Coercive Fields Exceeding 30 T in the Mixed-Valence Single-Molecule Magnet (Cp^iPr5)₂Ho₂I₃

Abstract

Mixed-valence dilanthanide complexes of the type (Cp^iPr5)₂Ln₂I₃ (Cp^iPr5 = pentaisopropylcyclopentadienyl; Ln = Gd, Tb, Dy) featuring a direct Ln–Ln σ-bonding interaction have been shown to exhibit well-isolated high-spin ground states and, in the case of the Tb and Dy variants, a strong axial magnetic anisotropy that gives rise to a large magnetic coercivity. Here, we report the synthesis and characterization of two new mixed-valence dilanthanide compounds in this series, (Cp^iPr5)₂Ln₂I₃ (1-Ln; Ln = Ho, Er). Both compounds feature a Ln–Ln bonding interaction, the first such interaction in any molecular compounds of Ho or Er. Like the Tb and Dy congeners, both complexes exhibit high-spin ground states arising from strong spin–spin coupling between the lanthanide 4f electrons and a single σ-type lanthanide–lanthanide bonding electron. Beyond these similarities, however, the magnetic properties of the two compounds diverge. In particular, 1-Er does not exhibit observable magnetic blocking or slow magnetic relaxation, while 1-Ho exhibits magnetic blocking below 28 K, which is the highest temperature among Ho-based single-molecule magnets, and a spin reversal barrier of 556(4) cm^–1. Additionally, variable-field magnetization data collected for 1-Ho reveal a coercive field of greater than 32 T below 8 K, more than 6-fold higher than observed for the bulk magnets SmCo₅ and Nd₂Fe₁₄B, and the highest coercive field reported to date for any single-molecule magnet or molecule-based magnetic material. Multiconfigurational calculations, supported by far-infrared magnetospectroscopy data, reveal that the stark differences in magnetic properties of 1-Ho and 1-Er arise from differences in the local magnetic anisotropy of the lanthanide centers.

Introduction

For the last three decades, the lanthanide elements have played a key role in advancing the field of single-molecule magnets, which have potential applications in the quantum sciences and high-density information storage.^1,2 The trivalent lanthanides are particularly well-suited for the design of single-molecule magnets, owing to their large single-ion anisotropies, which arise from the unquenched orbital angular momentum of the core-like 4f orbitals.^3,4 Judicious design of the electrostatic crystal field for a given lanthanide ion has been one of the most promising strategies to date for the design of mononuclear single-molecule magnets,⁵ in many cases giving rise to systems that exhibit magnetic blocking near liquid nitrogen temperatures.^6,7 In general, an axial ligand field can be used to stabilize the oblate electron density associated with the maximal M_J states of lanthanide ions such as Tb^III and Dy^III, whereas an equatorial crystal field stabilizes the prolate electron density associated with the largest M_J states of ions such as Er^III.^8,9 The series of mononuclear Dy^III metallocene compounds of the type [Dy(Cp^R)₂]⁺ (Cp^R = substituted cyclopentadienyl) well exemplifies this approach: the two Cp^R ligands provide a strong axial crystal field, and molecules in this class exhibit magnetic blocking temperatures (T_b, defined here as the temperature at which the magnetic relaxation time is 100 s) above 50 K.¹⁰

