Equiatomic Compounds

YbAuMg crystallizes in the orthorhombic TiNiSi type structure (space group Pnma), and its electronic structure was investigated by XPS measurements. The spectrum was recorded at room temperature with Al Kα excitation radiation (1486.6 eV), showing the two peaks for divalent Yb 4f_7/2 and 4f_5/2 at 0.5 and 1.7 eV binding energy, rendering the system purely divalent.²⁸⁰

Further Ternary Compounds

The tetrelides YbNi₂Ge₂, YbPd₂Si₂, and YbCu₂Si₂ all crystallize in the ThCr₂Si₂ type structure (space group I4/mmm). Their spectra show the 4f level and 4d core levels; in all of them, Yb³⁺ and Yb²⁺ are visible, and the divalent peaks are in the range of 0–2 eV for the 4f level and around 185 eV in the 4d spectra. The signal from the trivalent atoms forms a multiplet ranging from 5 to 12 eV and centered around 195 eV for the 4f and 4d spectra, respectively. Due to the presence of the two Yb valence species, these compounds are mixed valent.²⁸¹

The valence of Yb in YbInCu₄ was investigated by Maeda et al. in 2019 using HAXPES with an excitation energy of 8915–8965 eV at 20 and 70 K. The Yb 3d_5/2 spectra show a Yb²⁺ single peak at 1520 eV and the Yb³⁺ multiplet at 1525–1540 eV. With lower temperature, the intensity of the divalent Yb increases, while the trivalent Yb decreases. The mean valence at 70 K is +2.91 and +2.67 at 20 K.²⁸² Before this, investigation on Yb_0.5In_0.5Cu₂ via XPS measurements at 20 K and excitation energies of 90 to 500 eV also showed both species present in the spectra. A valence of +2.6 was calculated from the data.²⁷⁶ The series of YbInCu₄, YbCdCu₄, and YbMgCu₄ was investigated between 10 to 300 K. The Yb 4d XPS spectra show both Yb species in all samples. The valence of the Cd- and In-containing compounds gradually decreases with decreasing temperature, while the valence in YbMgCu₄ does not change to lower temperatures.²⁸³ Upon replacing In with a precious metal like Ag, Au, and Pd, YbAgCu₄, YbAuCu₄ and YbPdCu₄ can be obtained. The electronic structure of these three compounds was investigated by Kang et al. The XPS spectra were recorded with Al Kα radiation and an excitation energy of 1486.6 eV at a temperature around 110 K. The spectra show the 4f line of Yb and the Cu 3d, Pd 4d, Pt 5d, and Ag 4d lines. Due to the overlap of the transition metal signals with the emission of divalent Yb between 0 and 4 eV, no valence can be reliably determined. However, based on the high intensity of the trivalent Yb multiplet, it can be assumed that the three compounds have a valence close to Yb³⁺ and also that the Pd containing compound is closer to the trivalent state than the Au- and Ag-containing ones.²⁸⁴

YbPd₂Al₃ and the solid solution Yb_1–xCa_xPd₂Al₃ crystallize in the hexagonal YNi₂Al₃ type structure (P6/mmm), containing two crystallographically different Yb positions. The solid solution has a mixing of Yb and Ca on both Yb positions. The compounds were analyzed by XPS with Al Kα radiation (1486 eV). The spectra depict the Yb 4d lines and possess five peaks for the Yb³⁺ and two rather small peaks forming a doublet for the Yb²⁺, in which a partial overlap of the trivalent multiplet with the divalent Yb peaks occurs. The calcium-substituted samples Yb_0.33Ca_0.67Pd₂Al₃ and Yb_0.67Ca_0.33Pd₂Al₃ became oxidized due to the handling in air or due the X-ray radiation, leading to an increased Yb³⁺ content, which cannot be used to determine the real amount of Yb²⁺ in the samples.⁶⁷

The Kondo lattice compounds Yb₂Al₁₅Pt₆ and Yb₂Ga₁₅Pt₆ were investigated via XPS at an excitation energy of 5.95 keV at 20 to 300 K. The Yb 3d levels indicate the presence of both di- and trivalent Yb. Also, in the Al-containing compound, with decreasing temperature, the intensity of the Yb³⁺ multiplet (1524–1536 eV) decreases and the Yb²⁺ single peak (1520 eV) intensity is observable, shifting the valence from +2.89 at 250 K to +2.83 at 20 K. In comparison, the Ga compound possesses a lower Yb valence of +2.34. However, this valence changes only minimally toward lower temperatures, meaning the Yb valence in Yb₂Ga₁₅Al₆ has nearly no temperature dependence. The peak of divalent Yb is at 1568 eV, and the multiplet of trivalent Yb at 1574–1582 eV.²⁸⁵

Zintl Phases

The Zintl compounds Yb₁₄MnSb₁₁ and Yb₁₄ZnSb₁₁ (both Ca₁₄AlSb₁₁ type, space group I4₁/acd) were measured by Holm et al. to analyze the Yb valence by XPS analysis with an excitation energy of 1250 eV. The spectrum for the Mn-containing sample shows the Yb 4s, 4p_1/2, 4p_3/2, 4d_3/2, and 4d_5/2 core levels corresponding to the binding energies of 486, 395, 345, 197, and 188 eV. For the Zn sample, the Yb levels are slightly shifted and found at 484, 394, 345, 195, and 187 eV. Additional valence band scans with an excitation energy of 120 eV were taken, showing the Yb 4f multiplet for Yb³⁺ and the doublet of Yb²⁺, respectively. Also, it is stated that these compounds are prone to oxidation, leading to a higher amount of Yb³⁺ on the surface. The amount of trivalent Yb for Yb₁₄MnSb₁₁ is small compared to the divalent Yb and originates from the surface oxidation, in comparison to Yb₁₄ZnSb₁₁, which has a higher amount of Yb³⁺, leading to the assumption that trivalent Yb is intrinsically present in the sample, making Yb₁₄ZnSb₁₁ an intermediate Yb valence system.²⁸⁶

The Yb-filled skutterudites Yb_0.075CoSb₃, Yb_0.5CoSb₃, and YbFe₄Sb₁₂ have been studied by XPS measurements, showing the presence of both Yb²⁺ and Yb³⁺ in these compounds. The binding energies are in good agreement with Yb metal and Yb₂O₃, corresponding to divalent and trivalent Yb, respectively. The doublet for Yb²⁺ is located at 1–2.2 eV, while the multiplet corresponding to Yb³⁺ is between 6 and 14 eV.²⁸⁷

MAGNETIC RESONANCE SPECTROSCOPY

This chapter is supposed to give an overview about studies in which magnetic resonance spectroscopy was applied to intermetallic Yb compounds. Nuclear magnetic resonance (NMR) in these systems can on one hand be used directly on the ytterbium nucleus to investigate the electronic situation on the Yb atom itself, while on the other hand hetero nuclear NMR is important for the measurement of effects concerning the influence of Yb on its surrounding structure.^288,289

In addition, electron paramagnetic resonance (EPR) spectroscopy is a valuable option for paramagnetic species. Here most of the studies were conducted to investigate the interesting physical properties such as the Kondo effect or heavy Fermion behavior.^290−292 These methods are, so to say, complementary to many other methods like, e.g., structure determination, since NMR spectroscopy is mainly used to confirm the results of the obtained structural models since it is a site-specific technique. Temperature-dependent measurements of both methods can give information about the temperature of possible phase transitions as well as the electronic situations. Here, important information about the interactions of the 4f electrons and the conduction electrons in the intermetallic compounds are obtained.

Nuclear Magnetic Resonance (NMR) Spectroscopy

Starting with Yb NMR spectroscopy itself, it must be mentioned that in theory the application of NMR spectroscopy to two different Yb isotopes could be possible: ¹⁷¹Yb (S = 1/2, 14.3% natural abundance, 7.4 MHz T^–1) and ¹⁷³Yb (S = 5/2, 16.4% natural abundance, 1.3 MHz T^–1).²⁸⁸ In literature, to the best of our knowledge, except for the very first study on Yb metal, no ¹⁷³Yb study has been conducted, which is obviously due to the higher resonance frequency and the absence of a quadrupole moment in ¹⁷¹Yb.²⁸⁸

As for all compounds with ytterbium, the successful application of magnetic resonance is limited to the diamagnetic closed-shell systems. Besides Yb, only Sc, Y, La, and Lu can play a role here. Therefore, in principle one must exclude the trivalent Yb which has a paramagnetic ground state (4f¹³). The magnetic moment of Yb³⁺ leads to extremely short relaxation times and therefore to substantial line broadening and makes the detection of a NMR signal impossible.²⁸⁸ However, examples making use of these significant facts have been reported.

