Influence of the Rare Earth Cation on the Magnetic Properties of Layered 12R-Ba₄M⁴⁺Mn₃O₁₂ (M = Ce, Pr) Perovskites

Abstract

Material design is increasingly used to realize desired functional properties, and the perovskite structure family is one of the richest and most diverse: perovskites are employed in many applications due to their structural flexibility and compositional diversity. Hexagonal, layered perovskite structures with chains of face-sharing transition metal oxide octahedra have attracted great interest as quantum materials due to their magnetic and electronic properties. Ba₄MMn₃O₁₂, a member of the “12R” class of hexagonal, layered perovskites, contains trimers of face-sharing MnO₆ octahedra that are linked by a corner-sharing, bridging MO₆ octahedron. Here, we investigate cluster magnetism in the Mn₃O₁₂ trimers and the role of this bridging octahedron on the magnetic properties of two isostructural 12R materials by systematically changing the M⁴⁺ cation from nonmagnetic Ce⁴⁺ (f⁰) to magnetic Pr⁴⁺ (f¹). We synthesized 12R-Ba₄MMn₃O₁₂ (M= Ce, Pr) with high phase purity and characterized their low-temperature crystal structures and magnetic properties. Using substantially higher purity samples than previously reported, we confirm the frustrated antiferromagnetic ground state of 12R-Ba₄PrMn₃O₁₂ below T_N ≈ 7.75 K and explore the cluster magnetism of its Mn₃O₁₂ trimers. Despite being atomically isostructural with 12R-Ba₄CeMn₃O₁₂, the f¹ electron associated with Pr⁴⁺ causes much more complex magnetic properties in 12R-Ba₄PrMn₃O₁₂. In 12R-Ba₄PrMn₃O₁₂, we observe a sharp, likely antiferromagnetic transition at T₂ ≈ 12.15 K and an additional transition at T₁ ≈ 200 K, likely in canted antiferromagnetic order. These results suggest that careful variation of composition within the family of hexagonal, layered perovskites can be used to tune material properties using the complex role of the Pr⁴⁺ ion in magnetism.

Introduction

The push for new functional materials to meet ever-evolving societal demands necessitates the continuous discovery and development of materials with desired and tunable properties. Toward this end, the perovskite family and related structures have been a hotbed of material research over the past several decades as a significant portion of the periodic table can form stable ABX₃ perovskites and various more complex motifs.¹⁻⁵ABX₃ perovskites are technologically important in many applications, and often substituting additional cations on the A and/or B sites to form multinary perovskites is an important tool to tune the material’s properties for the desired applications.⁶⁻⁸ An opportunity to further expand perovskite functionality exists through layered permutations like hexagonal, perovskite materials that alternate ABX₃ layers and other motifs.^1,9−11 Within this family, polytypes comprising a multitude of stacking sequences exist. While these materials are more complex than the strictest definitions of perovskites, we refer to these layered, hexagonal perovskite-like structures as perovskites for the purpose of clarity in this work. Many of these structures show complex and varying interactions of the respective polyhedra within the structure, creating a parameter space in which material properties might be tuned by modifying subtle interactions between atoms/polyhedra within the layered structure.^1,11

Of particular recent interest is a subset of the hexagonal, layered perovskite family with the stoichiometry Ba₄MM′₃O₁₂, in which M= lanthanides, Nb, Ni, and Sn and M′ = Mn, Fe, Ru, and Ir.^1,11−18 Many members of this family have been investigated for interesting magnetic properties, including frustrated magnetism and possible spin liquid behavior.¹¹ They are possible quantum materials due to their mixture of corner-sharing and face-sharing octahedra for the M and M′ sites, respectively (Figure 1 for M′ = Mn), which results in multiple competing magnetic interactions at a range of length scales. Within the Ba₄MM′₃O₁₂ literature, an interesting example is Ba_1+xCeMn_xO_3+3x, referred to as the BCM family.¹⁹⁻²⁵ The BCM family forms three known polytypes, denoted 12R, 10H, and 6H due to rhombohedral (R) and hexagonal (H) symmetry and different number of a × b planes repeated in the stacking sequence within each unit cell.^21,22,26 While the 12R polytype is stable at the Ba₄CeMn₃O₁₂ stoichiometry, as oxygen vacancies are introduced, the 10H and 6H polytypes become the stable phases. In the case of BCM, these oxygen vacancies are charge compensated by Mn⁴⁺/Mn³⁺ redox behavior at high temperatures, reacting with steam to produce hydrogen or CO₂ to produce CO.^19,23,26

Figure 1.

Schematic of the 12R-Ba₄MMn₃O₁₂ structure aligned to (a) the a-axis and (b) the [110] plane.

