# Buckled Honeycomb Lattice Compound Sr3CaOs2O9
Exhibiting Antiferromagnetism above Room
Temperature

Gohil S. Thakur, Thomas C. Hansen, Walter Schnelle, Shuping Guo, Oleg

Janson, Jeroen van den Brink, Claudia Felser, Martin Jansen

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► To cite this version:

Gohil S. Thakur, Thomas C. Hansen, Walter Schnelle, Shuping Guo, Oleg Janson, et al.. Buckled Honeycomb Lattice Compound Sr3CaOs2O9 Exhibiting Antiferromagnetism above Room Temperature. Chemistry of Materials, 2022, 34 (10), pp.4741-4750. 10.1021/acs.chemmater.2c00740. hal-05330195

HAL Id: hal-05330195

https://hal.science/hal-05330195v1

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# Buckled Honeycomb Lattice Compound Sr₃CaOs₂O₉ Exhibiting Antiferromagnetism above Room Temperature

Gohil S. Thakur, Thomas C. Hansen, Walter Schnelle, Shuping Guo, Oleg Janson, Jeroen van den Brink, Claudia Felser, and Martin Jansen*

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Cite This: *Chem. Mater.* 2022, 34, 4741–4750

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Supporting Information

**ABSTRACT:** Synthesis, crystal structure, and magnetic properties of a new 2:1 ordered triple perovskite Sr₃CaOs₂O₉ are reported. The compound crystallizes in a *P*2₁/*c* space group and features a unique buckled honeycomb lattice of osmium. It exhibits long-range antiferromagnetic ordering with a high Néel temperature of 385 K as confirmed by susceptibility, heat capacity, and neutron diffraction measurements and is electrically insulating. This compound is also the first example of a 2:1-ordered osmate perovskite. Theoretical investigations indicate that Sr₃CaOs₂O₉ features a sizeable antiferromagnetic exchange between the puckered planes resulting in a high *T*<sub>N</sub>. The magnetic properties of the known compound Sr₃CaRu₂O₉ are elucidated in comparison. It shows antiferromagnetic order below *T*<sub>N</sub> ≈ 200 K.

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## 1. INTRODUCTION

Antiferromagnetic insulating materials offer exciting prospects for the device industry as active components in spin valve and opto-spintronic devices.¹⁻⁵ In such implementations, the spin of the electrons is used, rather than the charge, to store information, thereby circumventing the problem of Joule heating associated with the flow of electrons. Also, by virtue of the zero net moment displayed by antiferromagnets, electron spins produce no stray field and are practically insensitive to external magnetic disturbances which allow for a much denser stacking of components.⁴,⁵ Antiferromagnetic insulators are also expected to have a terahertz writing speed leading to ultrafast operations.⁶ Air-stable room-temperature antiferromagnetic insulators are thus highly desirable. Perovskite oxides present an excellent avenue to explore such materials due to their ubiquitous nature, excellent stability, structural robustness, and a wide range of atomic flexibility. In ordered double (A₂BB'O₆) or triple (A₃BB'₂O₉) perovskites, the B sites appear to be very versatile as a variety of metal atoms ranging from alkaline earth (Mg, Ca, Sr, and Ba) to alkali (Li, Na, and K) and transition metals can be substituted or doped at those sites, leading to a wide range of magnetic and electrical properties.⁷,⁸ The same stands true for the A-sites although to a limited extent. The resulting compositional and structural degrees of freedom enable the realization of various 1:1 or 2:1 ordered perovskites, given that certain size and charge requirements are fulfilled. Here, we report on a 2:1 ordered insulating triple perovskite Sr₃CaOs₂O₉ exhibiting a high Néel temperature. This compound is also exceptional in another

respect. Conventional perovskites with 2:1 ordering with *d*⁰ (nonmagnetic) metals (Nb, Ta, W, etc.) are abundant, while the ones with partially filled *d* orbitals (magnetically active) are quite uncommon.⁹,¹⁰ Sr₃CaRu₂O₉ has been the first reported example of a 2:1 ordered conventional perovskite containing a non *d*⁰ ion at the B site,¹¹ Sr₃CaIr₂O₉ being the only other isostructural compound reported to date.¹² In contrast, there are many compounds with this composition known with Ba occupying the A site. Accordingly, they are all derived from the hexagonal perovskite structure type featuring face-sharing M₂O₉ dimers (M = Ru and Os), for example, Ba₃MOs₂O₉ (M = Li, Na, Cu, and Zn) and Ba₃MRu₂O₉ (M = Li, Na, Cu, and rare-earth).¹³⁻²¹

In continuation to our expedition to find compounds containing osmium and featuring magnetic ordering transitions at high temperatures,²²⁻²⁵ we report the new compound Sr₃CaOs₂O₉ crystallizing in a conventional monoclinic triple-perovskite structure. Sr₃CaOs₂O₉ orders antiferromagnetically below *T*<sub>N</sub> ≈ 385 K. The previously known isostructural compound Sr₃CaRu₂O₉, whose magnetic properties were hitherto unreported, has also been studied using magnetization

Received: March 10, 2022

Revised: April 27, 2022

Published: May 13, 2022

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and electrical resistivity. It is found to be antiferromagnetic below $T_N \approx 200$ K and is electrically insulating.