¹⁷¹Yb NMR

In one of the already mentioned early studies²⁸⁹ of ¹⁷¹Yb NMR spectroscopy, the resonance of metallic Yb and the resonance in the intermetallic aluminide YbAl₂ (MgCu₂ type, space group Fd3m) were compared to other divalent ionic species, namely YbCl₂ (SrI₂ type, space group Pbca) and YbS (NaCl type, space group Fm3m). Knight shifts were determined to be around 0 ppm in the metal and about 7.76% in the intermetallic compound YbAl₂. No temperature dependence of the measured Knight shift was found.²⁸⁹

In a following study, the two aluminides YbAl₂ (MgCu₂ type, space group Fd3m), and YbAl₃ (Cu₃Au type, space group Pm3m) as prototypes for temperature dependent valence fluctuating systems were investigated with NMR spectroscopy. Here it was possible to detect a signal for the magnetic Yb³⁺ ion at low temperatures (1.4 to 4.2 for YbAl₃ and 4.2–80 K in the case of YbAl₂), which is hardly the case in other studies. A determination of the hyperfine field and the relaxation rates has been carried out as well. An extremely large Knight shift of ∼100% was identified in YbAl₃.²⁹³ In a recent ²⁷Al-NMR and Raman spectroscopic study, the partially divalent character of Yb in the cubic Laves phase YbAl₂ at room temperature was investigated by comparing the s electron densities with the observed isotropic resonance shifts δ(²⁷Al). Here, Yb is not comparable to the results obtained for the formally trivalent diamagnetic members of the series.²⁹⁴

The Kondo semiconductor YbB₁₂ (UB₁₂ type, space group Fm3m) has been characterized at low temperatures using ¹¹B as well as ¹⁷¹Yb NMR spectroscopy.^295,296 It was possible to observe a spin–echo signal at temperatures below 15 K for ¹⁷¹Yb. In this case, the results of the 1/T₁ relaxation of ¹⁷¹Yb is in contrast with the previous ¹¹B experiments. It is suggested that the large susceptibility arises from magnetic moments of the Yb³⁺ ion, which stands in contrast to results obtained via ¹¹B NMR spectroscopy. The effect of such a behavior is still not fully understood.²⁹⁵ The studies discussed above show the rare case of the occurrence of a detectable NMR signal for trivalent or valence fluctuating, magnetic ytterbium. Here, the NMR signal is found at drastic shifts compared to divalent ionic Yb standards.

In agreement with the structural analysis of Yb₃Ag₄Mg₁₂ (Gd₃Ru₄Al₁₂ type, space group P6₃/mmc) via X-ray diffraction (one Yb site), one single resonance for the ¹⁷¹Yb NMR spectra was observed. The temperature-dependent magnetic susceptibility measurements for this compound show the characteristics of a diamagnetic material, underlining the divalent character of Yb. The resonance of the strongly broadened spectrum recorded under static conditions applying the WURST-CPMG pulse sequence is found to be between 6800 and 7000 ppm, indicating a strong positive Knight shift. Between 200 and 300 K, the temperature dependence of the resonance shift was negligible, suggesting a strong orbital contribution to the Knight shift.⁹⁹

Recently, the influence on the ¹⁷¹Yb NMR signal, when substituting ternary Yb compounds with Ca, was shown. The divalent, ternary compounds YbZnSn (NdPtSb type, space group P6₃mc), YbPdSn₂, and YbAuIn₂ (both MgCuAl₂ type, space group Cmcm) as well as the solid solutions (Yb_0.5Ca_0.5)ZnSn, (Yb_0.5Ca_0.5)PdSn₂, and (Yb_0.5Ca_0.5)AuIn₂ were investigated with ¹⁷¹Yb NMR spectroscopy applying static WURST-CPMG pulse sequences.²⁹⁷ For all three ternary samples, the obtained results are in excellent agreement with the structural investigations and the magnetic susceptibility data for the compounds. In all cases, a single broadened ¹⁷¹Yb spectrum could be recorded, indicating one crystallographic Yb site and underlining the diamagnetic character of Yb²⁺ in this compound. For YbAuIn₂, the magnetic susceptibility data suggest paramagnetic impurities (resulting from intermediate-valent YbAuIn) in higher amounts than for the other compounds, which is given as the reason why here only a poor signal-to-noise-ratio was achieved in the NMR spectroscopic data. After Ca incorporation, a shift for the center of gravity as well as a line broadening is observed. This is due to the different local surrounding caused by the statistic mixing in a solid solution. As an example, the obtained NMR spectra are shown in Figure 13.

Figure 13.

NMR spectra of YbZnSn and YbPdSn₂ and the respective Ca-substituted variants Yb_0.5Ca_0.5ZnSn and Yb_0.5Ca_0.5PdSn₂.²⁹⁷

The germanide YbPtGe₂ crystallizes in the orthorhombic YIrGe₂ type structure (space group Immm) with two distinct Yb sites. Via ¹⁷¹Yb NMR spectroscopy, it was possible to prove that indeed two distinct Yb sites are present. Moreover, it becomes evident that one site is nearly divalent, while the Yb atoms on the other site are nearly trivalent. The authors explain this by the rather small shift of the observed signal. As mentioned above, in the case of paramagnetic ytterbium ions, larger Knight shifts are expected. Therefore, YbPtGe₂ is named a multivalent charge-ordered compound having two different Yb valences in one compound, with no dynamic behavior.²⁹⁸

Finally, in the compound YbGaGe (YPtAs type, P6₃/mmc) which has two Yb sites in an equivalent coordination, it is quite remarkable that, in a combined ¹⁷¹Yb and ^69,71Ga NMR spectroscopic study, the two different Yb sites could be identified separately from each other in NMR spectra recorded at 4.2 K, confirming the proposed crystal structure. Here, no hints for trivalent or valence fluctuating Yb atoms could be found. The Knight shifts are reported with 0.41% (4100 ppm) and 1.1% (11000 ppm), respectively, being in the typical range of divalent nonmagnetic ytterbium compounds.²⁹⁹

EPR

In contrast to the already discussed NMR spectroscopic studies on intermetallic Yb compounds, in which Yb should preferably be in the divalent state, an EPR signal should be detectable, when paramagnetic species such as the open-shell Yb³⁺ are present. Furthermore, it is possible to obtain electron spin resonance spectra which occur due to conduction electrons. Therefore, EPR spectroscopy is a method that is able to probe the local moments of unpaired 4f electrons of a lanthanide atom as well as the interaction with the surrounding delocalized conduction electrons.²¹¹ By temperature-dependent measurements of the g tensor and the line width of the signal, information about the ground state of f electron systems responsible for some important phenomena can be obtained.³⁰⁰ For the determination of the valence state of the Yb atom, the results of EPR spectroscopy can be combined with magnetic measurements. In many recent studies, EPR spectroscopy has been applied to investigate Yb compounds with exceptional low temperature physical properties, such as the Kondo effect and heavy Fermion behavior.

In Kondo systems, the EPR signal should be affected by the Kondo effect in two ways: a temperature-dependent g shift due to the local susceptibility and an additional contribution to the EPR line width.³⁰¹ At this point, it is interesting to note that it seems to be necessary to have ferromagnetic fluctuations in samples to observe any EPR signal, which could be shown by a study of antiferromagnetic (CeOsPO) and ferromagnetic (CeRuPO) samples, since only the latter give rise to an EPR signal.³⁰²

In this chapter, only some selected EPR spectroscopic studies on the most prominent examples of intermetallic Yb compounds shall be summarized. As already mentioned, this quite often goes hand-in-hand with exceptional physical properties of these compounds.

In the first part, some examples will be discussed in which the rare earth atoms were introduced as a substituent/dopant/impurity. Later, it was shown that it is possible to receive experimental EPR spectroscopic data on phase-pure unsubstituted/undoped Yb samples, so to say in a dense lattice.

In many systems, it was not possible to obtain EPR spectra and thereby information about the electronic structure of rare earth atoms by applying EPR spectroscopy on dense lattice systems. Due to ultrafast relaxation times, a doping or substitution of paramagnetic ions into diamagnetic compounds is necessary.²⁹⁰ One example for this is the EPR spectrum of ytterbium recorded in elemental gold (800 and 1600 ppm). Here, temperature-dependent measurements between 0.1 and 1 K resulted in the observation of a nonlinear behavior of the line width when lowering the temperature. This could be attributed to the Kondo effect.³⁰¹ In a study for the Yb-doped samples (100 up to 1000 ppm) with the composition MPd₃ (M = Sc, Y, Lu, La, and Ce), crystallizing in the cubic Cu₃Au structure (Pm3m), for all tested metals (Er³⁺, Gd³⁺, and Yb³⁺), a Γ₇ ground state indicating trivalent character of the ytterbium was found. The EPR spectrum of YPd₃ (1000 ppm Yb) given in reference³⁰⁰ is affected by the hyperfine interaction of the localized moment with the two isotopes ¹⁷¹Yb and ¹⁷³Yb resulting in additional satellites besides the central transition.