The BCM family thus presents a fascinating system to study the relationship between structural complexity and magnetic properties. A particularly interesting feature of this family is the Mn_xO_3+3x clusters that form from face-sharing MnO₆ octahedra along the c-axis of the unit cell (see Figure 1 for the x = 3 or 12R polytype; Mn₃O₁₂ face-sharing clusters are shown in magenta). The clusters are connected via corner-sharing MO₆ octahedra (Figure 1, gray). The BCM polytypes each have a different number of Mn⁴⁺ cations within the cluster (dimers in 6H, trimers in 12R, tetramers in 10H) and must also be influenced by the properties of the M cations as well as the possible presence of defects or nonstoichiometry.^1,24 It is known that clusters of transition metal or lanthanide cations/oxide polyhedra with highly correlated electrons can develop magnetic ordering, depending on the electron filling within the particular structure. Such behavior can be impacted by structural factors such as charge ordering, oxygen stoichiometry, and interactions with neighboring ions/polyhedra. Cluster behavior can emerge in these trimers due, in part, to the short M′–M′ distances (∼2.5 Å for 12R-BCM, for example). In the 12R structure family, cluster behavior has been observed for cases of M = Nb, Sn, and lanthanides with M′ = Mn, as well as for analogues where M′ = Ru, Ir.^{12−15,17,27,28} How cluster behavior among M′ is related to the bridging M cation is also poorly understood.

The presence of nonmagnetic Ce⁴⁺ as the bridging cation makes 12R-BCM an excellent reference case for understanding the broader role of the M bridging cation on the magnetic behavior of 12R structures, and in a broader sense on hexagonal perovskites.²⁰⁻²² Macias et al. reported the magnetic properties of 12R-BCM, showing a transition to long-range antiferromagnetic (AFM) order at T_N = 6 K with an anomalously large Weiss temperature (Θ < −2000 K) and an effective moment much lower than the expected value for three S = 3/2 Mn⁴⁺ cations.²¹ The suppressed moment supports possible cluster magnetism in the 12R-BCM Mn₃O₁₂ trimers, but this hypothesis was not explored further. Prior analysis was hampered by the low purity of the samples as well as the presence of nearly equivalent concentrations of Mn-containing secondary phases.

We focus here on 12R-Ba₄MMn₃O₁₂ and explore the effect(s) of replacing nonmagnetic M = Ce⁴⁺ with magnetic Pr⁴⁺. Comparing Ce⁴⁺ and Pr⁴⁺ structural analogues is apt because Ce⁴⁺ and Pr⁴⁺ have nearly identical ionic radii, are isovalent, and form isostructural 12R materials.²⁰ The lone f electron of Pr⁴⁺ (J_eff = 1/2) often leads to complex magnetic behavior or unique correlated phenomena;²⁹ we hypothesize that when Pr⁴⁺ is the bridging cation (M) in the 12R polytype, it may facilitate coupling effects/ordering of Mn₃O₁₂ trimers and therefore affect the overall material’s magnetic properties. However, the magnetic properties of 12R-BPM have not been reported.

In this work, we embark on a higher precision examination of the magnetic and thermodynamic properties of 12R-BCM and study 12R-BPM for the first time. We synthesize high phase purity 12R-BCM and 12R-BPM via established methods^20,25 and study their crystal structures using Rietveld refinements of synchrotron powder X-ray diffraction (PXRD) data. Magnetic and thermodynamic properties are investigated via DC magnetization, AC susceptibility, and heat capacity measurements. While we confirm that 12R-BCM is an AFM with T_N ≈ 7.5 K and cluster magnetism within its Mn₃O₁₂ trimers, 12R-BPM displays three magnetic transitions and complex behavior. Both materials exhibit indications of magnetic frustration. Our isostructural comparison of 12R-BCM and 12R-BPM highlights the importance of the role of the M cation bridging the Mn₃O₁₂ trimers in the magnetic properties of this polytype.

Experimental Section

Synthesis

Synthesis of 12R-BCM was performed by an established solid-state method.^20,25 BaCO₃ (99.999%, Sigma-Aldrich) and Ce₂(CO₃)₃·H₂O (99.9%, Sigma-Aldrich) precursor powders were first dried while MnO₂ (99.9%, Alfa Aesar) was used as-received. Stoichiometric amounts of each precursor powder were ground with an agate mortar and pestle prior to weighing and mixing. The precursor mixture was loaded into a 1″ diameter steel die and compacted into a pellet. A continuous force of 750 lbs. was applied while the press chamber was evacuated, prepressing the sample to remove air pockets. Force was then ramped to 17,000 lbs. at a rate of 1000 lbs/min, held for 15 min, and then force was released at the same rate, returning to 750 lbs. of force. The pressing environment was held at ≈10 °C and a vacuum of 1.0^–4 mTorr or below. The resulting green pellet was then fired at 950 °C in air to decompose the carbonates. The sample was loaded into a tube furnace held at 300 °C in a Pt-foil lined alumina crucible and ramped to the desired temperature at 5 °C/min, held at the desired temperature for 20 h, and then returned to 300 °C at the same ramp rate. After firing, the sample was ground by hand using an agate mortar and pestle. Three additional press-fire-grind iterations were performed with the first featuring a firing temperature of 1350 °C and the final two iterations using a firing temperature of 1500 °C.