## 2. EXPERIMENTS AND PROCEDURES

**2.1. Synthesis.** Black polycrystalline powder samples of $Sr_3CaOs_2O_9$ were prepared along a standard solid-state sealed tube method. Stoichiometric amounts of highly pure $SrO_2$ (Sigma-Aldrich, 98%), $SrO$ (Sigma-Aldrich, 97%), $CaO$ (Alfa Aesar, 99.9%), and $OsO_2$ (Alfa Aesar, min 83% $Os$) (total of 0.2 g) were ground, pelletized, and kept in a corundum crucible and placed in a quartz tube, which was sealed off under vacuum. Because the commercially available $OsO_2$ may contain a large amount of $Os$ metal, it was further oxidized prior to use by heating in presence of $PbO_2$, contained in a separate crucible, in an evacuated quartz tube at 753 K for 2 days. This treatment yielded highly pure and crystalline $OsO_2$. All the chemical manipulations were performed in an Ar-filled glovebox ($O_2$ and $H_2O < 1$ ppm). The tube was then heated at 1073 K for 48 h at a heating and cooling rate of 100 K per hour in a tubular furnace placed inside a fume hood. The tubes were cracked—open in a well-ventilated fume hood. The product is stable in air for months. A total of 2 g of sample for neutron studies was prepared in the same manner in several smaller batches. $Sr_3CaRu_2O_9$ was prepared by heating appropriate amounts of respective alkaline earth carbonates and $RuO_2$ in air at 1473 K as reported previously.¹¹

**2.2. Instruments for Physical Property Measurements.** Laboratory powder X-ray diffraction (PXRD) data were collected at room temperature on a HUBER G670 imaging plate Guinier camera with Cu $\alpha_1$ radiation ($\lambda = 1.5406$ Å), in a $2\theta$ range of $5-100°$.

Crystal structure was refined by a Rietveld profile fit of the powder X-ray data using the TOPAS-4.2.0.2 (AXS) program²⁶ starting with the $Sr_3CaRu_2O_9$ structure¹¹ as the initial model. Refined parameters were the cell constants, Wyckoff positions, scale factor, zero point of $\theta$, sample displacement (mm), background as a Chebyshev polynomial of 20th degree, 1/x function, crystallite size, and microstrain. The structure was satisfactorily refined in the monoclinic $P2_1/c$ space group.

Neutron diffraction data was recorded on a high-intensity powder diffractometer D20 at the HFR of ILL in Grenoble (France) in the frame of the experiment EASY-686.²⁷ High-resolution patterns were recorded at ambient temperature using a vertically focusing germanium (hhl) monochromator at a take-off angle of 118° at 1.36 Å (117) and 1.87 Å (115). A $2\theta$ scan (61 steps of step width 0.05° $2\theta$, the position sensitive detector's angular pitch being 0.05° as well, 60 s counting time per step, thus 61' in total) has been used to obtain very clean patterns through a maximum-likelihood approach by redundant measurements at different $2\theta$ angles. Medium resolution data (without detector scan) was recorded at 2.42 Å using a pyrolytic graphite (002) monochromator at 42° take-off while heating the sample on a linear temperature ramp from 1.8 to 395 K. Further, $2\theta$ scans (61 steps at 0.05°, 120 s per step, thus 122' in total) at the lowest temperature (1.8 K) and just above the transition temperature (395 K) were recorded to provide good differential data (despite the high temperature difference) for a detailed analysis of the magnetic structure. Crystallographic structure data obtained from the neutron powder refinement (at 1.36 Å) has been deposited with Fachinformationszentrum Karlsruhe, D-76344 Eggenstein-Leopold-shafen (Germany) and can be obtained on quoting the depository number CSD-2153716.

Magnetization data of powder samples were collected in the temperature range 2–350 K in applied magnetic fields $\mu_0H = 0.1, 1.0, 3.5$, and 7.0 T on a MPMS-XL7 and from 300 to 750 K on a MPMS-3 magnetometer (both from Quantum Design) in field cooled protocols. Isothermal magnetization curves were recorded for magnetic fields between $\pm 7$ T at $T = 1.8$ K. Diamagnetic corrections were applied.²⁸

**2.3. Computational Methods.** First-principles density functional theory calculations were carried out by using the experimental structure of $Sr_3CaOs_2O_9$ with two codes, Vienna Ab initio Simulation Package (VASP) and all-electron full-potential local-orbital code

FPLO.²⁹ Total energy calculations were performed in a plane-wave basis set using the projector augmented wave³⁰ method under a gradient generalized approximation (GGA)³¹ with PBE exchange-correlational functional and employing DFT + $U$³² methods as implemented in the VASP. We used an energy cutoff of 500 eV and a $2 \times 5 \times 4$ gamma-centered Monkhorst-Pack³³ k-point mesh to sample the Brillouin zones. All structures were relaxed with all the forces and tensors are below 0.01 eV Å⁻¹ and 0.2 kbar, respectively. Onsite Coulomb repulsion U and onsite Hund exchange J used for $Os$³⁴ were 2 and 0.4 eV, respectively. The FPLO was used for the tight-bonding Wannier function analysis. The Brillouin zone was sampled with a $3 \times 5 \times 7$ mesh.