While the trivalent lanthanides have long dominated the field, the discovery of divalent lanthanide ions with 4fⁿ5d¹ electronic configurations¹¹⁻¹⁴ has expanded the design toolkit for single-molecule magnets. For example, reduction of the bent metallocene complex [Tb(Cp^iPr5)₂]⁺ (Cp^iPr5 = pentaisopropylcyclopentadienyl) yields Tb(Cp^iPr5)₂, which features a half-integer spin Kramers ion Tb^II and a perfectly linear Cp–Tb–Cp angle.¹⁵ As a result, the magnetic relaxation times for Tb(Cp^iPr5)₂ are significantly longer than those of [Tb(Cp^iPr5)]⁺, and Tb(Cp^iPr5)₂ exhibits a record blocking temperature of T_b = 52 K for a mononuclear, nondysprosium single-molecule magnet. Exploiting this 4fⁿ5d¹ electronic configuration, some of us have also recently reported the first mixed-valence lanthanide complexes (Cp^iPr5)₂Ln₂I₃ (Ln = Y, Gd, Tb, Dy), prepared via one-electron reduction of the trivalent complexes (Cp^iPr5)₂Ln₂I₄.¹⁶ These compounds exhibit valence delocalization due to the formation of a singly occupied σ-bonding molecular orbital of 5d_z² parentage. Multiconfigurational complete active space self-consistent field (CASSCF) calculations carried out on the Tb and Dy variants revealed that the axial ligand field afforded by the Cp^iPr5 ligands and the σ electron serves to stabilize the maximal total |M_J| ground state for these compounds.¹⁶ In tandem with strong spin–spin coupling between the 4f electrons and the σ electron, this electronic structure gives rise to well-isolated, large total angular momentum ground states, large barriers to slow magnetic relaxation, and in the case of (Cp^iPr5)₂Dy₂I₃, a record blocking temperature of T_b = 72 K and the largest coercive magnetic field (H_c) reported to date for any molecule-based magnetic material.

Here, we present two new mixed-valence dilanthanide complexes in this family, (Cp^iPr5)₂Ln₂I₃ (1-Ln; Ln = Ho, Er). Detailed magnetic, computational, and spectroscopic analyses reveal that, while both compounds exhibit strong 4f−σ spin–spin coupling, the axial crystal field has a dramatically different effect on their electronic structures. In the case of 1-Er, the axial crystal field destabilizes the prolate maximal M_J levels of the individual Er^III centers, such that the compound does not behave as a single-molecule magnet. In contrast, for 1-Ho, which features Ho^III centers with maximal M_J states that are more oblate in character, the crystal field stabilizes the maximal possible total |M_J| ground state. As a result, this compound exhibits a record blocking temperature among holmium single-molecule magnets and a magnetic coercivity of 32.6 T—the largest reported to date for any single-molecule magnet or molecule-based magnetic material.

Results and Discussion

Synthesis and Characterization

The compounds 1-Ho and 1-Er were synthesized following the previously reported route to (Cp^iPr5)₂Ln₂I₃ (Ln = Y, Gd, Tb, Dy).¹⁶ In brief, the trivalent dilanthanide complexes (Cp^iPr5)₂Ln₂I₄ (Ln = Ho, Er) were synthesized via high-temperature salt metathesis between LnI₃ and one equivalent of NaCp^iPr5 in toluene. After filtration, solvent removal, and washing with pentane, (Cp^iPr5)₂Ho₂I₄ and (Cp^iPr5)₂Er₂I₄ were isolated as analytically pure yellow or pink powders, respectively. Reduction of (Cp^iPr5)₂Ln₂I₄ (Ln = Ho, Er) with excess KC₈ in n-hexane resulted in the formation of dark green-blue (Ho) or green (Er) solutions after several days. These solutions were filtered to remove KI and unreacted KC₈, concentrated, and stored at −35 °C. Analytically pure prismatic green-blue (1-Ho) or brown-green (1-Er) single crystals suitable for X-ray diffraction analysis were isolated after several days. The crystals were found to be indefinitely stable at room temperature under argon, although at ambient temperature in the presence of air and moisture, they decayed rapidly, forming yellow or colorless solids. The compounds are stable in pentane and hexane or electron-rich arene solvents such as 1,3,5-trimethylbenzene, but they decompose in benzene or toluene over the course of several minutes.