12R-BPM was synthesized by adapting a Pechini sol–gel method that was previously demonstrated for 12R-BCM.^20,25 All chemicals were purchased and used as-received: Ba(NO₃)₂ (Alfa Aesar ACS, 99+%), Pr(NO₃)₃·6H₂O (99.9%, Aldrich), Mn(NO₃)₂·4H₂O (98%, Alfa Aesar), and anhydrous citric acid (Fisher Scientific, certified ACS). The cation precursors and anhydrous citric acid at a 1:1.5 mol ratio was first dissolved in deionized water (∼125 mL for ∼5 g product) and stirred on a heated hot plate until most of the water had evaporated, leaving a viscous liquid. The resulting liquid was dried overnight at 110 °C in air, yielding a foam-like solid. This solid was ground into a powder and then self-combusted on a hot plate in air, after which the resulting solid was again ground and transferred to an alumina crucible for high-temperature processing. A subsequent calcination at 800 °C (ramped at 5 °C/min) in air was performed for a duration of 12 h to remove any remaining organics or precursor ligand residue. The calcined powder was reground, and then repeatedly sintered with intermittent grinding at 1250 °C (ramped at 10 °C/min) in air for 12 h over a total of 4 grinding/heating iterations, as adapted from the literature.²⁰

Characterization

Synchrotron PXRD measurements were performed at Stanford Synchrotron Radiation Lightsource (SSRL) beamline 2–1, employing an incident wavelength of 0.729 Å (17.0 keV). Powder samples were flame-sealed in 0.5 mm glass capillaries purchased from Charles Supper Company. Measurements were performed in a Debye–Scherrer geometry with capillaries spinning at approximately three rotations per second. Angle-resolved scans were obtained between 5 and 115° 2θ with 1° steps using a Pilatus 100 K area detector with a 700 mm sample-to-detector distance. Two-dimensional (2D) images were normalized to the incident beam current and subsequently integrated using a Python script developed at SSRL. Rietveld refinements were performed on the XRD data using TOPAS-academic.³⁰ An Oxford Instruments Cryojet was used to cool the sample capillaries to 100 K. The data collected at 100 K was deposited into the ICSD for both 12R-BCM (Deposition Number 2328392) and 12R-BPM (Deposition Number 2307846).

DC magnetization and AC susceptibility measurements were performed in a Quantum Design Physical Properties Measurement System (PPMS) from T = 2–350 K in applied fields up to μ₀H = 14 T. AC susceptibility was measured with a 1.5 Oe drive current at frequencies greater than 1500 Hz and with a 5 Oe drive current at frequencies lower than 1500 Hz. Heat capacity measurements were performed in a different PPMS on pressed pellets of powder in applied fields up to μ₀H = 9 T. Apiezon N grease was used to adhere the pellet to the puck. Three data points were collected at each temperature; the value used was the average of the second and third data points. A background was fit empirically to C_bg = aT³ + bT² between T = 12 and 20 K for 12R-BCM in the nonzero field (T = 12–30 K for μ₀H = 0 T) and between T = 17.5 and 30 K for 12R-BPM in nonzero field (T = 12–35 K for μ₀H = 0 T).

Results

Synthesis and Structure

To explore the extent of structural changes resulting from replacing Ce⁴⁺ for Pr⁴⁺ in 12R-BCM, synchrotron PXRD data were collected at T = 100 K (Figure 2) and T = 300 K (Figure S1) for both materials. Rietveld refinements show that both samples are primarily comprised of the 12R structure, with lattice parameters matching prior structural reports in the literature,^20,25 as displayed in Figure S1 and Tables S1–S2. The structures of the Ce and Pr analogues are nearly identical, with 12R-BCM only ∼0.25% larger in the in-plane (ab) direction and ∼0.14% larger along the c-axis compared to 12R-BPM. No 6H or 10H structural impurity is observed for either sample.

Figure 2.

Rietveld refinements of synchrotron PXRD data collected at 100 K for (a) 12R-BCM and (b) 12R-BPM. Observed (blue), calculated (red), and difference (black) plots are shown, and Bragg reflections are indicated by tick marks.