## 3. EXPERIMENTAL RESULTS AND ANALYSIS

**3.1. Structure.** A new 2:1 ordered osmium-containing perovskite $Sr_3CaOs_2O_9$ has been synthesized. The compound appears as a black air stable microcrystalline powder. The elemental ratio of metals was confirmed by scanning electron microscopy-energy dispersive X-ray analysis (see Figure S1 in the Supporting Information). On heating up to 1450 K in an argon atmosphere, $Sr_3CaOs_2O_9$ only partially decomposes to $Sr_3CaOs_2O_9$ (~85%), $Sr_2CaOsO_6$ (~10%), and $Os$ metal 5% (see Figures S2 and S3 in the Supporting Information). The structure was successfully refined using room-temperature powder X-ray data in the monoclinic space group $P2_1/c$ (#14), which was later confirmed by neutron diffraction. The structure of $Sr_3CaRu_2O_9$ was used as the initial model for refinement. A satisfactory $R_{wp}$ of 4.2% was obtained after the final refinement cycle. A trace amount (<1%) of elemental osmium is always apparent in the diffraction patterns of $Sr_3CaOs_2O_9$ and was therefore included in the refinement (Figure 1).

<figure><img src="image_10.png" /><figcaption>**Figure 1.** Laboratory PXRD data (red line) along with the Rietveld fit (blue line) of $Sr_3CaOs_2O_9$. Black line is the difference curve and vertical bars represent the Bragg reflections corresponding to respective phases. Inset shows the magnified area in the $2\theta$ range 32–44°.</figcaption></figure>

Crystallographic details and atomic coordinates obtained after the Rietveld refinement of the powder X-ray data are presented in Tables S1 and S2 in the Supporting Information. Rietveld refinement of the $Sr_3CaRu_2O_9$ phase was carried out to check the phase purity; the respective profile plot is shown in Figure S4 in the Supporting Information.

To confirm the crystal structure and site occupancies of atoms, especially the lighter ones, we employed high-resolution neutron diffraction measurements at two different wavelengths 1.87 and 1.36 Å. The structure refinement was carried out on the conjointly applied room-temperature data obtained at two wavelengths (Figure 2). In the neutron refinement, despite a small absorption correction, the (isotropic) thermal displacement parameter of one of the calcium positions remained unphysically negative indicating a possible mixed site occupancy. A more careful inspection (without soft constraints of $B_{iso} > 0$) of the X-ray data finally resulted as well in significantly negative isotropic displacement parameters for the Ca-positions. Therefore, we assumed a slight anti-site disorder on both Ca positions and, for reasons of formal charge equilibrium, on both Os positions.
<figure><img src="image_11.png" /><figcaption>**Figure 2.** Room-temperature powder neutron data (red circles) recorded at wavelengths 1.36 Å (upper) and 1.87 Å (lower) and their Rietveld fits (blue lines). Brown lines are the difference curves and upper and lower green vertical bars represent the Bragg reflections corresponding to the respective nuclear and magnetic cells of Sr₃CaOs₂O₉.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>**Figure 3.** Projections of the crystal structure of Sr₃CaOs₂O₉ in different crystallographic directions (a,b) and buckled honeycomb lattice of Os (c,d). Os1 (olive) and Os2 (blue) are labeled with different colors in (c,d) only for the purpose of clarity.</figcaption></figure>
<figure><img src="image_13.png" /><figcaption>**Figure 4.** (a) Temperature dependence of molar magnetic susceptibility in the high-temperature range (300–750 K) and (b) isothermal magnetization of Sr₃CaOs₂O₉. Inset of (a) shows the molar susceptibility data in the *T* range of 2–350 K.</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>**Figure 5.** (a) Temperature dependence of molar magnetic susceptibility of Sr₃CaRu₂O₉ at various fields in FC mode and (b) isothermal magnetization of Sr₃CaRu₂O₉ at *T* = 1.8 K. The inset of (a) shows an enlarged view of susceptibility near the magnetic transition ≈200 K.</figcaption></figure>

To gather maximum information, we conducted a final combined refinement of two neutron diffraction data sets recorded at 1.36 and 1.87 Å wavelengths and the X-ray data set at a wavelength of 1.54 Å. A weighting scheme of 30, 30, and 40% have been applied in this joint refinement. As a result, 5.2(2) % of the Ca position turns out to be occupied by Os⁵⁺, and in consequence about 2.6(1) % of the Os position by Ca²⁺. The structure parameters, atomic positions, and important bond lengths obtained from the aforementioned joint refinement are listed in Tables S1, S3a, and S4a, respectively, in the Supporting Information.