The solid-state structures of 1-Ho and 1-Er were obtained by single-crystal X-ray diffraction analyses (Figures 1a, S6, and S8). Both structures feature an Ln₂I₃ core with two crystallographically equivalent lanthanide ions connected by three bridging iodide ligands and capped with a (Cp^iPr5)⁻ ligand. The Ln···Ln distances in 1-Ho and 1-Er are 3.740(1) and 3.720(1) Å, respectively, within the range of those previously reported for (Cp^iPr5)₂Ln₂I₃ (Ln = Y, Gd, Tb, Dy).¹⁶ From these values, we calculated a formal shortness ratio for each compound—defined as the ratio of the experimental metal···metal distance to the sum of the metallic radii of the two metal atoms given by Pauling.¹⁷ Formal shortness ratios ≤1.22 suggest the presence of covalent metal–metal bonding,¹⁸ and for 1-Ho and 1-Er, the values are 1.183 and 1.177.

Figure 1.

(a) Structure of 1-Ho, as obtained from a single-crystal X-ray diffraction analysis (see Figure S8 for the structure of 1-Er). Dark blue, purple, and gray spheres represent Ho, I, and C atoms, respectively; H atoms have been omitted for clarity. Selected interatomic distances for 1-Ho and 1-Er, respectively: Ln–Ln = 3.740(1), 3.720(1) Å; Ln–Cp(cent) = 2.333(1), 2.313(1) Å. (b) Illustration of the σ-bonding SOMO for 1-Ho obtained from CASSCF-SO calculations. (c) Plot of the Ln–Ln distances in 1-Ln for Ln = Gd, Tb, Dy, Ho, Er (left axis), along with the corresponding Ln^III radii (right axis).¹⁷

The Ln–Cp_cent distances in 1-Ho and 1-Er are 2.333(1) and 2.313(1) Å, respectively. Across the (Cp^iPr5)₂Ln₂I₃ series (Ln = Gd, Tb, Dy, Ho, Er), the Ln–Cp_cent distance decreases monotonically from Gd to Er (Table S3), which is consistent with the expected trend based on the lanthanide contraction and indicates that the Ln–Cp interaction is predominantly electrostatic.¹⁹ While the Ln–Ln distance also decreases from (Cp^iPr5)₂Gd₂I₃ (3.769(1) Å) to (Cp^iPr5)₂Dy₂I₃ (3.713(1) Å), this distance increases in 1-Ho (3.740(1) Å) before decreasing again for 1-Er (3.720(1) Å) (Figure 1c and Table S3). Previously, we performed CASSCF and density functional theory calculations on (Cp^iPr5)₂Ln₂I₃ (Ln = Y, Tb, Dy) that revealed the singly occupied σ-bonding orbital originates predominantly from the 5d_z² (4d_z²) orbital on each lanthanide (yttrium).¹⁶ Consistent with these results, CASSCF calculations performed on 1-Ho and 1-Er (Figure 1b, see Section 9 of the Supporting Information for details) indicate that the greatest contribution to the bonding interaction is the 5d_z² orbital on each lanthanide. Upon progressing from Gd to Er in the (Cp^iPr5)₂Ln₂I₃ series, the 5d_z² contribution decreases monotonically from 71.6 to 67.6%. For all compounds, there are also smaller contributions from the 6s and 6p_z orbitals on each lanthanide (Figure S36). While the 6s contribution increases monotonically from Gd to Er (from 3.9 to 5.5%), the 6p_z orbital contribution first increases from Gd to Dy (from 3.1 to 4.4%) and then decreases from Dy to Ho (from 4.4 to 3.0%). Interestingly, CAS(n,7)SCF calculations on the high-spin ground term of each free Ln^III ion in the gas phase indicate that the 6p orbitals decrease in energy from Gd^III to Dy^III, but then increase for Ho^III (Figure S37). Of note, a similar trend has been reported based on experimental atomic spectra for the lanthanides, where the 4fⁿ6s² to 4f^(n–1)6s²6p¹ and 4fⁿ to 4f^(n–1)6p¹ excitations in Ln⁰ and Ln^II, respectively, peak for n = 10 (see Figure S38).^20,21 In tandem with the overall decreasing contribution from the 5d_z² orbitals to the σ bond in 1-Ln, such an increase in the 6p orbital energy would lead to a decrease in overall atomic orbital contributions to the σ bond, and consequently a weaker and longer bond, consistent with the crystal structures.