Comparing the low- and room-temperature PXRD data (Figures 2 and S1) indicates that for both materials, no structural differences or symmetry lowering are present between 100 and 300 K, beyond anisotropic thermal expansion similar to that observed at elevated temperatures for 12R-BCM.²⁵ Lattice parameters and refinement details are listed in Table S1. Comparing the lattice parameters of 12R-BPM at 100 and 300 K reveals anisotropic lattice contraction (0.0018% in-plane and 0.0014% out-of-plane), implying that upon cooling, the Mn₃O₁₂ trimers become proportionally closer in the ab plane than along the c-axis.

A summary of the weight fractions of each phase identified via Rietveld refinement is presented in Table S2, confirming the high phase purity of 12R-BCM and 12R-BPM. This sample of 12R-BCM has a phase purity of 98.39 ± 0.1 wt %, consistent with previous reports using the same synthesis.²⁵ Very small (<1 wt %) amounts of impurity phases Ba₄Mn₃O₁₀, BaCeO₃, and CeO₂ were identified via Rietveld refinement. In comparison to our 98.39 ± 0.1 wt % 12R-BCM sample, the prior magnetic investigation in the literature used 11–31 wt % 12R-BCM.²¹ Our samples possess no measurable quantity of either Ba₆Mn₅O₁₆ or BaMnO₃, whereas in comparison, the previous magnetic report of 12R-BCM possessed these impurities at levels of >11.5 and >5.5 wt %, respectively.²¹ By removing these magnetically active impurities, a higher confidence is achieved in isolating the behavior of 12R-BCM. The 12R-BPM sample studied here similarly has very high phase purity of 96.6 ± 0.5 wt %, with small impurity phases of Ba₄Mn₃O₁₀ and BaPrO₃. While both impurities found in our 12R-BPM sample are magnetic, the very low fraction of these impurities limits signals from their magnetic behaviors from contributing to our magnetic results at detectable levels, as discussed below.

Magnetic Properties

To probe the effects of the M⁴⁺ cation on the magnetism of these materials, we measured the DC magnetization (M ) of polycrystalline samples of both 12R-BCM and 12R-BPM as a function of temperature and the applied field. Figure 3(a,b) shows isothermal field sweeps performed at several temperatures for each sample. The 12R-BCM data are consistent with the reported long-range antiferromagnetic (AFM) order (Figure 3a);²¹ there is no hysteresis or net moment at T = 2 K. In contrast, at low temperature, 12R-BPM (Figure 3b,c) displays hysteresis with a small net moment and a distinctive wasp-waisted appearance that persists at least up to T = 100 K and is gone at T = 300 K. A comparison of the low-field regions of the two materials is given in Figure S2, confirming that 12R-BCM has no discernible net moment or hysteresis.

Figure 3.

(a, b) Magnetization (M) as a function of applied field for (a) 12R-BCM and (b) 12R-BPM. (c) Magnified low-field view of M vs applied field for 12R-BPM. (d) DC susceptibility (χ) of 12R-BCM in low applied fields. (e, f) χ of 12R-BPM in low applied fields. The dashed lines denote the approximate position of each material’s low-temperature transition. ZFC signifies zero-field-cooled, and FC signifies field-cooled.

Zero-field-cooled (ZFC) and field-cooled (FC) DC susceptibility (χ) as a function of temperature at low applied fields is shown in Figure 3d–f for both samples. 12R-BCM displays a peak at approximately T ≈ 7 K (Figure 3d), consistent with the T_N = 6 K reported previously.²¹ In 12R-BCM, a small amount of splitting below the T_N is observed for the first time (Figure 3d). Variable-frequency AC susceptibility measurements (Figures S3–S4) of 12R-BCM show a peak in the real part (χ′) but no frequency dependence, consistent with AFM order and suggesting that the ZFC-FC splitting is more likely due to sample disorder than to a spin glass state.

The magnetic behavior of the 12R-BPM sample is more complex than that of 12R-BCM. Like 12R-BCM, the 12R-BPM susceptibility data display a peak that appears consistent with AFM order, albeit at T ≈ 12.5 K (Figures 3e and 4b), which is ∼5.5 K higher than the peak observed for 12R-BCM. Further evidence for AFM order in 12R-BPM is the lack of a significant change in the field-dependent magnetization on either side of this peak (see Figure 3c, T = 2 and 20 K). However, it is apparent in the μ₀H = 0.1 T data of 12R-BPM (Figure 3e) that ZFC-FC splitting exists above the peak at T ≈ 12.5 K. To probe this ZFC-FC splitting further, we measured up to T = 300 K in several applied fields, as shown in Figure 3f. This reveals an additional transition occurring for 12R-BPM at approximately T₁ ≈ 200 K, with significant ZFC-FC splitting beneath it. The presence of hysteresis and a small net moment below this transition, coupled with the absence of atomic rearrangement confirmed by XRD, suggests that below this, ≈200 K transition is either a weak ferrimagnetic or a canted AFM state. These potential ground states are consistent with the wasp-waisted appearance of the magnetization curves (Figure 3c), as wasp-waisted behavior is thought to arise from competition between AFM and FM ground states.²¹

Figure 4.