Figure 3 shows the crystal structure of Sr₃CaOs₂O₉ in different crystallographic orientations. It is isostructural to Sr₃CaM₂O₉ (M = Ru and Ir) and is best described as a 2:1 ordered triple perovskite where Ca and Os both occupy distinct crystallographic positions. The CaO₆ octahedra are corner shared with OsO₆ and occur alternatively after every pair of corner-shared OsO₆ octahedra; hence, the ordering scheme 2:1. While viewing through the *c*-axis, one can easily appreciate the 2:1-layered sequence of the ordered cation octahedra running along the crystallographic *b* direction. This cation ordering is driven by a large charge difference of 3 and ionic radii mismatch by ~0.45 Å between Ca²⁺ and Os³⁺ cations.³⁵ Because of the distortions driven by deviation from the ideal cubic perovskite structure, significant tilting and distortion of the CaO₆ and OsO₆ octahedra is observed. The corner shared connectivity pattern of tilted OsO₆ octahedra gives rise to a unique two-dimensional buckled honeycomb lattice of Os, where the average distance between the two adjacent Os atoms is ~4.0 Å (Figure 3c,d). This kind of corner shared-buckled honeycomb lattice has been observed before only in the isostructural compounds Sr₃Ca(Ru/Ir)₂O₉.¹⁰,¹¹ Moreover, a honeycomb pattern of

Os is even rarer and in fact has only been reported previously in Li₂.₁₅Os₀.₈₅O₃ (although, edge-shared).³⁶ Bond distances between Os and O are in a range of 1.88–2.06 Å and agree well with those reported in the literature.²²,³⁷⁻⁴⁰ However, the Ca–O distances in Sr₃CaOs₂O₉ appear to be slightly shorter (2.19–2.24 Å) than expected, as far as their ionic radii are concerned.³⁵ These short Ca–O distances comply with a small degree of an anti-site disorder at the Ca and Os positions. Such shortened distances also appear in the two isostructural Ir and Ru compounds indicating that there might exist a similar slight B site disorder, which, however, is not explicitly mentioned in those reports.¹¹,¹² This small Ca–Os disorder might manifest as stacking faults, locally altering an ideal layer sequence of 2:1. Further high-resolution transmission electron microscopy studies are required to consolidate this claim. It is important to note that not many perovskites containing Os are known and most of them contain Ba as an A cation. While most of the Ba containing triple perovskites derive from the aristotype hexagonal perovskite, the Sr containing representatives tend to form variants of the ideal cubic perovskite structure.¹¹,¹²

**3.2. Magnetism, Conductivity, and Specific Heat.** Figure 4 displays the temperature-dependent susceptibility and isothermal magnetization data of Sr₃CaOs₂O₉. The magnetic susceptibility of Sr₃CaOs₂O₉ is small and exhibits an anomaly at *T*<sub>N</sub> = 385 K (Figure 4a), which we assign to the antiferromagnetic ordering of the Os moments. Lower field data (Figure S5 in the Supporting Information) confirm the basically antiferromagnetic ordering but with a very weak ferromagnetic component (of the order 1 × 10⁻³ µ<sub>B</sub>/f.u), possibly due to very small spin canting or defects. Below the Néel temperature, *χ*<sub>m</sub>(*T*) decreases (inset of Figure 4a) but increases again below ≈150
$K$, indicating possible paramagnetic impurities displayed as 'Curie tail'. Moreover, the overall field dependence suggests some trace ferromagnetic contamination with high Curie temperatures. Above $T_N$, the corrected susceptibility is paramagnetic but does not follow a clear Curie-Weiss law; therefore, it was not possible to determine the paramagnetic effective moment. The linear field dependence of the magnetization at $T = 1.8$ K confirms the antiferromagnetic nature of the ordering. The para- and ferromagnetic contributions are invisible on this scale.

$Sr_3CaRu_2O_9$ appears to be predominantly antiferromagnetically ordered with a transition temperature of 200 K (Figure 5). There are few tiny ferromagnetic like transitions also at a lower temperature, most prominent one at ~170 K. An estimation of the total weak ferromagnetic component was made based on isothermal magnetization studies. A very small value of saturated moment ~0.007 $\mu_B$/ $Ru^{5+}$ is estimated, which is contributed by trace ferromagnetic impurity, most probably $SrRuO_3$ (~0.5%) as adjudged by the weak transition at ~170 K observed at a low field. This further supports principle antiferromagnetic ordering of the bulk sample. The susceptibility in the paramagnetic state does not follow a Curie-Weiss law, preventing the estimation of any effective moment or the strength of magnetic interactions. Figure 6 shows the specific heat

<figure><img src="image_15.png" /><figcaption>**Figure 6.** Specific heat near the expected transition of $Sr_3CaOs_2O_9$ showing a pronounced anomaly at the magnetic transition temperature.</figcaption></figure>

data of $Sr_3CaOs_2O_9$. The magnetic ordering in $Sr_3CaOs_2O_9$ at ~385 K is confirmed by a heat capacity measurement, which clearly shows a pronounced anomaly centered around 385 K. A jump of ~10 J/mol·K is observed. An antiferromagnetic ordering at such high temperatures is rare in perovskite compounds. Notably, the other isostructural compound $Sr_3CaIr_2O_9$ displays paramagnetic behavior with a vanishingly small susceptibility associated with a possible $J_{eff} = 0$ ground state of $Ir^{5+}$ ions,¹² whereas $Sr_3CaRu_2O_9$ is found to be antiferromagnetic below 200 K. A growing body of high-temperature magnetic compounds containing osmium opens new avenues to explore high-temperature magnetism in 5d compounds and especially in otherwise scarcely investigated osmates.