UV–vis–NIR spectra collected for solutions of 1-Ho and 1-Er in n-hexanes display features associated with σ-to-π transitions below 400 nm and strong absorption (ε ≥ 11,000 M^–1 cm^–1) associated with σ-to-σ* transition at higher wavelengths (Figures S9–S12). These results are again consistent with spectra reported previously for Dy and Tb analogues and further support the existence of Ln–Ln bonding interactions in 1-Ho and 1-Er. Diffuse reflectance spectra collected for powder samples of these 1-Ln compounds all exhibit similar features in the visible region (Figures S13 and S14).

Magnetic Properties

Variable-temperature zero-field cooled dc magnetic susceptibility data were collected for 1-Ho and 1-Er between 2 and 300 K under an applied field of 1000 Oe. Corresponding molar magnetic susceptibility times temperature (χ_MT) versus T data for both compounds are shown in Figure 2. At 300 K, the χ_MT values are 47.01 and 37.78 emu K/mol for 1-Ho and 1-Er, respectively, significantly higher than the values predicted for noninteracting Ln^III (4fⁿ) and Ln^II (4fⁿ5d¹) ions (30.97 and 25.54 emu K/mol, respectively, within the L–S coupling model¹⁴). As the temperature is lowered from 300 K, χ_MT reaches a maximum value of 55.94 emu K/mol for 1-Ho and 42.40 emu K/mol for 1-Er at 110 and 80 K, respectively. These values are close to the theoretical values predicted for parallel alignment of the lanthanide 4fⁿ electrons with one unpaired σ-bonding electron (58.47 and 48.04 emu K/mol, respectively). For 1-Ho, dc magnetic susceptibility data collected after cooling under an applied field of 1 T clearly diverge from the zero-field cooled data at 28 K (Figure 2, inset), which is indicative of magnetic blocking below this temperature. In contrast, field-cooled and zero-field cooled data collected for 1-Er overlay with one another, confirming the absence of magnetic blocking (Figure S17).

Figure 2.

Temperature dependence of the static magnetic susceptibility–temperature product (χ_MT) for 1-Ho (orange) and 1-Er (green). Magnetic susceptibility data were collected under an applied field of 1000 Oe. Black solid lines represent the calculated data obtained using full model Hamiltonian from projected CASSCF-SO parameters with exchange terms downscaled by 50% for 1-Ho and 20% for 1-Er, as described in the text. Inset: field-cooled (FC) and zero-field-cooled (ZFC) magnetic susceptibility data for 1-Ho under an applied field of 1000 Oe.

Ac magnetic susceptibility data collected for 1-Ho under zero dc field and temperatures between 33 and 48 K revealed a frequency-dependent peak in the molar out-of-phase susceptibility (χ_M″) and a simultaneous decrease in the molar in-phase susceptibility (χ_M′), confirming magnetic blocking on a millisecond-to-second time scale (Figure 3; see Section 6 of the Supporting Information for details). The relaxation time, τ, at each temperature was extracted by fitting the corresponding plots of χ_M′ and χ_M″ using a generalized Debye model (Figures S18, S19 and Table S4).^22,23 Lower-temperature relaxation times were extracted from dc relaxation data collected between 23.5 and 26 K, by fitting the time-dependent decay of the magnetization to an exponential function (see Figure S20, Table S5, and Section 6 of the Supporting Information). The combined ac and dc relaxation times were used to generate the plot of ln(τ) versus 1/T shown in Figure 3b.²³ The ac relaxation data (blue data points) are linear, consistent with an Orbach relaxation process, and could be fit using the Arrhenius equation ln(τ) = ln(τ₀) + U_eff(k_BT)⁻¹ to extract a barrier to magnetic relaxation of U_eff = 556(4) cm^–1 and τ₀ = 2.4(6) × 10^–11 s; from these data, we also calculated T_b = 27.5(2) K. Notably, this relaxation barrier is among the highest reported for any holmium-based single-molecule magnet,²⁴⁻²⁸ surpassed only marginally by the value of U_eff = 577(6) cm^–1 reported for [Ho^IIINi₅^II(quinha)₅F₂(dfpy)₁₀](ClO₄)·2EtOH (H₂quinha = quinaldic hydroxamic acid; dfpy = 3,5-difluoropyridine) (Table S6).²⁸

Figure 3.