Some examples of EPR spectra of Yb in undoped nonmetallic phases such as hydride (YbH_x)³⁰³ or oxide phases (Yb_xY_1–xBa₂Cu₃O_y)³⁰⁴ are reported. In these systems, a narrowing of the observed EPR line is described because of the spin-glass ordering and the absence of heavy Fermion behavior as well as exchange narrowing. In an early example, it is reported that the temperature-dependent EPR spectra of pure YbBe₁₃ and substituted diamagnetic Y_1–xYb_xBe₁₃ (x = 0.01 and 0.09) are identical, which is linked to the rather large separation of ∼500 pm of the rare earth atoms in the NaZn₁₃ type structure (Fm3c), leading to a small crystal field splitting (Γ₇ → Γ₆ → Γ₈) and next to no interaction between the magnetic moments except for some RKKY exchange. For the exact CEF, the differences in the literature were already discussed above. In this EPR spectroscopic study, the valence state of Yb was determined to be trivalent with a Γ₇ ground state, equivalent to Eu and Sm, and in contrast to Ce which is in an intermediate valence state in this structure type.²³⁶

When looking in the literature, the application of EPR spectroscopy to intermetallic Yb compounds showing heavy Fermion behavior is the most prominent one. Especially, the compound YbRh₂Si₂ was the first compound in which the direct investigation of the EPR signal of the rare earth ion responsible for the Kondo effect, up to 25 K, so below and above the Kondo temperature, without any doping, substitution, or impurities, was possible. The detection of the signal was thought to be impossible until this proof. In previous studies of doped samples (e.g., with Gd³⁺), one cannot exclude the influence of the dopant on the Kondo lattice. The exact origin of the EPR signal in this dense Kondo lattice below the relatively high Kondo temperature of T_K = 20 K in this compound is yet unclear.^158,305,306 A similar EPR signal could be detected a little later in the isostructural silicide YbIr₂Si₂. The results are in good agreement with those of the Rh compound. Way below the Kondo temperature of 40 K, it was possible to detect a strong EPR signal down to 1 K. Therefore, it is the second example of strong, intense EPR lines in a dense Kondo heavy Fermion system.³⁰⁷ In the past years, more examples of direct EPR detection in heavy Fermion compounds were reported. For YbNiAl₂, the trivalent state of the Yb atom was confirmed by measuring an intense EPR spectrum below 20 K. However, here the authors mention that the intensity of the signal obtained at temperatures below 20 K was about an order of magnitude lower than for YbRh₂Si₂. By increasing the temperature, the EPR signal disappeared. The reason for the appearance of the EPR signal at low temperatures in this dense heavy Fermion compound is not only the already mentioned ferromagnetic fluctuations but also magnetic anisotropy as well as cumulative effects of the surrounding crystal field and spin–orbit interactions.³⁰⁸

For the case of the above-mentioned heavy Fermion superconductor β-YbAlB₄, an interesting dual nature behavior of the EPR signal was observed. At high temperatures, an EPR signal was found for the Yb as well as for the Pauli-paramagnetic Lu compound. The Lu compound shows the characteristic temperature dependence of a conduction electron spin resonance over the whole temperature range (4.2 to 295 K), while in comparison, at 4.2 K, the Yb compound shows a hyperfine splitting caused by the ¹⁷¹Yb isotope, confirming the characteristics of an Yb³⁺-caused spin resonance. This is a unique behavior of the dual nature observed in EPR spectroscopy.²¹¹

For the compounds YbBiPt and YbRh₂Pb, EPR measurements could be performed at temperatures of up to 110 K, although for discussion of the nature of the compounds, measurements at 4.4 K were used. The results give hints about the crystal electric field (CEF) for the Yb³⁺ atom in these ternary compounds. For the plumbide, an extremely small hybridization of the 4f electrons and the conduction electrons is suggested together with weak RKKY interactions. In contrast, the bismuthide shows a strongly broadened CEF due to large hybridization effects.²⁹⁰ In this context, one must mention one important class of isostructural compounds. All Yb compounds with the general formula YbT₂Zn₂₀ (T = Fe, Co, Ru, Rh, Os, Ir)³⁰⁹ exhibit heavy Fermion behavior. Therefore, a comparison of the spectroscopic properties such as for the above-mentioned silicides Yb(Ir,Rh)₂Si₂ was possible.³⁰⁹ Here, the Co and Fe compounds have been investigated with EPR spectroscopy. In an analogous way to the already mentioned studies, it was possible to detect a spectrum without any dilution or paramagnetic impurity. A direct investigation of the dense Yb lattice was possible.^290,305,309 A comparison of the EPR absorption of the Co and Fe compounds (Figure 14) gave hints about the involvement of the d electrons of the magnetic atoms. With the Co compound EPR absorption being higher by a factor of 10, it was proposed that the increasing number of available d electrons also plays a crucial role in the intensity of the EPR signal and not only the localized magnetic moment of the f electrons on the rare earth atom.

Figure 14.

EPR spectra of YbCo₂Zn₂₀ and YbFe₂Zn₂₀. Reprinted from ref (290) with permission from Elsevier.

¹⁷⁰Yb MÖSSBAUER SPECTROSCOPY

¹⁷⁰Yb is a Mössbauer-active isotope and thus allows studies of the ytterbium valence state, the coordination geometry, and magnetic hyperfine field splitting. The energy E_γ amounts to 84.25 keV. The decisive point for ¹⁷⁰Yb Mössbauer spectroscopic studies is the very low natural abundance of ¹⁷⁰Yb of only 3%, forcing long data collection times. The basic nuclear moment data for the different ytterbium isotopes (¹⁷⁰Yb, ¹⁷¹Yb, ¹⁷²Yb, ¹⁷⁴Yb, ¹⁷⁶Yb) have been summarized by Stevens and Dunlap;³¹⁰ however, ¹⁷⁰Yb is the usually studied isotope. Its basic Mössbauer spectroscopic characteristics are: I_e = 2 (nuclear spin operator in the excited state); I_g = 0 (nuclear spin quantum number in the ground state); transition energy of 84.25 keV; TmB₁₂ as the usual source (typically 20 mCi) with a half-life of 130 d; and natural line width of 2.03 mm s^–1.^{288,311−313}

The ¹⁷⁰Yb isomer shift values for divalent and trivalent ytterbium vary only over a small range. For purely ionic compounds, representative values are δ = −0.49 mm s^–1 for Yb^IISO₄ and +0.09 mm s^–1 for Yb^IIICl₃.³¹¹ It is clear that this marginal separation of the Yb^II and Yb^III isomer shifts hampers the studies of valence changes.³¹⁴ However, the ¹⁷⁰Yb data is very sensitive to the hyperfine splitting of the nuclear energy levels and thus allows detailed studies of the magnetic ordering phenomena. The basics for the ¹⁷⁰Yb Mössbauer spectroscopic data with respect to magnetic hyperfine splitting are summarized in a concise resource letter by Cadogan and Ryan.³¹² In the large field of ytterbium intermetallics, the magnetic ordering of the trivalent compounds often sets in only at very low temperatures. Consequently, ¹⁷⁰Yb Mössbauer spectra have frequently been measured down to the mK range. Determination of the quadrupole splitting parameter is the important feature for discriminating divalent and trivalent ytterbium. Yb^II has a filled 4f shell and thus no 4f contribution to the electric field gradient at the ¹⁷⁰Yb nucleus. The Yb^III compounds, in contrast, show paramagnetic quadrupole triplets.³¹⁵ Typical examples for divalent ytterbium intermetallics are the binary ytterbium–cadmium phases YbCd, YbCd₂, Yb₁₄Cd₅₁, YbCd_5.7, and YbCd₆³¹⁶ or the ternary stannide Yb₃Pd₂Sn₂.^317,318

The magnetically ordered Yb^III compounds show more or less well-resolved hyperfine field splitting. From the hyperfine field value H_hf, one can derive the ordered moment μ through the relation H_hf = Cμ with a value of C = 102 T/μ_B for Yb³⁺ (derived from accurate measurements of the paramagnetic hyperfine constant of ¹⁷⁰Yb³⁺ in the cubic Γ₇ state).^319−321 Due to the meaninglessness of the isomer shift value, the ¹⁷⁰Yb Mössbauer spectroscopic studies on intermetallic compounds only report on the quadrupole splitting parameters and the magnetic hyperfine fields.

Temperature-dependent measurements in the magnetically ordered regimes allow for monitoring the evolution of the magnetic hyperfine field with decreasing temperature. These data can be fitted with an S = 1/2 law, and the magnetic ordering temperature can be derived as complementary experiment to the magnetic characterization. Data of binary Yb₃Pd₄³²² is presented in Figure 15. Further related examples are YbNiBC,³²³ or samples from the solid solution Yb₅Si_xGe_4–x.³²⁴ In several cases, the crystal field properties have also been derived from the ¹⁷⁰Yb Mössbauer spectroscopic data and compared to L_III-edge X-ray absorption spectra and magnetic data. An exemplary investigation is the ¹⁷⁰Yb Mössbauer spectroscopic characterization of YbCu₃Al₂.³²⁵

Figure 15.

Temperature dependence of the hyperfine field at the ¹⁷⁰Yb nuclei in Yb₃Pd₄ (T_N = 3.2 K). The thermal variation follows an S = 1/2 mean field law (dashed line). Reprinted from ref (322) with permission from Elsevier.

Early work on ¹⁷⁰Yb Mössbauer spectroscopic data focused on the rocksalt type monopnictides YbP, YbAs, and YbSb (space group Fm3m),^326−328 which are Kondo-frustrated antiferromagnets with very low Néel temperatures <1 K (Table 3). Although the three phases have cubic symmetry, inhomogeneous hyperfine fields/hyperfine field distributions have been observed. Thus, ¹⁷⁰Yb Mössbauer spectroscopy is an excellent complementary tool for monitoring structural distortions. In the following, many other binary, ternary, and quaternary intermetallic phases have been characterized through their ¹⁷⁰Yb Mössbauer spectra. Some selected phases, which all have their own peculiarity, are shortly discussed in the following.