Figure 7 shows the DC electrical resistivity of $Sr_3CaOs_2O_9$ in the temperature range 115–300 K. Room-temperature resistivity, $\rho^{300K} \sim 1$ kΩ-cm indicates that the material is electrically insulating in nature and exhibits an activated-type behavior at low temperatures with resistivity increasing by at least 3 orders of magnitude. A simple Arrhenius fit in the high-temperature region was attempted to extract a band gap ($E_g = 0.35$ eV); however, the curve is linear only in a small range of high temperatures (225–300 K) and deviates from linearity at lower temperatures. Rather the resistivity fits almost perfectly to $\rho(T) \propto [\exp(\Delta/T)^{1/4}]$ equation in the almost entire temperature range (Figure 7 inset). This may be indicative of a three-dimensional hopping of charge carriers. Resistance measurement data up to 560 K on $Sr_3CaOs_2O_9$ as well as on $Sr_3CaRu_2O_9$ are shown in the SI, Figure S6. Activated conduction behavior is observed, especially also in the

<figure><img src="image_16.png" /><figcaption>**Figure 7.** Resistivity versus temperature curves for $Sr_3CaOs_2O_9$. Left and right insets show the $\ln\rho$ versus $1/T$ and $\ln\rho$ versus $1/T^{1/4}$ plots, respectively, along with the linear fits (black line).</figcaption></figure>

paramagnetic regime above $T_N$ for $Sr_3CaOs_2O_9$. Thus, both compounds are insulators.

**3.3. Neutron Diffraction and Magnetic Structure.** To determine the magnetic structure, we collected neutron diffraction data above and below the expected magnetic transition temperature. The data below $T_N$ shows at least two nuclear Bragg peaks with additional intensity, which can be assigned to magnetic ordering. The curve in Figure 8 shows the variation of intensity of the peak,

<figure><img src="image_17.png" /><figcaption>**Figure 8.** Temperature dependence of intensity of the magnetic and nuclear peak of $Sr_3CaOs_2O_9$ containing the overlapping Bragg reflections (–111) and (–202).</figcaption></figure>

containing the overlapping Bragg reflections (–111) and (–202), with temperature. This also confirms a $T_N$ of ~385 K observed in the susceptibility and heat capacity studies. The magnetic structure, however, could not be solved unambiguously, resulting in two models with almost equally good fits as explained below.

All magnetic scattering intensity lays on top of nuclear peaks, and the propagation vector is $\kappa = (000)$. This propagation vector, together with the known crystal symmetry of the chemical unit cell and the two positions of the $Os^{3+}$ magnetic ions serve as the input for the symmetry analysis of possible magnetic ordering schemes. The representation analysis of the low-temperature magnetic structure was performed with the program BasIreps⁴¹⁻⁴³ as part of the FullProf suite.⁴⁴ All predicted symmetry allowing spin configurations were checked on the observed data with Rietveld refinements by FullProf.⁴⁵,⁴⁶ A difference pattern from data acquisitions of 2 h each at 2.41 Å at 1.8 and 395 K, respectively (Figure 9) has been used at this purpose, where the high-temperature data have been corrected for
<figure><img src="image_18.png" /><figcaption>**Figure 9.** Rietveld fit (blue line) of the difference pattern (pattern at 1.8 K minus isotropic thermal expansion-corrected pattern at 395 K (red dots with estimated error bars) with the pure magnetic phase. Green dots are the difference of observed and calculated intensities. Positions of strong nuclear peaks are excluded (light blue background) because of a remaining misfit due to the thermal expansion. Black lines indicate Bragg peak positions.</figcaption></figure>

thermal expansion and re-interpolated accordingly. Only four out of $4^2 = 16$ combinations of the four irreducible representations (see Table S5) for each one of the two $Os^{5+}$ ions provide sets of calculated diffraction peaks consistent with our experimental data. Two of them refine to purely ferromagnetic structures with all spins parallel and must be excluded according to the susceptibility data. The remaining two representations, however, cannot be distinguished unambiguously by Rietveld refinement, despite a small preference for one of them.