(a, b) DC susceptibility (χ) of (a) 12R-BCM and (b) 12R-BPM collected in several applied fields. The insets show the ZFC and FC data collected at μ₀H = 1 T; the dashed lines denote the approximate position of each material’s low-temperature transition. (c, d) Inverse susceptibility data and Curie–Weiss fits (blue lines) for (c) 12R-BCM and (d) 12R-BPM.

While several impurities found in our 12R-BCM and 12R-BPM samples are magnetic, these phases are only present at very low phase fractions (see Table S2), and we do not observe peaks at their respective ordering temperatures in our susceptibility data (Ba₄Mn₃O₁₀ is reported AFM below T_N ≈ 40 K; BaPrO₃ is AFM below T_N ≈ 11.7 K),^31,32 confirming that the observed magnetic behavior contains very little contribution from magnetic secondary phases.

DC susceptibility data collected at higher applied fields are listed in Figure 4. For 12R-BCM (Figure 4a), the data have a peak at T_N ≈ 7 K, and the 1 and 5 T data sets are coincident above T ≈ 50 K. A small amount of ZFC-FC splitting is evident at μ₀H = 1 T below T_N (Figure 4a, inset). Analogous data were collected for 12R-BPM, as shown in Figure 4b, where the transition at T₂ ≈ 12.5 K is evident, and no ZFC-FC splitting is observed at μ₀H = 1 T (Figure 4b, inset). 12R-BPM’s transition at T₁ ≈ 200 K is visible in the μ₀H = 1 T data but suppressed in the μ₀H = 5 T data. Above this transition, 12R-BPM’s 1 and 5 T data sets are mostly coincident.

Curie–Weiss fits of the high-temperature (T = 250–350 K) inverse susceptibility data (Figure 4c,d) were performed for both samples with diamagnetic corrections (χ₀, see Table 1). This temperature range was chosen to be above the T ≈ 200 K transition of 12R-BPM; however, we note that the 12R-BPM inverse susceptibility data in this range are still not linear, implying that fits for 12R-BPM may not meaningfully represent the paramagnetic regime. The extracted parameters are given in Table 1; unfortunately, the small fit range led to large uncertainties in some cases. The extracted Weiss temperatures (Θ) are large and negative for both samples, indicating strong AFM interactions. The Θ extracted for 12R-BCM is approximately −130 to −220 K, an order of magnitude lower than the previously reported value of −2000 K, which was attributed to short-range interactions persisting up to near-room temperature.²¹ We posit that our extracted values are more reflective of the intrinsic behavior of 12R-BCM due to the much higher phase purity of our sample. Compared to 12R-BCM, 12R-BPM exhibits an even larger Θ ≈ −520 K, indicating even stronger AFM correlations. Nevertheless, comparing these Θ values to the low Neél temperatures suggests the presence of strong magnetic frustration in both 12R-BCM and 12R-BPM.

Table 1. Parameters Extracted from Curie–Weiss Fits^a.

	12R-BCM	12R-BCM	12R-BCM	12R-BPM
temp. fit range (K)	47–100	250–350	250–350	250–350
applied field (T)	1	1	5	5
C (K emu mol–1)	0.9(0.05)	1.8(0.5)	1.17(0.7)	9.6(4.6)
Θ (K)	–42(3)	–223(70)	–128(120)	–522(197)
μeff, f.u. (μB)	2.65(0.07)	3.8(0.5)	3.1(0.9)	9(2)
μeff, Mn (μB)	1.53(0.04)	2.2(0.3)	1.8(0.5)	---
χ0 (emu Oe1– mol–1)	3.63 × 10–3	3.48 × 10–3	3.98 × 10–3	–5.33 × 10–3

^aFit uncertainties are given in parentheses.

The effective magnetic moment per formula units (μ_eff,f.u.) extracted from Curie–Weiss fits of 12R-BCM (see Table 1) are low compared to the expected value for three independent S = 3/2 Mn⁴⁺ cations (6.71 μ_B). The fact that our fits give an average value of ∼3.4 μ_B is indicative of correlations between the magnetic cations, consistent with the structural motif of the Mn₃O₁₂ clusters. Indeed, our extracted value (∼3.4 μ_B) is closer to the expected value for one Mn⁴⁺ (∼3.9 μ_B). Upon assuming simple AFM alignment, if the Mn₃O₁₂ motifs of 12R-BCM form magnetic clusters, then the net moment per formula unit should be approximately S = 3/2, equivalent to one Mn⁴⁺ cation. Our data are consistent with this hypothesis.