Table 3. ¹⁷⁰Yb Mössbauer Spectroscopy Derived Parameters for Selected Intermetallic Ytterbium Compounds^a.

Compound	Structure Type	TM/K	TMb/K	BHf/T	μ/μB	Reference
YbBe13	NaZn13	TN = 1.28	0.05	172	1.73	(336)
YbB12	UB12	–	0.04	<10	<0.1	(337)
YbP	NaCl	TN = 0.41	0.045	81	0.79	(326)
YbAs	NaCl	TN = 0.58	0.045	81	0.82	(326)
YbSb	NaCl	TN = 0.32	0.045	64	0.63	(326)
YbNi5	CaCu5	TC = 0.55	0.05	399(2)	3.9	(338)
Yb3Pd4	Pu3Pd4	TN = 3.2(1)	0.05	63(5)	0.62(5)	(322)
YbCu3Al2	PrNi2Al3	TN = 1.95	0.12	290(10)	2.84(10)	(325)
YbPtAl	TiNiSi	TN = 5.8	4.2	159	1.56	(329)
Yb3Cu4Ge4	Gd3Cu4Ge4	TN = 7.5	1.45	370	3.6	(332)
				148	1.45
Yb2Co3Al9	Y2Co3Al9	TN = 1.2	0.06	95	0.93	(333)
YbNiSb	MgAgAs	TN = 0.85	0.13	108(10)	1.06(10)	(334)
YbNiSn	TiNiSi	TN = 5.65	1.48	870(20)	0.85(2)	(125)

^aParameters include: magnetic ordering temperature, T_m; measurement temperature for the Mössbauer spectrum, T_MB; magnetic hyperfine field, B_hf; and magnetic moment at the ¹⁷⁰Yb nuclei, μ. Note that Yb₃Cu₄Ge₄ shows two sub-spectra with different hyperfine fields. Standard deviations are given in parentheses, when available.

The incommensurate modulated structure of YbPtAl (TiNiSi type, space group Pnma, wave-vector k = 0.30, 0, 0) was studied by a combination of neutron powder diffraction and ¹⁷⁰Yb Mössbauer spectroscopic data.³²⁹ The low-temperature spectroscopic data (0.025 K) clearly shows that the modulated structure is not an antiphase one. The maximum moment of 2.5 μ_B was derived from the 1.6 K spectrum.

The ¹⁷⁰Yb Mössbauer spectroscopic data of YbNiAl₄ (YNiAl₄ type, space group Cmcm) is an important complementary result to specific heat data. While the latter points to the onset of magnetic ordering, no hyperfine field splitting is evident from the ¹⁷⁰Yb Mössbauer spectra down to 1.5 K.²³ This is consistent with an intermediate ytterbium valence, since the temperature dependence of the magnetic susceptibility also revealed a substantially reduced experimental magnetic moment.

The ytterbium valence change induced by substitution was studied for the solid solutions Yb₅Ge_4–x(Sb,Ga)_x with x ≤ 1 (Sm₅Ge₄ type, space group Pnma).³³⁰ For influencing the ytterbium valence, the germanium atoms are partially substituted by gallium with lower and antinomy with higher electron count. The Yb^II/Yb^III ratio could be derived from well-resolved ¹⁷⁰Yb Mössbauer spectra at 5 K through the subsignals with and without quadrupole splitting (vide infra). The Mössbauer spectroscopic data show an almost gradual increase of the Yb^II/Yb^III ratio from ∼0.95 for Yb₅Ge₃Ga to ∼1.55 for Yb₅Ge₃Sb.

The quadrupolar phase transition at 80 K in YbAl₃C₃ (ScAl₃C₃ type, space group P6₃/mmc) was monitored by ¹⁷⁰Yb Mössbauer spectroscopy.³³¹ Spectra were collected in the entire range from 0.04 to 150 K. No magnetic ordering of the Yb³⁺ moments was evident down to the lowest measurement temperature. The symmetry reduction (loss of the mirror plane perpendicular to the 6₃ screw axis) is well expressed in the course of the quadrupole splitting in the ¹⁷⁰Yb spectra in the sequence 85 K → 80 K → 77 K → 75 K with a nonaxial quadrupolar hyperfine interaction in the low-temperature phase. Also in this case, ¹⁷⁰Yb Mössbauer spectroscopy served as a valuable complementary probe for studying a structural phase transition.

Yb₃Cu₄Ge₄ with Gd₃Cu₄Ge₄ type structure (space group Immm) is one of the remarkable ytterbium intermetallics, since it exhibits two crystallographically independent ytterbium sites 4e and 2d.³³² Although the magnetic data indicate a single transition temperature into the magnetically ordered state, these two ytterbium sites show distinctly different magnetic hyperfine spectra (Figure 16) with ordered moments of 3.6 μ_B for the 4e and 1.45 μ_B for the 2d site. Integration of the subspectra is consistent with the 2:1 multiplicity of the individual Wyckoff positions.

Figure 16.

¹⁷⁰Yb Mössbauer spectra of Yb₃Cu₄Ge₄. The spectrum at 15 K was taken in the paramagnetic range, while the 1.45 and 6.5 K spectra are derived from the magnetically ordered phase. The subspectra are marked by different solid lines. Reprinted from ref (332) with permission from Elsevier.

¹⁷⁰Yb Mössbauer spectroscopy was employed to differentiate the magnetic behavior of the Yb atoms in the isotypic compounds Yb₂Co₃Al₉ and Yb₂Co₃Ga₉ (Y₂Co₃Ga₉ type, space group Cmcm).³³³ The aluminum compound shows a stable ²F_7/2 ground state and well-resolved hyperfine field splitting (95 T) at 0.06 K, while Yb₂Co₃Ga₉ is a paramagnetic heavy-Fermion material showing no hyperfine field splitting over the whole temperature range.

The solid solution Yb_1–xIn_xCu₂ is structurally derived from the cubic Laves phase (space group Fd3m, vide ultra). The sample with the composition Yb_0.4In_0.6Cu₂ shows a sharp valence transition around 50 K. ¹⁷⁰Yb Mössbauer spectra at 4.2 K indicate that the Yb³⁺ ions exhibit no magnetic hyperfine field splitting in the cubic environment; however, it shows a strong 4f–5d hybridization.¹⁹¹

The final example shows the necessity of complementary techniques for the precise understanding of structure–property relations. The half-Heusler phase YbNiSb (MgAgAs type, space group F43m) has been characterized through ¹⁷⁰Yb Mössbauer spectra at 0.13 and 1.4 K.³³⁴ Spectra in the magnetically ordered regime revealed enlarged and inhomogeneous line widths. Based on these results, it was argued that the quadrupolar hyperfine interaction of the paramagnetic phase has no cubic site symmetry. Later, precise single crystal X-ray diffraction data showed that YbNiSb samples are a mixture of equiatomic YbNiSb as the main component along with a distribution of YbNi_xSb domains with different nickel content.³³⁵ Thus, the magnetically split spectrum is a superposition of the magnetically split subspectra of the distribution of YbNi_xSb domains.

Many other interesting examples for ¹⁷⁰Yb Mössbauer spectroscopic studies on ytterbium intermetallics have been published. In such a review, one can only present selected examples. Besides the data discussed above, we have added some further examples in Table 3 with respect to their basic Mössbauer spectroscopic data.

Besides the many ¹⁷⁰Yb Mössbauer spectroscopic studies under ambient conditions, some investigations were carried out under application of external magnetic fields or high pressure. The heavy Fermion silicide YbRh₂Si₂ was additionally studied by ¹⁷⁰Yb Mössbauer spectroscopy as a complementary tool to ESR spectroscopy.³³⁹ The ESR data for this silicide gave hint for a slow relaxation rate. This issue could be clarified by ¹⁷⁰Yb Mössbauer spectroscopy. The ¹⁷⁰Yb spectrum only shows a single signal, which does not match with a simulated spectrum for slow relaxation at an applied field of 0.4 T. The ¹⁷⁰Yb data thus indicate that the Yb³⁺ ions relax more rapidly than expected from the ESR data. YbRh₂Si₂ was furthermore studied at 1.3 K and pressures ranging from 6.4 to 16.5 GPa.³⁴⁰ The experiments show a continuous line broadening with increasing pressure. The pressure-induced first-order magnetic phase transition sets in around 10 GPa. The line broadening indicates increasing magnetic hyperfine field splitting and thus an increase of the ordered moment at the ytterbium nuclei with a value of 1.9 μ_B (≡191 T) at 16.5 GPa, still reduced when compared with the free ion value of 4 μ_B.¹⁰⁵

The technical details for ¹⁷⁰Yb Mössbauer spectroscopy under high-pressure conditions are well documented in an article by Schöppner et al.,³⁴¹ which focuses on the pressure-induced ytterbium valence change in YbCuAl (ZrNiAl type, space group P62m). The compound was studied at 4.2 K from 0 to 130 kbar pressure. The ¹⁷⁰Yb spectra show a continuous increase of the quadrupole splitting parameter with increasing pressure, manifesting the valence transition toward trivalent ytterbium with 4f¹³ configuration. This ground state is achieved already at around 50 kbar.