(a) Plot of in-phase (χ_M′) and out-of-phase (χ_M″) molar magnetic susceptibility collected for 1-Ho from 33 to 48 K under zero applied field. (b) Plot of the natural log of the relaxation time versus 1/T for 1-Ho. Blue circles represent data extracted from fitting the χ_M′ and χ_M″ data using a generalized Debye model. Yellow circles represent data extracted from fitting dc relaxation data (see Section 6 of the Supporting Information for details). The black line represents a fit to the Arrhenius equation. The τ_± (1σ) uncertainty ranges for each τ value are indicated with error bars (see Tables S4 and S5).²³

Variable-field magnetization data collected for 1-Ho by first cooling the sample under zero field and then sweeping the field between +7 and −7 T revealed open magnetic hysteresis at temperatures as high as 30 K (Figure S22). At 7 T, the magnetization reached 11.3 μ_B, higher than the predicted spin-only moment of 9 μ_B for two Ho^III (4f¹⁰) ions and one unpaired electron, as a result of orbital angular momentum contributions from the 4f electrons. Additional data were collected after magnetizing the sample at 100 K using a 7 T field, cooling to 21, 23, 24, or 25 K, and then sweeping the field from +7 to −7 T (Figure S23). At 7 T and 21 K, the sample magnetization was 11.9 μ_B, slightly higher than that achieved when the sample was cooled under zero field, indicating that the magnetization is not saturated by a 7 T field. From these demagnetization data, we estimate a lower bound for the coercive field of H_c > 7 T for temperatures ≤21 K.

Variable-field magnetization data were also collected for 1-Ho at 20 K and magnetic fields between +35 and −35 T (Figure 4). It was possible to fully saturate 1-Ho at these higher fields, revealing a saturation magnetization of M_s = 13.5 μ_B and H_c = 20.1 T (Figures 4, red trace and S24). The coercive field was also measured at even lower temperatures, by first magnetizing the sample at 35 T and 100 K, cooling to the desired temperature, and then sweeping the field to −35 T. From these data, we found H_c = 27 T at 16 K (Figure 4, purple trace) and H_c = 32.6 T at 8 K (Figure 4, blue trace) and 5.3 K (Figure S26), values that vastly exceed the coercivities of the commercial magnets SmCo₅ (4.3 T at 4.2 K) and Nd₂Fe₁₄B (5.0 T at 80 K).²⁹

Figure 4.

Variable-field magnetization data obtained for 1-Ho between ±35 T at 20 K (red) overlaid with field-cooled magnetization data collected at 16 K (purple) and 8 K (blue), as described in the text. All data were collected using a sweep rate of 1.7 kOe/s. The dotted lines in the 20 K data are guides for the eye; the measured values in these regions showed an anomalous jump (see Figure S25), which is an artifact likely due to sample movement at such high fields.

Electronic Structure and Magnetic Coupling

The starkly different magnetic properties of 1-Ho and 1-Er are consistent with predictions from the simple qualitative model previously developed for guiding lanthanide single-molecule magnet design.⁵ In particular, the axial crystal field experienced by the lanthanide ions in these compounds should stabilize M_J states with oblate electron densities, such as the maximal M_J states for Ho^III, and destabilize M_J states that are more prolate in character, such as the maximal M_J states of Er^III (see Figure S39a for a qualitative illustration of this concept, and the reader is referred to a detailed discussion of these points in ref (5)). CASSCF-SO calculations were carried out on 1-Ho and 1-Er to quantitatively evaluate differences in their electronic structures and magnetic anisotropies (see Section 9 of the Supporting Information for full details).

