Widely Spaced Planes of Magnetic Dimers in the Ba6Y2Rh2Ti2O17-δ Hexagonal Perovskite
SStructure and magnetism of the Ba Y Rh Ti O hexagonal perovskite Loi T. Nguyen, Daniel B. Straus and R. J. Cava
Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA
ABSTRACT
We report the synthesis and initial characterization of Ba Y Rh Ti O , a hexagonal perovskite, prepared at ambient pressure in air at 1500 o C. In the crystal structure, face-sharing RhO octahedra form Rh O dimers in a layered triangular geometry. The material displays a small effective magnetic moment, which must arise from the Rh ions present, and a negative Curie-Weiss temperature. The transport band gap and optical band gaps are very similar, near 0.16 eV, and thus Ba Y Rh Ti O is a semiconductor. A large upturn in the heat capacity at temperatures below 1 K, suppressed by magnetic fields larger than 2 Tesla, is observed. A very large Sommerfeld-like T-linear term in the specific heat (γ=166 mJ/mol f.u-K ) is seen, although the material is highly insulating at low temperatures. These results suggest the possibility of a spin liquid ground state in this material. Keywords : hexagonal perovskite, face-sharing octahedra, magnetic rhodium oxide, spin liquid.
NTRODUCTION
After the discovery of superconductivity in Na
CoO .1.6H O , the search for structurally and chemically related superconductors became of significant interest . A metal-insulator transition was found in Na x RhO at x = 0.67, for example, but superconductivity was not observed . This was attributed by some researchers to the strong spin-orbit coupling present for the 4 d transition metal Rh, which defeats the superconductivity . Rhodium-based compounds exhibit a variety of other interesting properties, however, from photocatalyst and photo-electrolytic electrodes (e.g. LuRhO and AgRhO ) to intermetallic superconductors, Y Rh Si (T c =4.4 K) , Zr Rh (T c =11.2 K) , TaRh B (T c =5.8 K) and NbRh B (T c =7.6 K) . Spin liquids display a novel magnetic state in which the magnetic moments remain fluctuating down to temperatures near absolute zero. In quantum spin liquids (QSLs) the magnetic wave functions are entangled at low temperatures. Although at the time of this writing no QSL material is universally accepted, candidates are frequently members of the magnetically frustrated family of materials, because in such cases there is a degeneracy of equivalent energy states present at low temperatures. Although there appears to be no single experimental characteristic that signifies the presence of a QSL state, candidates often show the absence of conventional magnetic ordering, a broad continuum of magnetic excitations in inelastic neutron scattering spectra, and large upturns in the heat capacity at low temperatures. QSL candidates have been proposed based on copper, cobalt, ruthenium, iridium, and rare earth ions . Here we report a new kind of candidate material, a rhodium-oxide-based compound that shows some of the characteristics of a spin liquid. This rhodate, Ba Y Rh Ti O synthesized in air at ambient pressure at 1500 o C, is an ordered hexagonal perovskite analogous to Ba Y Ti O . The crystal structure is based on Rh O dimers, made from two face-sharing RhO octahedra, in a ayered triangular array. The distance between two Rh ions within the dimer is about 2.6 Å, allowing for strong Rh-Rh interactions. The triangular layers of dimers are well-separated by non-magnetic YO octahedra and TiO tetrahedra. Hence, there may be competition between the magnetic interactions within the Rh O dimers and the in-plane and out of plane magnetic interactions in the three-dimensional structure made from stacked triangular layers of dimers. The material is a semiconductor with transport and optical band gaps of about 0.16 eV, effective magnetic moment of about 1.5 µB per formula unit, a Curie Weiss theta of about -2.8 K, no magnetic ordering observed down to 0.35 K, and an anomalous heat capacity is seen at low temperatures. The magnetic moment, which is low but present, makes this a rare but not unique example of a magnetic rhodium oxide . The heat capacity at low temperatures (~0.35 K) follows a power law with an exponent of 0.57, much smaller than the expected value of 3, and shows an upturn under zero applied magnetic field that is suppressed by applied fields larger than 2 Tesla. Only about 1/3 of the magnetic entropy expected for a spin ½ system is recovered on heating from very low temperatures in zero field, suggesting that spin fluctuations hold on to a significant amount of magnetic entropy at very low temperatures in this material. Finally, the presence of heavy quasiparticles in this electrically insulating spin liquid candidate is supported by the large observed Sommerfeld constant, 166 mJ/mol f.u-K . . EXPERIMENTAL