¹⁷⁰Yb Mössbauer spectroscopic data was collected for the TiNiSi type stannide YbNiSn (space group Pnma) up to 7 GPa.³⁴² A remarkable feature is the increase of the Curie temperature with increasing pressure with a maximum of T_C = 7.6 K at 1.7 GPa followed by a rapid decrease. In parallel, the quadrupole splitting parameter and the magnetic hyperfine field increase from ambient pressure to 7 GPa. The maximum field of 175 T corresponds to an ordered moment of 1.72 μ_B.

Also, the heavy Fermion compound Yb₂Ni₂Al (W₂CoB₂ type, space group Immm) shows a pressure-driven first-order magnetic phase transition.³⁴³ A crossover from a nonmagnetic heavy Fermion state to a magnetically ordered state occurs at pressures >8 GPa and below 2 K. The ¹⁷⁰Yb Mössbauer spectrum (1.8 K data) at the highest pressure of 9 GPa showed an ordered moment of ≈1 μ_B at the ytterbium nuclei.

Finally, we turn toward an interesting extension of ¹⁷⁴Yb Mössbauer spectroscopy which was realized recently using synchrotron radiation as the Mössbauer spectroscopy source. The classical experiments all used the ¹⁷⁰Yb isotope. The main disadvantage is its low natural abundance of only 3% as compared to 31.8% for ¹⁷⁴Yb. The synchrotron radiation-based technique is described in a resource article by Masuda et al.,³⁴⁴ and exemplified for an YbB₁₂ (UB₁₂ type, space group Fm3m) sample. Further advantages of this new technique are the higher brilliance of the synchrotron radiation as compared to X-rays deriving from a radioactive isotope, and there is no need for isotope enrichment. Along with the use of a windowless avalanche photodiode detector, fast data collections are possible, and this technique will also be helpful for future high-pressure studies. Two further examples for the application of ¹⁷⁴Yb Mössbauer spectroscopy are Yb₂Fe₁₄B (Nd₂Fe₁₄B type, space group P4₂/mnm)³⁴⁵ and α-YbAlB₄ (YCrB₄ type, space group Pbam).³⁴⁶

THERMOELECTRICS

Thermoelectric materials are usually heavily doped semiconductors which can produce a charge flow when exposed to a temperature gradient. Depending on the charge carrier type in the respective material, these are denoted as p- or n-type semiconductors. The quality of a thermoelectric material is usually given by the dimensionless figure-of-merit zT which basically incorporates the Seebeck coefficient as well as the thermal and electrical conductivity. Details regarding these values and their interplay can be found in a number of reviews.^347−352 However, the determination of the Seebeck coefficient can also be used for identifying magnetic transitions and other physical phenomena as it is very susceptible to changes in the electronic states. In the following chapter, examples of classical intermetallic Yb-compounds as well as examples of Zintl phases, being the more typical thermoelectric materials, will be addressed.

Binary Compounds

We will start this chapter with selected examples of classical intermetallic materials. For this, the binaries YbAl₃, YbSi₂, YbB₆, YbCd₆, and Yb₃Si₅ as well as the solid solutions Yb_1–xSc_xAl₂, Yb_1–xIn_xCu₂, and YbCu_5–xAg_x have been chosen. From the ternary systems, equiatomic YbPtBi, YbNiSn, and YbPtGe, as well as YbAlB₄, YbNiAl₄, YbRh₂Al₂₀, and YbT₂Zn₂₀ (T = Fe, Co, Ru, Rh, Os, Ir), Yb₂Pt₃Sn₅, Yb₂T₃X₉ (T = Rh, Ir; X = Al, Ga), Yb₂Pt₆Al₁₅, and Yb₂Ni₁₂P₇ were selected.

YbAl₃ (Cu₃Au type, space group Pm3m) is, as mentioned before, a well studied compound due to the ambivalent nature of the Yb atoms leading to a change of the Yb valence with temperature.¹¹³ Due to this phenomenon, the Seebeck coefficient of intermediate valent/valence fluctuating Yb compounds is often significantly higher than expected. This is also the case for YbAl₃ where the Seebeck coefficient reaches values over −80 μV K^–1 near 120 K,³⁵³ and YbSi₂ (AlB₂ type, space group P6/mmm),³⁵⁴ also a mixed valent compound, shows values between −50 and −35 μV K^–1 between 300 and 525 K. The electrical resistivity, however, possesses abnormally large values due to spin-disorder scattering. YbSi₂ shows an almost temperature-independent electrical resistivity and a total thermal conductivity between 8 and 11 W m^–1 K^–1, leading to a zT between 0.08 at 300 K and 0.04 at 525 K. YbB₆ adopts the cubic CaB₆ type structure (space group Pm3m) and exhibits a certain phase width between x = 5.7 and 6.3.³⁵⁵ Therefore, this compound can be used to study and tune the thermoelectric properties. The compounds with x = 5.7, 5.9, and 6.0 exhibit a negative Seebeck coefficient of approximately −100 μV K^–1 between 300 and 1050 K. In contrast, the samples with x = 6.1 and 6.3 start with a positive Seebeck coefficient of +100 μV K^–1, which gradually changes to negative values at higher temperatures. YbCd₆, despite the same sum formula, crystallizes in a totally different crystal structure (YCd₆ type, space group Im3). Instead of octahedral B₆ clusters, here a quasi-crystal (QC) approximant with a shell-like structure is present. Both the QC YbCd_5.7 and the approximant YbCd₆ were investigated with respect to their thermoelectric properties. Both show small positive Seebeck coefficients between +10 and +20 μV K^–1. The striking feature is a maximum in the electrical resistivity around 70 K for YbCd_5.7. A similar trend can be seen for the different compositions of the quasi-crystals, leading to zT values of 5 × 10^–3 near RT.^356,357 Finally, Yb₅Si₃ (Mn₅Si₃ type, space group P6₃/mcm) should be discussed as the last binary representative. Again, this compound is valence instable and shows fluctuations between di- and trivalent Yb, leading to two sign changes in the Seebeck coefficient. Below ∼40 K, it is negative with a rather sharp minimum at 10 K, followed by a broad maximum with positive values (∼13 μV K^–1) around 100 K, and again a change to a negative Seebeck coefficient close to 300 K. The resistivity is, compared to the close-shell system Lu₅Si₃, enhanced by a factor of close to two, caused again by the valence fluctuation.³⁵⁸

The solid solution Yb_1–xSc_xAl₂ (MgCu₂ type, space group Fd3m) was studied to probe the influence of “chemical pressure” on the properties of the valence fluctuating system YbAl₂. Different compositions with x = 0.6–1 were synthesized and investigated. Magnetic susceptibility measurements clearly indicate that the intermediate valence (IV) state gets more pronounced with increasing Sc content and a shift toward more Yb³⁺ is visible. Samples with a pronounced IV state at the same time exhibit a drastically negative Seebeck coefficient up to −50 μV K^–1 below 50 K for x = 0.9. This leads to a maximum in the power factor (S²/ρ) of 160 μW cm^–1 K^–2 for x = 0.9 around 50 K.³⁵⁹

Since Yb_1–xIn_xCu₂ (MgCu₂ type, space group Fd3m) shows a temperature-induced first-order valence phase transition, its Seebeck coefficient was investigated for x = 0.6 to probe the fine structure of the conduction electron band closely associated with the magnetic state. The temperature dependence of the Seebeck coefficient starts with a positive sign at high temperatures and exhibits a change of sign near 200 K. Around 40 K, a minimum with S = −16 μV K^–1 is visible, coinciding with the temperature of the valence phase transition.³⁶⁰

Equiatomic Ternary Compounds

For the ternary compounds, we will start with selected equiatomic representatives, i.e., YbNiSn, YbPdGe, YbPtGe, and YbPtBi. For YbNiSn (TiNiSi type, space group Pnma), the thermoelectric properties were studied to obtain further information about the crystal field splitting. Inelastic neutron scattering should yield three crystal field excitations based on the crystal structure. However, only two excitations were visible; therefore, the thermoelectric properties were determined to gain a deeper insight. The temperature dependence of the Seebeck coefficient shows a broad minimum around 100 K along with a peak at 7.5 K and a change of sign below 5 K. From these investigations, the degeneracy of two crystal field excitations was deduced.³⁶¹ YbPdGe (YbAuSn type, space group Imm2) and YbPtGe (TiNiSi type, space group Pnma) show a very similar behavior. The Seebeck coefficient shows a broad maximum around 120 K followed by a maximum at 30 K. Three contributions were deduced: a Mott’s diffusion term as well as a Kondo and a resonance term. While the first one is small and temperature-independent, the Kondo term originates from Kondo scattering of conduction electrons by the 4f spins. The inelastic contribution to the resonance term originates from inelastic scattering of the conduction electrons by magnetic interactive spins, respectively.³⁶² Finally, YbPtBi (MgAgAs type, space group F43m) was investigated. This compound is of particular interest since it exhibits one of the largest Sommerfeld coefficients known (γ = 7.4 J mol^–1 K^–2).¹³⁷ Thin films of YbPtBi exhibit also a negative Seebeck coefficient with −54 μV K^–1.³⁶³

Further Ternary Compounds

While the silicides and germanides adopt the tetragonal body centered ThCr₂Si₂ type structure (space group I4/mmm), the pnictide-based Zintl phases of the same chemical composition crystallize in the trigonal space group P3m1 and adopt the Ce₂O₂S type structure.