Consistent with results obtained previously for (Cp^iPr5)₂Ln₂I₃ (Ln = Tb, Dy), both 1-Ho and 1-Er feature a one-electron metal–metal σ bond that is predominantly of 5d_z² parentage (Figures 1b, S28, and S29). To separate the different effects arising from the crystal field, spin–orbit coupling, and exchange interactions, we adopted the following approach based on our prior work.^16,30 First, from a CASSCF calculation of the high-spin ground state of the full molecule, we froze the σ-bonding orbital; we then substituted one Ln^III center with a closed-shell 4f¹⁴ Lu^III center and performed two CASSCF calculations for the high and low spin configurations of the remaining open-shell Ln^III center interacting with the σ electron. Finally, we mixed these states with spin–orbit coupling and projected the ab initio Hamiltonian onto a model Hamiltonian describing each of the crystal field, spin–orbit, and exchange interactions uniquely, and this calculation was repeated for the other Ln^III centers (see Tables S7 and S8; note that the z-axis is defined as the Ln–Ln axis).

For 1-Ho, the single-ion anisotropy arising from the combined crystal field of the Cp^iPr5 ligand and the coaxial σ electron (without the 4f−σ spin–spin coupling; Table S9) is easy-axis type, stabilizing a mixed 86%| ± 7> + 12%| ± 8> ground pseudodoublet (g_z = 17.9) for each ion. Of note, this ground state is not the maximal M_J = ±8, and it is significantly more mixed than the single-ion ground states calculated for (Cp^iPr5)₂Tb₂I₃ and (Cp^iPr5)₂Dy₂I₃, and is separated from the first excited (pseudo)doublet (87%| ± 8> + 12%| ± 7>) state by only 46 cm^–1, compared to corresponding energy gaps of more than 200 cm^–1 calculated for the Tb and Dy variants.¹⁶ The calculated 4f−σ spin–spin coupling in 1-Ho is dominated by the isotropic spin–spin term, with a value of approximately +1960 cm^–1, corresponding to J_4f–σ = +490 cm^–1 for a −2J Heisenberg Hamiltonian (Table S7). This value is comparable to those obtained from similar calculations on (Cp^iPr5)₂Tb₂I₃ (J_4f−σ = +519 cm^–1) and (Cp^iPr5)₂Dy₂I₃ (J_4f−σ = +524 cm^–1).¹⁶

Using the projected parameters for both Ln^III centers to build a model Hamiltonian for the complete molecule, we found that 1-Ho has a majority M_J = ±33/2 ground state arising from the ¹⁰Q_33/2 multiplet (see Figure S39b, S = 9/2, L = 12, J = 33/2), corresponding to parallel alignment of all angular momenta, with a majority M_J = ±31/2 first excited state at 87 cm^–1 (see Figure S30 and Table S10). Using this model Hamiltonian to calculate the magnetic susceptibility, the low-temperature maximum was well-reproduced. We note, however, that the high-temperature slope is too flat (Figure S31), implying that the 4f−σ exchange is overpredicted by CASSCF-SO, just as was previously found for 1-Gd.¹⁶ Indeed, the CASSCF-SO-based model predicts two doublets with small angular momentum (i.e., through which magnetic relaxation can readily proceed) at 938 and 939 cm^–1 (Table S10), which are substantially higher in energy than the experimental relaxation barrier of U_eff = 556(4) cm^–1. We previously found that dynamic correlation effects could reduce the exchange coupling, and that this could be replicated simply by down-scaling the CASSCF-SO-calculated exchange parameters.¹⁶ Downscaling all exchange terms for 1-Ho by 50% gives a calculated high-temperature magnetic susceptibility in good agreement with experiment (Figure 2) and two doublets with small angular momentum at 503 and 510 cm^–1, in good agreement with the measured value of U_eff (see Figure 5a and Table S11). We note that a 50% downscaling is rather drastic, compared to the 20% downscaling required previously for (Cp^iPr5)₂Tb₂I₃.¹⁶ Because of this, we also performed multistate complete active space second-order perturbation theory (CASPT2) calculations (see the Supporting Information) on the two halves of 1-Ho, which indeed reduced the isotropic spin–spin exchange coupling by approximately 60% (Table S12). However, there is a significant change in the crystal field terms and the predicted magnetic susceptibility is in poor agreement with experiment (Figure S33). Hence, CASPT2 appears not to be appropriate in this case, although it does support a large downscaling of the exchange terms arising from dynamic correlation.