A few assumptions need to be made hereafter due to the low number of observations (mainly two unambiguous Bragg peak intensities) and the possible number of parameters describing the magnetic ordering. First, we assume that the $Os^{5+}$ ions on both positions show the same magnetic moment. The reason why the two hereafter described solutions cannot be unambiguously distinguished is the accidental overlap of the (–111) and the (–202) reflections. The two reflections are only 0.04° apart from each other in 2θ at a wavelength of 2.4 Å, which is virtually indistinguishable by any neutron diffractometer, it would require a resolution of $\Delta d/d$ of about $10^{-3}$, which is technically inaccessible today, by an order of a magnitude. The only other distinctive feature is the intensity ratio of the bespoken (–111) and (–202) peak to a less intense, higher angle peak regrouping (220), (–513), and (113).

One solution, with a more intense (–111) peak, corresponds to the representation $\Gamma 1$ (Shubnikov group $P2_1/c'$, #14.78) for both $Os^{5+}$-ion positions with main spin vector components perpendicular to [010] and tilted to the plane of buckled honeycomb lattice of osmium. Another one, with a more intense (–202) peak, corresponds

to $\Gamma 3$ (Shubnikov group $P2_1/c'$, #14.77), with main vector components parallel or antiparallel to [010] and, thus, inside the plane of the puckered honeycomb lattice of osmium. The two solutions shall be called “$\Gamma 1$” and “$\Gamma 3$” hereafter. Both magnetic structures are best described using spherical coordinates, as this allows for Rietveld refinement with a single constrained magnetic moment for both osmium positions, thus, with five independent parameters describing the two vectors, rather than six.

In the solution $\Gamma 1$, the magnetic moments are tilted to the puckered honeycomb lattice plane, defined by the positions of either osmium (Figures 10a and 11a). The vectors are tilted by 66° for the moments of the Os1 positions and by 64° for Os2. Whereas the moments are not fully perpendicular to this plane, they are almost perpendicular to the direction of the *b*-axis. They are tilted to the *ac*-plane normal to the *b*-axis by 5.6° for moments of Os1 and by 4.2° for those of Os2. In the buckled planes, each osmium has three closest neighbors of the other osmium position, and six osmium positions form a puckered (chair conformation) hexagonal ring, alternatingly by Os1 and Os2. Os1 positions are on one side of the plane, Os2 on the other. In a plane, all osmium moments belonging to one position point in roughly the same direction with a deviation from a perfect parallel alignment by 8.8° for Os1 and 8.4° for Os2, respectively. The angle between the next neighbors is 171.0° for the two neighbors of each Os-position in the direction of the *b*-axis (or the four out of six edges of the buckled hexagonal ring not perpendicular to the *b*-axis) and 177.5° for the remaining third of closest Os–Os distances, that is, those “bonds” perpendicular to the direction of the *b*-axis.
<figure><img src="image_19.png" /><figcaption>**Figure 10.** View perpendicular to the puckered planes: magnetic moments of osmium in hexagonal neighborhood, Os1 (olive) and Os2 (blue) oxygen-coordination polyhedra, oxygen atoms form octahedra corners. (a) First solution (Γ1) with vectors out of the puckered lattice plane and (b) second solution (Γ3) with vectors parallel to *b*-axis.</figcaption></figure>

<figure><img src="image_20.png" /><figcaption>**Figure 11.** View in direction of the *b*-axis: magnetic moments of osmium in hexagonal neighborhood, Os1 (olive) and Os2 (blue) oxygen-coordination polyhedra, oxygen positions form octahedra corners. (a) First solution (Γ1) with vectors tilted to the puckered planes and (b) second solution (Γ3) with vectors parallel to *b*-axis.</figcaption></figure>

In the solution Γ3 (Figures 10b and 11b), the magnetic moments are lying in the puckered honeycomb lattice plane, defined by the positions of either osmium atoms. The vectors are tilted by only 0.6° for the moments of the Os1 positions and by 0.1° for Os2. They derive from the direction of the *b*-axis by 5.8° for moments of Os1 and 4.7° for those of Os2, respectively. In a puckered honeycomb lattice plane, all osmium moments belonging to one position point in roughly the same direction with a deviation from perfect parallel alignment by 11.6° for Os1 and 9.5° for Os2. The angle between the next neighbors is 169.5° for the two neighbors of each Os-position in the direction of the *b*-axis (or the four out of six edges of the puckered hexagonal ring not perpendicular to the *b*-axis) and 178.8° for the remaining third of the closest Os–Os distances, that is, those “bonds” perpendicular to the direction of the *b*-axis.

Regarding the large error bars on the angles of both solutions, which exceed largely the aforementioned deviations from collinearity or perpendicularity, we can consider further assumptions to obtain a less correlated fitting result.

The only angle that needs refinement is the moment orientation perpendicular to the *ac*-plane in the solution Γ1. All other angles mentioned should be constrained to be 0, 90 or 180° respectively. In the case of Γ1, this results in refining only the *x* and *z* components of the moments, constraining them to the same amount over the two positions, setting the *y* component zero, respectively, in spherical coordinates, fixing the azimuthal *φ* angle to zero, and constraining the amount of the inclination angle *θ* to be the same for both positions and thus, two rather than five independent parameters. Even though, the error bar on the remaining inclination angle in the spherical representation remains enormous. The magnetic moment vectors are standing at a 71.6° angle on the buckled planes. The magnetic moment amounts here to 1.41(9) *μ*<sub>B</sub>. The inclination angle *θ* can further be constrained to be 90°–*β*, the monoclinic angle without the degradation of the fit and resulting in a magnetic moment of 1.419(8) *μ*<sub>B</sub>. The moment vectors then form an angle of 70.5° with the buckled planes.