YbRh₂Si₂ is an antiferromagnetic heavy Fermion compound;^{162,163,364,365} therefore, investigations of the thermoelectric properties (TEP) can give important information on the behavior of the conduction electrons. The TEP contain information about the relaxation time and the DOS of the quasiparticles at the Fermi level E_F. It is interesting to note that at very low temperatures, the TEP is commonly positive for Ce heavy Fermion compounds, in agreement with the Kondo picture, while it is negative for Yb heavy Fermion compounds.³⁶⁶ Field-dependent measurements of the Seebeck coefficient S(H) have been conducted down to 120 mK and up to 16 T.³⁶⁷ Above 3.5 T, a cascade of sharp anomalies can be observed, pointing toward topological transitions of the Fermi surface. Upon substitution of rhodium by cobalt according to Yb(Rh_1–xCo_x)₂Si₂,^368,369 the Kondo temperature decreases significantly, and the sole large minimum in the thermopower that is observed for YbRh₂Si₂ splits into two minima. In addition, the absolute thermopower is strongly reduced with increasing x, in line with a weaker exchange coupling of the 4f and the conduction electron states making pure YbCo₂Si₂ a stable trivalent system.^241,242,369 However, still two minima are observed in the Seebeck coefficient, indicating weak residual Kondo scattering in line with a tiny residual hybridization between 4f and conduction electron states. A comparative study of the thermoelectric response under magnetic field of YbRh₂Si₂ and YbAlB₄ showed a significant difference in the Seebeck coefficient near the quantum critical points of both compounds. When approaching the critical field, S/T is drastically reduced in YbRh₂Si₂; however, an enhancement in β-YbAlB₄ is observed.³⁷⁰

YbPd₂Si₂ is another heavy Fermion material within the group of Yb intermetallics and has been studied broadly.^371−373 In the range between 1.5 and 300 K, the Seebeck coefficient is negative with a minimum around 50 K, which was attributed to the intermediate valence of this compound.³⁷⁴ Investigations of YbNi₂Si₂ and YbCu₂Si₂ revealed a similar behavior with minima between 50 and 100 K; however, the Seebeck coefficient gets positive for YbNi₂Si₂ below ∼20 K, which was assigned to the antiferromagnetic ordering of this compound.^375,376 High-pressure studies of YbCu₂Si₂ revealed that a magnetic phase transition emerges at T_m = 1.9 K around T_C = 10.2 GPa which shifts to higher temperatures with increasing pressure.³⁷⁷ This was later confirmed by high-pressure measurements of the Seebeck coefficient.³⁷⁵ YbPd₂Ge_1.7 also exhibits a nonmonotonous behavior and shows a negative Seebeck coefficient down to low temperatures, where again the sign changes.³⁷⁸ The solid solutions YbCu₂Si_2–xGe_x³⁷⁹ and Yb_1–xLa_xCu₂Si₂³⁸⁰ finally were studied with respect to their thermoelectric properties. Materials with large Seebeck coefficients at low temperatures can be utilized for cryogenic Peltier elements for cooling infrared sensors on satellites. With this respect, the solid solutions were investigated to maximize the zT at cryogenic temperatures. In both cases, an enhancement of the power factor as well as a shift of the maximum to higher temperatures was observed. Alongside this, a reduction of the thermal conductivity was noted, leading to an overall higher zT. The observed changes were attributed to the changes in the unit cell dimensions that can be envisioned as “chemical pressure”.

YbAlB₄ and YbNiAl₄, although having the same chemical composition, adopt two different structure types. YbAlB₄ is furthermore dimorphic and crystallizes either in the orthorhombic YCrB₄ (α-YbAlB₄; space group Pbam) or ThMoB₄ (β-YbAlB₄; space group Cmmm) type structure (vide ultra). Due to the superconductivity observed in β-YbAlB₄²⁰⁴ and its heavy Fermion characteristics, the quantum-critical point (QCP) is of special interest. During these investigations, it became clear that the Seebeck coefficient for β-YbAlB₄ behaves significantly different compared to YbRh₂Si₂. −S(T)/T becomes large for β-YbAlB₄ near the zero-field QCP, while for YbRh₂Si₂, −S(T)/T is strongly suppressed.^370,381

Also, in the CeCr₂Al₂₀ type structure (space group Fd3m), several Yb-containing compounds are known that exhibit Kondo or heavy Fermion properties. Similar to the examples discussed before, the members of the YbT₂Zn₂₀ (T = Fe, Ru, Os, Co, Rh, Ir) series also exhibit heavy Fermion Kondo lattices. In their thermoelectric properties, all members show large, negative minima (between −75 and −45 μV K^–1); however, variations with respect to the transition metal T can be observed. The local minimum in S(T) and the local maximum in ρ(T) can be correlated to the transition metals and the Kondo temperatures of the respective compounds as well as with the influence of the crystalline electric field splitting.³⁸² Wei and co-workers have shown, that the compounds of the YbT₂Zn₂₀ (T = Co, Rh, Ir) series exhibit increasing figures of merit with increasing mass of the transition metals at low temperatures, peaking at zT = 0.07 at 35 K for YbIr₂Zn₂₀.³⁸³

Finally, the thermoelectric investigations on Yb₂Pt₆Al₁₅ (Sc_0.6Fe₂Si_4.9 type, space group P6₃/mmc),³⁸⁴ Yb₂T₃Al₉ (T = Rh, Ir; Y₂Co₃Ga₉ type, space group Cmcm),³⁸⁵ Yb₂Pt₃Sn₅ (own type, space group Pnma),³⁸⁶ and Yb₂Ni₁₂P₇ (Zr₂Fe₁₂P₇ type, space group P6)³⁸⁷ should be addressed. While the first two representatives have been characterized as heavy Fermion systems, Yb₂Pt₃Sn₅ is a rare example of a heterogeneous mixed-valence system. Yb₂Ni₁₂P₇ finally exhibits a crossover between Fermi-liquid and non-Fermi-liquid behavior and seems to be in close proximity to a quantum critical point. For both Yb₂Pt₆Al₁₅ and the Yb₂T₃Al₉ (T = Rh, Ir) series, the temperature dependence of the Seebeck coefficient shows a minimum at low temperatures, as expected for Yb-based Kondo lattice systems. While the platinum compound reaches −70 μV K^–1 around 35 K, Yb₂Rh₃Al₉ and Yb₂Ir₃Al₉ show a change of sign near 250 K and minima of −15 μV K^–1 and −25 μV K^–1 at 30 and 40 K, respectively. For the latter, an additional anomaly is observed near their Néel temperature.³⁸⁵ A single anomaly in S(T) is observed for Yb₂Pt₆Al₁₅ indicating that the Kondo energy scale is close to the CEF splitting. The temperature observed is compatible with a Kondo scale of the order of 60 K. The accordance of these temperatures supports the picture of a Kondo lattice with a large characteristic energy in which the whole multiplet is involved in the low-temperature physics.³⁸⁴ Yb₂Pt₃Sn₅ also shows a minimum in the Seebeck coefficient (−38 μV K^–1 at 60 K),³⁸⁶ which is typical for intermediate valent Yb compounds such as YbAgCu₄ and YbCu₂Si₂.³⁷⁴

Zintl Phases

Zintl phases are usually the class of materials that come to mind when speaking about thermoelectric properties. Due to their semiconducting properties, they can be utilized to produce energy based on a temperature gradient. In many cases, the materials have to be optimized with respect to their electronic properties like charge carrier concentration.

One compound with outstanding thermoelectric properties is probably Yb₁₄MnSb₁₁ (Ca₁₄AlSb₁₁ type, space group I4₁/acd). In 2006, Brown et al. reported that Yb₁₄MnSb₁₁ “achieves quadrupled efficiency and virtually doubled figure of merit over the current state-of-the-art, SiGe”.³⁸⁸ The material reaches a figure of merit of ∼1.0 at 1223 K (Figure 17). The Seebeck coefficient is positive in the whole temperature range and increases linearly with increasing temperature, reaching +185 μV K^–1 at 1275 K. Since the resistivity also shows a linear behavior with temperature and Hall measurements indicate a constant carrier concentration over the investigated temperature range, the compound can be considered a heavily doped semiconductor. The high figure of merit finally arises from the low thermal conductivity of Yb₁₄MnSb₁₁, which is on the scale of a glass (7–9 mW cm^–1 K^–1).

Figure 17.

Figure of merit zT of Yb₁₄MnSb₁₁. Maximum zT value of ∼1.0 at 1200 K. Reprinted with permission from ref (388). Copyright 2006 American Chemical Society.

Since the initial report of Yb₁₄MnSb₁₁ being a high-zT material, numerous reports have been published that modified the original compound via the formation of solid solutions as well as investigations on isostructural compounds. In the following part, selected publications have been chosen to illustrate the overall ideas.