Figure 5.

(a) Ground state splitting calculated for 1-Ho from the full model Hamiltonian using projected CASSCF-SO parameters with exchange terms downscaled by 50%. States given in a 0.01 T field along z to quantize the M_J projection. (b) Transmission spectra for 1-Ho collected at 4.2 K under applied fields ranging from 0 to 17.5 T. (c) Plots of applied-field spectra (T_B) divided by the zero-field spectrum (T₀), where B is the applied field. The spectra have been offset vertically for better visual clarity.

Following the same approach for 1-Er, we found that the single-ion anisotropy arising from the Cp^iPr5 ligand and the coaxial σ electron (without 4f−σ spin–spin coupling; Table S13) stabilizes a 67%| ± 5/2> + 20%| ± 3/2> ground doublet (g_x = 12.6, g_y = 1.2, g_z = 0.9) for each Er^III center, which is separated by only 21 cm^–1 from the first excited pseudodoublet (40%| ± 7/2> + 25%| ± 3/2> + 22%| ± 5/2>). The CASSCF-SO-calculated 4f−σ exchange coupling is again dominated by the isotropic spin–spin term with a value of approximately +1380 cm^–1, which corresponds to J_4f−σ = +460 cm^–1 for a −2J Heisenberg Hamiltonian (Table S8). Building a model Hamiltonian for the complete molecule revealed a ground ⁸Q_31/2 multiplet (S = 7/2, L = 12, J = 31/2; Table S14), corresponding to parallel alignment of all angular momenta, as found for 1-Ho. However, as the single-ion anisotropy is of strong easy-plane type, the resulting crystal field states are inverted compared to those of 1-Ho (Figure S34) and consist of very mixed doublets, e.g., the ground doublet is 50%|⁸Q_31/2, ±11/2> + 15%|⁸Q_31/2, ±9/2> + 12%|⁸Q_31/2, ±13/2> with a first excited state (34%|⁸Q_31/2, ±13/2> + 23%|⁸Q_31/2, ±9/2> + 17%|⁸Q_31/2, ±11/2>) at ∼1 cm^–1. Such an electronic spectrum would not be expected to give rise to any single-molecule magnet behavior, in agreement with experimental magnetic data for 1-Er. Calculated magnetic susceptibility data obtained with the model Hamiltonian and the exchange terms downscaled by 20% are in good agreement with the experimental data (Figure 2).

Far-Infrared Magnetospectroscopy (FIRMS)

To probe the calculated ground-state splitting for 1-Ho and 1-Er experimentally, we analyzed both compounds using far-infrared magnetospectroscopy (FIRMS). This technique provides a means of directly measuring the energies of magnetic microstates, and can be used to validate experimental U_eff values for systems where relaxation occurs between the ground and low-lying excited states.³¹ Two types of field-dependent transitions can be observed: purely electronic transitions, governed by the magnetic dipole selection rule ΔM_J = 0, ±1,^31,32 and mixed vibronic transitions, involving a simultaneous change in both electronic and vibrational states due to spin-phonon coupling.³³ Here, we focused on analysis of the magnetic dipole transitions between M_J sublevels.