In the solution Γ3, no angle remains to be refined and in the Cartesian description as well only one parameter, the amount of magnetic moment, remains to be refined, the *y*-component of the Cartesian vector. It must be noted here that the quality of refinement is equal to the one with five or six refinable parameters. The magnetic moment amounts here to 1.88(1) *μ*<sub>B</sub>. See Table S6 for the two solutions and S7 for more details.

**3.4. DFT Analysis.** Despite the thorough experimental characterization of Sr<sub>3</sub>CaOs<sub>2</sub>O<sub>9</sub>, two questions remain open: what causes its unusually high long-range antiferromagnetic ordering temperature

<figure><img src="image_21.png" /><figcaption>**Figure 12.** (a) Nonmagnetic GGA band structure of Sr<sub>3</sub>CaOs<sub>2</sub>O<sub>9</sub> (thin black lines) and the Fourier-transform of the Wannier Hamiltonian (thin blue lines) obtained by projecting the GGA bands onto Os 5d *t*<sub>2g</sub> orbitals (left panel) as well as DOS (right panel) for the same calculation. O 2p, Os 5d *t*<sub>2g</sub> and *e*<sub>g</sub> contributions are highlighted. (b) DOS in a full-relativistic antiferromagnetic DFT + U calculation of the Γ1 configuration, which corresponds to the experimental magnetic ground state. Note the emergence of the band gap between the valence and polarization bands.</figcaption></figure>
<figure><img src="image_22.png" /><figcaption>**Figure 13.** Os-centered Wannier functions with the $t_{2g}$ symmetry. Note the sizable contributions of O 2p orbitals. For the highlighted (orange line) pair of Os atoms, sizable hopping is facilitated only by the yz and zxxz orbitals. Green and red spheres are Os and O, respectively.</figcaption></figure>

and how the Os magnetic moments are oriented with respect to the crystal axes.

We start with the latter problem. Our refinements of neutron diffraction data reveal two possible solutions: (i) $\Gamma 1$ with Os moments oriented nearly perpendicular to the puckered planes (Figure S7a) or (ii) $\Gamma 3$ with Os moments lying in-plane parallel to the *b* crystal axis. To distinguish between these two solutions, we performed full-relativistic total energy GGA + *U* calculations for the respective magnetic configurations. The $\Gamma 1$ configuration has the lowest energy, separated from the $\Gamma 3$ configuration by 2.32 meV/Os (Table S8). Band gaps of $\Gamma 1$ and $\Gamma 3$ amount to 1.097 (1.062) eV. The lengths of the magnetic moment of Os amount to 1.842 (1.780) $\mu_B$ for $\Gamma 1$ and $\Gamma 3$, respectively. Theoretical crystal structures and magnetic moments of Os are listed in Table S10 and S11 in the Supporting Information, respectively.

To understand the root cause of the high magnetic ordering temperature, we perform nonmagnetic DFT calculations. The band structure (Figure 12a, left panel) features a 24-bands manifold, which has a dominantly Os 5d $t_{2g}$ character with an admixture of O 2p states. This manifold is well separated by sizable band gaps from the rest of the valence band dominated by O 2p states as well as the bottom of the polarization band having the dominant Os $e_g$ contribution (Figure 12a, right panel). The nonzero density of states (DOS) of the Fermi level indicates the metallic behaviour, which is at odds with the experiment. This discrepancy stems from the underestimation of electronic correlations and the neglect of the spin-orbit coupling in the Os 5d shell. The insulating state $\Gamma 1$ configuration is readily restored in DFT + *U* calculations, as shown in Figure 12b.

Despite the spurious metallic ground state, the nonmagnetic band structure of $Sr_3CaOs_2O_9$ harbors information on the electron transfer integrals that underlie the magnetic exchange. To extract this information, we project the 24-bands manifold onto a Wannier basis of the $t_{2g}$ orbitals of Os. In this way, we obtain the transfer integrals between the pertinent Os 5d orbitals (xy, yz, and xz) for each pair of Os atoms directly from the respective matrix elements. First, we consider the transfer integrals within the puckered honeycomb planes. We find that each of three nearest neighbor Os–Os bonds features two sizable transfer integrals ranging between 220 and 300 meV (Table S9). These pertain to $t_{2g}$ orbitals of Os having the same orbital character and facilitated by O 2p contributions, as can be seen in Figure 13 (left and central panels). Hence, a sizable antiferromagnetic exchange between the nearest neighbors can be expected. The third pair of orbitals is essentially decoupled, as evidenced by the minute O 2p contribution of the respective Wannier function (Figure 12, right panel). Transfer integrals between the second neighbors amounts to 90–110 meV, all longer range terms within the buckled planes are considerably smaller. The presence of the second neighbor exchange indicates that the buckled layers are magnetically frustrated.