Yb₁₄MnSb₁₁ can be modified on the Yb, the Mn, and the Sb position, either by isovalent atoms, often leading to structural distortions and therefore changes in the electronic structure, or by elements which exhibit different formal oxidation states, leading to changes in the overall electron count. Isovalent substitutions on the Yb position can, for example, be realized by Ca. The solid solution Yb_14–xCa_xMnSb₁₁ shows that the substitution of Yb by Ca reduces the carrier concentration leading to an increased Seebeck coefficient and at the same time to an increased electrical resistivity. In addition, the mass difference between Ca and Yb leads to a significantly reduced density and mass-disorder scattering is observed, resulting in a lowered lattice thermal conductivity. However, these changes do not lead to a significant improvement of zT. In addition, compositions with values of x > 4 get highly air-sensitive, making the characterization of the thermoelectric properties impossible.^389,390

As for a substitution of Yb via a trivalent rare earth element, Sc and Y,³⁹¹ La,³⁹² Lu,^393,394 as well as the full RE³⁺ (La–Lu) series³⁹⁵ have been reported. While for the latter only the thermochemistry and thermal stability was analyzed, for the other substitutions the influence on the thermoelectric properties was also investigated since the trivalent rare earth cations change the carrier concentration. The Sc- and Y-substituted specimens show higher resistivities and thus higher Seebeck coefficients; however, an overall reduction of the zT is observed.³⁹¹ Also for the Lu-substituted compounds, a reduced carrier concentration was reported as well as a reduced peak zT.³⁹⁴ Another study, however, reported an increased carrier concentration upon Lu substitution leading to a ∼30% improvement in zT at 670 K.³⁹³ For La-substituted Yb_14–xLa_xMnSb₁₁, finally an increased zT was reported for x ∼ 0.4 with a peak zT of 1.15 at 1150 K.³⁹²

Also for the Mn position, an isovalent substitution is possible, e.g., in Yb₁₄Mn_1–xZn_xSb₁₁.³⁹⁶ The substitution shows a slight improvement up to x ≤ 0.4 by reducing the lattice thermal conductivity at low temperatures; however, only a negligible impact at high temperatures is observed. This is based on the reduction of spin disorder scattering leading to an overall improvement of about 10% with a maximum thermoelectric figure of merit ∼1.1 at 1275 K for x = 0.4. Substituting Mn²⁺ for Al³⁺, however, again leads to a reduction of the carrier concentration,^397,398 similar to the substitution of Yb²⁺ by RE³⁺. For x = 0.6 and 0.8, an improvement of 30% was observed, equal to a zT = 1.3 at 1223 K.

Finally, modifications on the Sb positions should be mentioned. In the solid solution Yb₁₄MnSb_11–xBi_x, overall lower zT values are observed,³⁹⁹ while Yb₁₄MnSb_11–xTe_x shows an improved zT of 1.11 for x = 0.07 at 1240 K.⁴⁰⁰ This, again, can be attributed to a reduced carrier concentration.

Furthermore, the low-temperature behavior of the thermoelectric properties has been studied at ambient and increased pressure. Also in the range between 4.2 and 300 K, the Seebeck coefficient for Yb₁₄MnSb₁₁ is positive and increases upon heating.⁴⁰¹ Increasing the pressure up to 2.3 GPa leads to a further increase of the Seebeck coefficient in the same temperature range.⁴⁰²

Besides Yb₁₄MnSb₁₁, other Yb-containing compounds with the same composition and crystal structure were also investigated. As examples, Yb₁₄MgSb₁₁, Yb₁₄MnBi₁₁, and Yb₁₄MgBi₁₁ will be discussed. Yb₁₄MgSb₁₁ has, compared to its Mn-containing analogue, an increased Seebeck coefficient which leads to an increase of 45% in the figure of merit (zT = 1.02 at 1075 K) at the same temperature.⁴⁰³ The addition of iron leads to the formation of nanosized inclusions, which lead to an even further increase of zT.^404,405 Yb₁₄MnBi₁₁ and Yb₁₄MgBi₁₁ are both metallic in nature, and Yb₁₄MgBi₁₁ has an increased carrier concentration in comparison to the isostructural antimonide which compensates potential improvements of the thermoelectric properties. Overall, the zT values of both compounds reach ∼0.2 at 875 K.⁴⁰⁶

The MT₂X₂ compounds that adopt the trigonal Ce₂O₂S type structure (space group P3m1) with the general composition M^IIT^II₂Pn₂ can also be considered as valence precise Zintl phases. M is a divalent alkaline earth or rare earth metal (Ca, Sr, Eu, Yb), while T is a divalent transition metal (Mn, Zn, Cd) or Mg, and Pn finally a pnictogen (As, Sb, Bi). These compounds are considered to be “electron precise” according to the Zintl formalism.

In the following paragraph, just a small number of studies will be mentioned as there is a plethora of studies related to the optimization of the thermoelectric properties by different strategies. One of the first reports is on the solid solution Ca_xYb_1–xZn₂Sb₂ from Gascoin and co-workers.⁴⁰⁷ They showed that YbZn₂Sb₂ has the smallest Seebeck coefficient but at the same time the smallest electrical resistivity. CaZn₂Sb₂ in contrast exhibits an over two times larger Seebeck coefficient but also a 7-fold larger resistivity. The solid solution shows an intermediate behavior, depending on the composition. Subsequently, numerous solid solutions were investigated with respect to improving the TEP; for example, substitution of Yb by Eu according to Eu_xYb_1–xZn₂Sb₂^408,409 or by La as in Yb_1–xLa_xZn₂Sb₂.⁴¹⁰ But also high-quality single crystals of YbZn₂Sb₂ were grown and investigated.⁴¹¹ Despite modifications by chemical substitution, nanoporous⁴¹² or Yb-deficient materials (Yb_1−δZn₂Sb₂)⁴¹³ were also synthesized and investigated. But not only the substitution of the Yb is possible. Also, the formation of solid solutions with respect to the Zn or Sb position can influence the thermoelectric properties. For example, the solid solutions YbZn_2–xMg_xSb₂,⁴¹⁴ YbZn_2–xMn_xSb₂,^415,416 YbZn_2–xCd_xSb₂,⁴¹⁷ and YbZn₂Sb_2–xBi_x⁴¹⁸ should be named. Finally, it has been proven that Mg can substitute on both the Yb and Zn sites.⁴¹⁹ Besides YbZn₂Sb₂, also YbMg₂Sb₂,⁴²⁰ YbMg₂Bi₂,^421−423 YbMn₂Sb₂,⁴²⁴ YbCd₂Sb₂, and the solid solutions YbCd_2–xMn_xSb₂⁴²⁵ have been investigated in great detail.

Finally, two other classes of important thermoelectric materials should be addressed: clathrates and skutterudites. Although clathrates are structurally very versatile materials, hardly any ytterbium-containing ones have been reported. Detailed information on the different clathrate structures and their applications can be found in a review.⁴²⁶ The key features that lead to their intriguing thermoelectric properties are the “rattling” atoms within the structure. These are located in the large polyhedra that form the framework and can effectively scatter the heat-carrying phonons, therefore reducing the thermal conductivity. The reports on Yb-substituted clathrates are mainly examples of type-I clathrates, which crystallize in space group Pm3n and exhibit the general formula G₈[F₄₆], with F being the framework and G being the guest atoms. In the type-I clathrates, two different polyhedra can be found, a 20-vertex pentagonal dodecahedron and a 24-vertex tetrakaidecahedron. For the framework, different elements and elemental combinations are known as well as a large number of guest atoms occupying these polyhedra.⁴²⁶ The number of Yb-based type-I clathrates (Na₄Si₂₃ type, space group Pm3n), however, is extremely low. To the best of our knowledge, no pure Yb clathrates have been reported, but the solid solutions Ba_8–xYb_xGa₁₆Si₃₀,⁴²⁷ Ba_8–xYb_xGa₁₆Ge₃₀,⁴²⁸ Ba_8–xYb_xNi_0.1Zn_0.54Ga_13.8Ge_31.56,⁴²⁹ Ba_8–xYb_xNi_3.8Si_42.2,⁴³⁰ and Ba_8–xYb_xCu_4.9Si_41.1⁴³⁰ have been investigated experimentally. In addition, first principle studies on Ba₆Yb₂Au₆Ge₄₀⁴³¹ have been conducted. For the silicide, it was shown that the substitution of Ba by Yb is possible, but only to a certain extent of x = 0.25 to 0.38.⁴²⁷ The substitution led to a slight decrease of the Seebeck coefficient, however, also to a significant decrease of the lattice thermal conductivity which resulted in a slight overall increase of zT for Ba_7.75Yb_0.25Si_31.9Ga_14.1.⁴²⁷ For the germanide series Ba_8–xYb_xGa₁₆Ge₃₀, in principle the same trend is observed. Here, samples with x = 0 to 1.3 could be synthesized and investigated, and again a decrease in the Seebeck coefficient is visible for x ≤ 0.7 alongside a decrease of the lattice thermal conductivity leading to a zT of 1.1 (950 K) for Ba_7.5Yb_0.5Ga₁₆Ge₃₀. This is an increase of 90% compared to the Yb-free sample.⁴²⁸ Also in Ba_8–xYb_xNi_0.1Zn_0.54Ga_13.8Ge_31.56,⁴²⁹ a slightly increased zT (15%, zT = 0.91 at 900 K) was reported for x = 0.3. In this case, the electrical resistivity and lattice thermal conductivity decrease with increasing x, the Seebeck coefficient, however, stays constant. Yb substitution in Ba_8–xYb_xNi_3.8Si_42.2 and Ba_8–xYb_xCu_4.9Si_41.1 revealed that the majority of the Yb precipitated as secondary phases. The solubility limit is only about 1% on the Ba site. The multiphase samples showed both a lower electrical resistivity and a lower Seebeck coefficient with respect to the unsubstituted compounds; however, the thermal conductivity increases. Overall, the thermoelectric figure of merit of the Ni-based system is not improved, while a slight enhancement above 800 K is observed for Ba_8–xYb_xCu_4.9Si_41.1.⁴³⁰ For Ba₆Yb₂Au₆Ge₄₀, finally, the thermoelectric properties were calculated using the full-potential linearized augmented plane wave method based on density functional theory. It was shown that the substitution enhances the density of states at the bottom of the conduction band, leading to an increased Seebeck coefficient due to an increased effective mass of the conduction band.⁴³¹