Transmission spectra were collected on microcrystalline powder samples of 1-Ho and 1-Er between 20 and 700 cm^–1 at 5.5 K under applied fields ranging from 0 to 17.5 T (see Figures 5b and S27a). To discern magnetic dipole transitions from field-independent signals originating from molecular vibrations and instrument response, we divided the spectra collected under applied fields by the corresponding zero-field spectrum for each compound, to arrive at the normalized spectra shown in Figures 5c and S27b. For 1-Ho, these spectra feature clear field-dependent signals at transition energies of 179 and 286 cm^–1 (Figure 5c). Using the model Hamiltonian described above (including 50% downscaling of exchange terms), we calculated all the magnetic dipole transitions for 1-Ho in this energy range (Figure S32). The two strongest transitions occur at 231 and 307 cm^–1 (Figure S32; corresponding to the transitions 90%|¹⁰Q_33/2, ±33/2> → 76%|¹⁰Q_33/2, ±27/2> and 90%|¹⁰Q_33/2, ±33/2> → 64%|¹⁰O_31/2, ±29/2> + 21%|⁸Q_31/2, ±29/2>, respectively), in reasonable agreement with the experimental data. On the other hand, the corresponding spectra collected for 1-Er feature multiple field-dependent signals over a broad range of energies <150 cm^–1 (Figure S27), indicating the existence of multiple low-lying magnetic microstates such as those predicted from our computational results (Figure S34).

Conclusions

Two new mixed-valence dilanthanide complexes, (Cp^iPr5)₂Ho₂I₃ (1-Ho) and (Cp^iPr5)₂Er₂I₃ (1-Er), were synthesized and characterized for comparison with the first, previously reported complexes of this type (Cp^iPr5)₂Ln₂I₃ (Ln = Y, Gd, Tb, Dy).¹⁶ Structural and spectroscopic data are consistent with the presence of lanthanide–lanthanide bonding in 1-Ho and 1-Er, while CASSCF calculations indicate that the bonding interactions arise from a singly occupied σ-type bonding orbital that is predominantly 5d_z² in character, as also found previously for the Gd, Tb, and Dy complexes. Interestingly, in comparing the series of complexes, while the Ln–Ln distance steadily decreases from Gd to Dy, consistent with the expected decrease in ionic radii, it increases again in the Ho and Er variants, which computations suggest is due to a decrease in the 6p orbital contribution to bonding. Static and dynamic magnetic susceptibility data collected for 1-Ho revealed that this compound exhibits a record blocking temperature of 27.5 K among holmium single-molecule magnets and an exceedingly large magnetic coercivity (H_c ≥ 32.6 T at 8 K) that surpasses that of commercial bulk magnets. In contrast, 1-Er does not behave as a single-molecule magnet. These results are consistent with the well-established qualitative crystal field model for optimizing lanthanide single-ion anisotropies, which predicts that axial ligand fields will stabilize maximal M_J states that are oblate in character, such as those of Ho^III, and destabilize maximal M_J states that are prolate in character, such as those for Er^III. CASSCF-SO calculations, supported by FIRMS data, reveal that the strong axial crystal field in these compounds favors a maximal total angular momentum ground state for 1-Ho, whereas the ground state for 1-Er is nonmaximal and highly mixed. Ultimately, the results here for 1-Ho are significant, as Ho^III single-molecule magnets with large coercivities have previously been elusive, due in large part to the fact that Ho^III is a non-Kramers ion with lower anisotropy in its 4f shell than Tb^III or Dy^III.⁵ Our results highlight that by harnessing Ln–Ln bonding interactions within an appropriate ligand field, it is possible to design new high-performance single-molecule magnets even with previously seemingly intractable lanthanide ions.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/jacs.4c06250.

• The synthesis, X-ray crystallographic analysis, and FT-IR spectra for all compounds; UV–vis-NIR spectra; and additional experimental details for DC and AC magnetic susceptibility measurements, DC magnetic relaxation measurements, variable field magnetization measurements, far-infrared magnetospectroscopy, and computations (PDF)

Author Contributions

^◆ H.K. and K.R.M. contributed equally.

The authors declare no competing financial interest.