Interlayer hoppings of 120–130 meV are facilitated by two inequivalent paths with Os–Os distances of 5.789 and 5.818 Å (Figure S8). Hence, we can expect a sizable and non-frustrated interlayer exchange. To estimate this exchange quantitatively, we turn to full-relativistic DFT + *U* calculations of different magnetic

configurations. We construct an antiferromagnetic configuration with the flipped Os spin orientation of the second plane (AFM-flip) compared to the experimentally proposed magnetic structure (AFM-exp) (Figure S7b); in configuration AFM-exp (AFM-flip), the Os moments in the neighboring planes are antiparallel (parallel). Then, we perform total energy DFT + *U* calculations for two antiferromagnetic configurations along [101] and [001] directions. The AFM-exp configurations are energetically favorable by 8.83 and 8.89 meV/Os, respectively. We can therefore conclude that $Sr_3CaOs_2O_9$ features a sizable antiferromagnetic exchange between the puckered planes. This corroborates the high long-range antiferromagnetic ordering temperature of this compound.

## 4. CONCLUSIONS

In conclusion, we demonstrate here structural and magnetic properties of a new triple perovskite $Sr_3CaOs_2O_9$. It shows a 2:1 ordering at the B sites and is thus the first example of osmate perovskites exhibiting such ordering. $Sr_3CaOs_2O_9$ shows long-range antiferromagnetic ordering at an unexpectedly high $T_N$ of ~385 K, which is confirmed by calorimetric and neutron diffraction studies. Such high $T_N$ is surprising in a compound with only 5d magnetic atoms and is attributed here to the sizeable interlayer interaction. Thus, the recently growing body of Os-based perovskites with high transition temperatures offers exciting avenues for discovering interesting magnetic materials and studying their intriguing interplay of spin, orbital, and lattice degrees of freedom.

### ■ ASSOCIATED CONTENT

**Supporting Information**

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.chemmater.2c00740.

Elemental analysis and thermal analysis results; RT powder XRD and Rietveld fit data; magnetic susceptibility of $Sr_3CaOs_2O_9$ at several applied magnetic fields; High-temperature resistivity data, experimental antiferromagnetic structures; three first-nearest and three second-nearest neighbors of intraplane and two neighbors of interplane for $Sr_3CaOs_2O_9$; Rietveld refinement parameters for diffraction data; atomic parameters and bond lengths obtained from Rietveld refinement; irreducible presentations; theoretically calculated energy differences of two antiferromagnetic structures; and crystallographic data (PDF)

### ■ AUTHOR INFORMATION

**Corresponding Author**

Martin Jansen – Max Planck Institute for Chemical Physics of Solids, 01187 Dresden, Germany; Max Planck Institute for
Solid State Research, 70569 Stuttgart, Germany;
● orcid.org/0000-0003-0762-0985; Email: M.Jansen@
fkf.mpg.de

## Authors

**Gohil S. Thakur** — Max Planck Institute for Chemical Physics of Solids, 01187 Dresden, Germany; Faculty of Chemistry and Food Chemistry, Technical University, 01069 Dresden, Germany;
● orcid.org/0000-0002-1362-2357

**Thomas C. Hansen** — Institut Laue-Langevin, 38000 Grenoble, France;
● orcid.org/0000-0003-4611-2393

**Walter Schnelle** — Max Planck Institute for Chemical Physics of Solids, 01187 Dresden, Germany

**Shuping Guo** — Institute for Theoretical Solid State Physics, Leibniz IFW Dresden, 01069 Dresden, Germany;
● orcid.org/0000-0003-4536-6893

**Oleg Janson** — Institute for Theoretical Solid State Physics, Leibniz IFW Dresden, 01069 Dresden, Germany

**Jeroen van den Brink** — Institute for Theoretical Solid State Physics, Leibniz IFW Dresden, 01069 Dresden, Germany

**Claudia Felser** — Max Planck Institute for Chemical Physics of Solids, 01187 Dresden, Germany

Complete contact information is available at:
https://pubs.acs.org/10.1021/acs.chemmater.2c00740

## Author Contributions

The manuscript was written through contributions of all the authors. All authors have given approval to the final version of the manuscript.

## Funding

Open access funded by Max Planck Society.

## Notes

The authors declare no competing financial interest.

## ACKNOWLEDGMENTS

G.S.T. thank the Würzburg-Dresden Cluster of Excellence ct.qmat (project no: F009161-553-1A0-1030102) for partial financial support. The authors acknowledge the financial support from the German Research Foundation (Deutsche Forschungsgemeinschaft, DFG) via SFB1143 project no. A5 and under Germany's Excellence Strategy through Würzburg-Dresden Cluster of Excellence on Complexity and Topology in Quantum Matter—ct.qmat (EXC 2147, project no. 390858490). The authors thank Marcus Schmidt for thermogravimetric analysis and differential scanning calorimetry measurements. The authors thank Ulrike Nitzsche for technical assistance.

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