We note there are two linear regions of the 12R-BCM inverse susceptibility data in Figure 4c—roughly 50 < T < 100 K and 200 < T < 350 K—suggesting that different behavior is occurring in these temperature ranges, such as short-range correlations below T ≈ 150 K. Indeed, a Curie–Weiss fit of the 12R-BCM data in the lower temperature linear region (from 47–100 K, Table 1) yields an even lower μ_eff,f.u. than in the higher-temperature region, consistent with strengthening of intertrimer correlations and short-range ordering.

For 12R-BPM, we used Curie–Weiss fitting to determine a μ_eff,f.u. but did not extract a μ_eff,Mn from this fit due to the presence of both Mn⁴⁺ and Pr⁴⁺ in the material. The μ_eff,f.u. of 12R-BPM is significantly higher than that of 12R-BCM, consistent with the addition of Pr⁴⁺ (J_eff = 1/2). The extracted value (9 μ_B) is within error of the calculated value based on a free-ion model of three Mn⁴⁺ cations and one J_eff = 1/2 Pr⁴⁺ (7.2 μ_B). The large error is likely due to the fitted data not being fully paramagnetic, as discussed above, and the small fit range. Interestingly, 12R-BPM does not appear to exhibit the same suppression in the effective moment that 12R-BCM does, possibly reflecting fewer short-range correlations in this temperature range compared to 12R-BCM.

Thermodynamic Properties

To examine the entropy changes associated with the low-temperature transitions, heat capacity measurements were collected on powder samples of 12R-BCM and 12R-BPM in applied fields from 0–9 T. The molar heat capacity (C_p, Figure 5a) shows that 12R-BCM has a λ peak at T_N = 7.75 K, very close to the peak observed in the magnetization measurements. For 12R-BPM (Figure 5b), a sharp λ peak at T₂ = 12.15 K is observed, in reasonable agreement with the T₂ ≈ 12.5 K transition in the susceptibility data and consistent with long-range AFM order and the lower transition observed in the susceptibility data. The peak in the 12R-BPM heat capacity data is much larger per mole than for 12R-BCM. No significant changes in the amplitude of either material’s peak were observed in applied fields up to μ₀H = 9 T for either material (Figure 5a,b). However, the peak positions shift to lower temperatures by approximately 0.1 K in an applied field of μ₀H = 9 T for both materials, as shown in Figure S6. This confirms that the origins of these peaks are magnetic.

Figure 5.

Heat capacities of 12R-BCM and 12R-BPM. (a, b) Molar C_p; the dashed lines indicate the background (C_bg) for each zero-field curve extrapolated to T = 0 K. (c, d) C_mag calculated by subtracting C_bg from the molar C_p. (e, f) Magnetic entropy normalized per formula unit.

The background of each C_p curve was fit empirically to C_bg = aT³ + bT²; the zero-field fits are shown in Figure 5a,b. The heat capacity related to the magnetic transition(s) (C_mag) shown in Figure 5c,d was calculated by subtracting the background (C_bg) from C_p. The onsets of the transitions are relatively sharp in both materials, although the C_mag of 12R-BPM at T₂ ≈ 12.15 K is approximately six times higher than that of 12R-BCM at T_N = 7.75 K, suggesting that Pr⁴⁺ plays an important role in this T₂ ≈ 12.15 K magnetic transition. Additionally, at low temperatures, the C_p of 12R-BPM exhibits a wide shoulder that resembles the 12R-BCM peak at 7.75 K.

We calculated the entropy (S) per formula unit released by these transitions (Figure 5e,f) by integrating C_mag/T as a function of the temperature to yield the entropy released by these transitions. As the magnetic cations are complex, the data were normalized per formula unit rather than per magnetic cation. The entropy released by the transition in 12R-BCM plateaus at approximately 0.5 k_B ln(2), a relatively low value that is consistent with cluster magnetism. The entropy released by the low-temperature transition(s) of 12R-BPM plateaus at approximately 1.3 k_B ln(2), reflecting a large contribution of the Pr⁴⁺ cation to the low-temperature magnetic behavior.

To investigate the transition at T₁ ≈ 200 K observed in the 12R-BPM susceptibility data, we measured C_p up to approximately T = 250 K in several applied fields for both materials, as shown in Figure S7. While a slight anomaly is observed at T ≈ 220 K in 12R-BPM, a similar anomaly is also visible in the 12R-BCM data, despite the 12R-BCM sample having no noticeable transition near that temperature in the magnetic data. The appearance of this anomaly near 220 K for both samples suggests that this is likely due to instrumental or sample mounting artifacts instead sample behaviors. The lack of a signature in the heat capacity implies that the T₁ transition in 12R-BPM is relatively weak and is consistent with the XRD data showing that it is not related to a structural transition.