Finally, one report on a type-VIII clathrate (G₈[F₄₆]; own type, space group I43m) has been published, which investigated the substitution in Ba_8–xYb_xGa₁₆Sn₃₀.⁴³² Here, an improvement of the Seebeck coefficient up to x = 1.0 was observed. Overall, the situation is similar to the type-I clathrates: a substitution adjusts the Seebeck coefficient as well as the electrical and thermal conductivity, leading to an improvement of the figure of merit zT. In Ba_6.5Yb_1.5Ga₁₆Sn₃₀, this leads to a maximum zT of 1.35 at 489 K.

The last class of materials that should be discussed with respect to their thermoelectric properties are Yb-containing skutterudites. The name of this class of materials derives from the mineral skutterudite CoAs₃ with the general formula TX₃ (CoAs₃ type, space group Im3). In the crystal structure of the skutterudites, two empty cavities can be found that can accompany a number of different atoms. In the late 1970s, Jeitschko and co-workers coined the term “filled skutterudites” for compounds with the general composition MT₄X₁₂ (LaFe₄Sb₁₂ type, space group Im3).^433−436 In 1996, Sales⁴³⁷ and Fleurial⁴³⁸ showed that filled skutterudites exhibit excellent thermoelectric properties at elevated temperatures. The reviews by Uher from 2001 and Sales from 2003 summarize the important aspects of skutterudites.^439,440 One of the first Yb-containing filled skutterudites investigated for its physical properties was YbFe₄Sb₁₂. Magnetic measurements indicate an intermediate valence state and a slightly enhanced Sommerfeld coefficient.^441,442 In these reports, the potential for YbFe₄Sb₁₂ to exhibit good thermoelectric properties was outlined. Low-temperature thermoelectric property measurements showed that YbFe₄Sb₁₂ is a p-doped metal with a low carrier density. The high electrical resistivity leads to a zT < 0.02 below 300 K.⁴⁴³ The investigations of the high-temperature properties lead to a zT = 0.4 at 670 K.⁴⁴⁴ Within the solid solution Yb_yFe_4–xNi_xSb₁₂, even zT values near 1 (750–850 K) could be obtained for x = 0.6–0.8.⁴⁴⁵

Due to the chemical versatility of the filled skutterudites, numerous compositions were investigated with respect to their thermoelectric properties. Within the field of Yb-based compounds, YbCo₄Sb₁₂ showed an excellent performance, leading to a large number of studies of tuned and improved materials. Therefore, only some examples will be summarized in the next paragraph. Studies on different compounds of the Yb_xT₄Sb₁₂ series (x = 0.1–0.8, T = Fe, Co, Rh, Ir) showed that the physical properties seem to correlate with the filling x and the electronic situation modified by changing T.⁴⁴⁶ At the same time, studies on Yb_yCo₄Sn_xSb_12–x indicated a maximum zT of 0.1 at 300 K for Yb_0.44Co₄Sb₁₂.⁴⁴⁷ More detailed studies including Hall effect, electrical resistivity, Seebeck coefficient, and thermal conductivity measurements were conducted on the solid solution Yb_yCo₄Sb_12–xSn_x for y = 0.19 and 0.5. It was shown that substituting Sn on the Sb site does not alter the Fermi level with respect to the conduction band; instead, a p-type band for a sufficiently large Sn content x was observed. Therefore, this is not a valid method to optimize the thermoelectric properties of Yb-filled skutterudites.⁴⁴⁸ Double substitution according to Ba_0.08Yb_0.09Co₄Sb₁₂, however, led to a broad range of resonant phonon scattering and which resulted in a strong suppression in the lattice thermal conductivity. Therefore, high zT values of 1.36 at 800 K could be observed.⁴⁴⁹ A similar value in zT (1.36 at 850 K) could be observed for Al_0.3Yb_0.25Co₄Sb₁₂.⁴⁵⁰ By the help of ball-milling in combination with hot-pressing, the value of x in Yb_xCo₄Sb₁₂ could be improved to almost 0.5, leading to a zT of 1.2 at 823 K.⁴⁵¹ In recent years, studies addressing the band conversion in Yb_xCo₄Sb₁₂,⁴⁵² the achievement of ultralow thermal conductivities in Yb_xCo_4–yFe_ySb₁₂ with x = 0.25–0.5 and y = 0.1–0.5,⁴⁵³ the synthetic approach on Yb_xCo₄Sb₁₂,⁴⁵⁴ and introducing nanoinclusions⁴⁵⁵ have led to a deeper understanding of the possibilities to tailor the thermoelectric properties in skutterudite materials.

SUMMARY AND OUTLOOK

The present review impressively underlines that the family of ytterbium-based intermetallic compounds covers extremely broad facets of crystal structures along with interesting and, in some cases, even outstanding physical properties. This interplay is mostly driven by the ytterbium valence: divalent (4f¹⁴), intermediate-valent, or trivalent (4f¹³) ytterbium. Thus, one observes simple diamagnets, Pauli or Curie–Weiss paramagnets as well as valence fluctuating compounds, Kondo behavior, heavy Fermion ground states, or sometimes even superconductivity.

Some of the trivalent ytterbium intermetallics have gained deep interest due to these physical properties. The phases have been meticulously studied with respect to their properties using magnetic and transport measurements, specific heat data, NMR, ESR, and Mössbauer spectroscopy, elastic and inelastic neutron scattering, XAS and XPS data, as well as detailed thermoelectric measurements, then allowing the development of structure–property relations.

Among the binary Yb intermetallics, YbAl₂ and YbAl₃ have received the most attention due to their Kondo behavior. Overall, however, the number of binary compounds studied in detail is rather low compared to the ternary systems, given the significantly larger combinatory manifold in the ternary systems. Here, YbRh₂Si₂ is the most outstanding phase with >350 publications on this compound. It exhibits a non-Fermi-liquid behavior along with antiferromagnetic ordering at T_N = 70 mK. A quantum critical point at ambient pressure is suggested, at which the magnetic ordering can be suppressed by a magnetic field of only B_c = 60 mT. Yb₂Pt₂Pb exhibits a Shastry–Sutherland lattice that causes a high anisotropy in the magnetic susceptibility with an about 30 times larger value for χ₍₁₀₀₎ as compared to χ₍₀₀₁₎. Finally, among the series of YbT₂Zn₂₀ compounds, the cobalt-containing representative YbCo₂Zn₂₀ exhibits Kondo interactions, and from specific heat measurements, a large Sommerfeld coefficient of γ = 7.9 J^–1 mol^–1 K^–2 was deduced. Finally, Yb₁₄MnSb₁₁ is one of the most promising p-type thermoelectric materials with a high zT > 1, making this compound suitable for different applications.

Although most of these studies are located in basic research, they help with a deeper understanding of complex intermetallic compounds and motivate for future studies. Especially, the ytterbium-based thermoelectric materials might find application. Even though the family of ytterbium intermetallics is large, a weak point concerns the overall systemization of the property data, since only few larger isotypic series of compounds exist. Already, the equiatomic YbTX phases crystallize with more than 10 different structure types; many of them are superstructures of the aristotype AlB₂. The probably best investigated, and thus comparable, series of isotypic compounds concerns the CeCr₂Al₂₀ type zinc compounds YbT₂Zn₂₀ with T = Fe, Co, Ru, Rh, Os, and Ir.

The study of ytterbium intermetallics is still a vivid field in solid state chemistry and physics. Besides the discovery and characterization of new phases, the understanding and systemization of the structure–property relations is an important future task.

Data Availability Statement

The data underlying this study are available in the published article.

Author Contributions

^$ These authors contributed equally. CRediT: Stefan Engel conceptualization, formal analysis, writing-original draft, writing-review & editing; Elias C. J. Gießelmann conceptualization, formal analysis, writing-original draft, writing-review & editing; Maximilian Kai Reimann conceptualization, formal analysis, writing-original draft, writing-review & editing; Rainer Pöttgen conceptualization, formal analysis, project administration, supervision, validation, visualization, writing-original draft, writing-review & editing; Oliver Janka conceptualization, formal analysis, funding acquisition, investigation, supervision, validation, visualization, writing-original draft, writing-review & editing.

Funding is provided by the Deutsche Forschungsgemeinschaft DFG (JA 1891-10-1).

The authors declare no competing financial interest.