Discussion

Although 12R-BCM and 12R-BPM are isostructural down to 100 K, 12R-BPM exhibits a magnetic transition at T₁ ≈ 200 K—which has no analogue in 12R-BCM—and at least one additional low-temperature transition (T₂ ≈ 12.15 K). Below the 12R-BPM T₁ transition, we observe a small net moment on the order of 0.05 μ_B per f.u. and hysteresis with a characteristic wasp-waisted appearance (Figure 3c). This suggests that the order is likely canted AFM or ferrimagnetism. The large, negative Weiss temperature supports that the overall correlations are AFM. We rule out a structural phase transition near this T₁ transition using the 100 and 300 K synchrotron PXRD data (Figure 2), which show no signs of symmetry changes. In addition, there was no hysteresis when we measured magnetization while warming and cooling through this temperature (Figure S5) and no peak in the heat capacity at this temperature (Figure S7). Instead, our results indicate that this T₁ transition in 12R-BPM is a purely magnetic or electronic transition. The wide temperature regime over which this transition occurs may indicate some heterogeneity in the 12R-BPM sample.

While the most significant differences between 12R-BCM and 12R-BPM are attributed to the substitution of Pr⁴⁺ for Ce⁴⁺, our results may additionally be consistent with a hypothesis that 12R-BPM’s T₁ ≈ 200 K transition is caused by a small amount of oxygen vacancies (below 1%). Oxygen vacancies could cause some reduction of Pr⁴⁺ or Mn⁴⁺ to Pr³⁺ or Mn³⁺. The formation of oxygen vacancies in 12R-BCM, thought to be charge compensated by Mn⁴⁺ to Mn³⁺ transitions, and the influence of oxygen vacancies on phase stability have been reported previously.²⁶ To combat oxygen-vacancy formation, our 12R-BCM and 12R-BPM samples were thoroughly annealed in air, under which conditions we expect negligible quantities of oxygen vacancies.

The 150–200 K behavior of both 12R-BCM and 12R-BPM is consistent with many previous reports of non-Curie–Weiss behavior of Mn⁴⁺ cations near-room temperature.^33,34 Our assignment of the T₁ transition in 12R-BPM as arising from Mn instead of Pr is supported by the short-range ordering of Mn at a similar temperature in 12R-BCM (∼150 K) as well as the observed ferrimagnetic order at 42 K of the Nb⁵⁺ analogue, Ba₄NbMn₃O₁₂, whose trimers are composed of Mn³⁺Mn₂⁴⁺O₁₂, yielding a net cluster moment of S = 2.¹² In addition, the T₁ transition may be influenced by oxygen-vacancy-induced reduction of Mn⁴⁺ to Mn³⁺, although this effect should be small since the oxygen vacancies in these samples are expected to be near dopant levels. The role of partial reduction on the M′ site of 12R materials is not well described by theory, but many examples exist in the literature that are related to what we observe here. A similar onset in the magnetization at approximately T ≈ 200 K was observed in isostructural 12R material Ba₄Ni⁴⁺Fe³⁺Fe₂⁴⁺O_11.5, in which one highly oxidized Fe⁴⁺ is reduced to Fe³⁺; this onset was attributed to interactions between the mixed valent Fe ions.²⁸ However, given that 12R-BCM does not display this transition at 200 K, we cannot rule out the possibility that the presence of Pr⁴⁺ is at least in part responsible for this behavior. Further work elucidating the magnetic structure and definitively studying the role of Pr⁴⁺ or oxygen vacancies in the observed transition will be essential to understanding this transition.

Due to the presence of Pr⁴⁺, the low-temperature magnetic behavior—and ground state—of 12R-BPM is more complex than the AFM order of 12R-BCM at T_N ≈ 7.75 K. Given that the T₂ ≈ 12.15 K feature in 12R-BPM releases ∼3× as much magnetic entropy (and occurs about 5.5 K higher) than the 12R-BCM’s AFM transition at T_N ≈ 7.75 K, the 12R-BPM T₂ transition must involve the Pr⁴⁺ cations in addition to the Mn₃O₁₂ trimers. There is no significant effect on the net magnetic moment of 12R-BPM due to this T₂ transition, suggesting that it has AFM character, consistent with the extracted Weiss temperature. Another feature may be present in the heat capacity data of 12R-BPM: C_p and C_mag display a shoulder below the peak at T₂ ≈ 12.5 K (Figure 5b,d). This shoulder is similar in magnitude to (and present over the same temperature range as) the sole peak present for 12R-BCM at T_N ≈ 7.75 K, and a direct comparison to illustrate this point is shown in Figure S8. The 12R-BPM heat capacity data could therefore be interpreted as a superposition of behavior strongly shared with 12R-BCM plus a stronger peak associated with both the Pr and Mn sublattices. This interpretation suggests that behavior similar to that occurring through the AFM transition in 12R-BCM, which is likely associated with intratrimer ordering, may also be occurring in 12R-BPM. Altogether for 12R-BPM, we conjecture that at T₁ ≈ 200 K, canted AFM intertrimer order develops; then, at T₂ ≈ 12.15 K, the Mn₃O₁₂ trimers and Pr⁴⁺ cations order antiferromagnetically; and finally, full intratrimer and Pr⁴⁺ AFM order occurs at T₃ ≈ 7.5 K. However, neutron diffraction data will be necessary to fully understand the magnetic structures of these materials and validate these hypotheses.

Substituting the bridging nonmagnetic Ce⁴⁺ cation between the Mn₃O₁₂ trimers with Pr⁴⁺ (J_eff = 1/2) also has a significant effect on the cluster magnetism of these materials. In 12R-BCM, we observe an onset of short-range AFM correlations at T ≈ 150 K and full AFM order at T_N ≈ 7.75 K. That the Mn₃O₁₂ trimers in 12R-BCM exhibit cluster magnetism is supported by the results of Curie–Weiss fitting, which yielded an effective moment much smaller than that expected for three Mn⁴⁺ cations. Instead, it was much closer to the value for S = 3/2 per formula unit, which is the net spin expected for this cluster assuming AFM interactions. Our observation of likely cluster magnetism in 12R-BCM is consistent with observations of cluster magnetism in isostructural 12R-Ba₄NbMn₃O₁₂ and analogues with Mn replaced by Ru or Ir.^12,14,15 Interestingly, the effective moment of 12R-BPM is within error of the calculated value for three Mn⁴⁺ cations and a Pr⁴⁺, suggesting that different behavior may be occurring compared to 12R-BCM. Perhaps the Mn₃O₁₂ trimers in 12R-BPM exhibit less cluster-like behavior due to interactions between Pr⁴⁺ and these trimers, and/or a small amount of Pr³⁺ or Mn³⁺ defects might be present, both of which could raise the total effective moment.

Although their magnetic structures are necessarily different, the long-range intratrimer order at low temperature in both materials must be mediated by the M⁴⁺O₆ octahedra, which are corner-sharing with six Mn₃O₁₂ trimers; in turn, each Mn₃O₁₂ trimer is corner-sharing with six M⁴⁺O₆ octahedra—three at each end of the trimer. This plethora of competing magnetic interactions is a likely source of the magnetic frustration suggested by the large ratio of the Weiss temperature to the Neél temperature for both materials (∼37 for 12R-BCM and ∼41 for 12R-BPM).

Conclusions

We have studied the crystal structures and magnetic properties of two members of a family of hexagonal perovskites in the 12R structure, Ba₄CeMn₃O₁₂ and Ba₄PrMn₃O₁₂, where the Ce/Pr site bridges the c-axis-aligned trimers of face-sharing MnO₆ octahedra. While the two materials are isostructural, susceptibility and heat capacity measurements reveal the striking influence of composition on resulting properties. 12R-BCM is a frustrated AFM below T_N ≈ 7.75 K, and the Mn₃O₁₂ trimers exhibit cluster magnetism. We show for the first time that the substitution of Pr⁴⁺ (f¹) for nonmagnetic Ce⁴⁺ strongly influences the magnetic properties of 12R-BPM. 12R-BPM exhibits three magnetic transitions: the first, at T₁ ≈ 200 K, results in a small net moment and is likely a canted AFM or a ferrimagnetic state. We suggest that this transition may be related to the known non-Curie–Weiss behavior of Mn⁴⁺ near-room temperature. The main low-temperature transition occurs at T₂ ≈ 12.15 K, which is ∼5.5 K higher than the main 12R-BCM transition; we conjecture that this is related to the AFM ordering of both the Pr and Mn₃O₁₂ trimer sublattices. The f electron contributed by Pr⁴⁺ likely increases the degree of intratrimer interactions as well as being an additional magnetic cation within the structure. Finally, there may be a weak additional transition at T₃ ≈ 7.5 K related to full intratrimer AFM order. Our data suggest that both 12R-BCM and 12R-BPM are highly frustrated, likely due to the complexity of these structures coupled with the unique magnetic behavior of the Pr⁴⁺ ion. While full understanding of the subtle magnetic transitions observed in this work will require a further, in-depth study of their magnetic structures, including with neutron diffraction/scattering, our results demonstrate that a rich field of material design awaits within layered, hexagonal perovskite materials.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.chemmater.3c03014.

• Additional crystallographic details, magnetic data, and heat capacity data (PDF)

• 12R-BCM_100K (CIF)

• 12R-BPM_100K (CIF)

The authors declare no competing financial interest.