A polycrystalline sample of Ba Y Rh Ti O was synthesized by solid-state reaction using BaCO (dried in the oven at 120 o C for 3 days), Y O (dried in the furnace at 1000 o C overnight), RhO and TiO (Alfa Aesar, 99.9%, 99.99%, 99.9%, and 99.9%, respectively) in stoichiometric ratios as starting materials. The reagents were mixed thoroughly, placed in alumina crucibles, and heated in air at 900 °C for 24 hours. The resulting powder was reground, pressed into pellets, and eated in air at 1100, 1300 and 1500°C for 24 hours at each temperature. The phase purity and crystal structure were determined through powder X-ray diffraction (PXRD) using a Bruker D8 Advance Eco with Cu Kα radiation and a LynxEye-XE detector. The structure refinement was performed with GSAS . The crystal structure drawings were created by using the program VESTA . The SEM/EDS characterization was performed by using a XL30 FEG-SEM equipped with an EVEX EDS in-situ Tensile Stage, and a Gatan MiniCL imaging system. This high-resolution field-emission SEM has an optimum image resolution of 2nm. The EDS system provides X-ray acquisition characteristics sufficient for obtaining a high-resolution two-dimensional elemental distribution map over the sample surface. The magnetic susceptibility of Ba Y Rh Ti O powder was measured in a Quantum Design Physical Property Measurement System (PPMS) DynaCool equipped with a VSM option. The magnetic susceptibilities between 1.8 and 300 K, defined as M/H, where M is the sample magnetization and H is the applied field, were measured at different applied magnetic fields. The sample was pressed, sintered, and cut into pieces with the approximate size 1.0 × 2.0 × 1.0 mm . for the transport measurement. The resistivity was measured by the dc four-contact method in the temperature range 200 to 300 K in the PPMS. Four Pt contact wires were connected to the samples using silver paint. Below 200 K the sample resistance was too high to be accurately characterized. The specific heat was measured from 200 to 1.8 K in the PPMS DynaCool equipped with a heat capacity option, and to temperatures down to 0.35 K by using a He system in the PPMS. The optical bandgap was determined by using a Thermo Scientific Nicolet 6700 FT-IR spectrometer with an ATR sample holder. The bandgap was estimated from the observed absorption data based on the relation αhυ = A (hυ – E g ) n , where A is a constant, α is the absorption oefficient (cm −1 ), E g is the bandgap, and n is 0.5 for a direct transition (n = 2 for an indirect transition). Thermogravimetric Analysis (TGA) was conducted using a TA Instruments SDT Q600 under flowing Ar:H (95:5%). Around 10 mg of Ba Y Rh Ti O was loaded into an alumina pan and heated from 25℃ to 1000℃ at the rate 0.5℃/hr. The sample was kept at 1000℃ for 30 min, then cooled to room temperature at the rate 5℃/hr. The phase assemblage of the final mixture was determined by using powder XRD. RESULTS and DISCUSSION Ba Y Rh Ti O crystallizes in a hexagonal structure with the space group P / mmc (No. 194). Its powder X-ray diffraction pattern and structural refinement are shown in Figure 1 . The structure of Ba Y Ti O was employed as a starting model for the refinement - in the current case the Ti occupies only the layers of tetrahedra while only the Rh are found in the dimers. The structural refinement is of excellent quality and indicated the absence of Ti/Rh/Y mixing disorder to within the sensitivity of the method (a few percent). The inset to Figure 1 shows the SEM and EDS images collected on the powder sample to confirm that all the elements are present in a single substance. While a variety of Rh compounds have been synthesized under high pressure, such as BaRhO , CaRhO , SrRu Rh x O , Sr Rh O , and Lu Rh O , to our knowledge, Ba Y Rh Ti O appears to be the only Rh O dimer compound synthesized at ambient pressure. Figure 1b shows the TGA data of Ba Y Rh Ti O , reduced under the flow of Ar:H (95:5%) from 25 to 1000 o C. The final product is a mixture of Rh, BaTiO and Ba Y O , identified by using power XRD. The mass loss is calculated to be around 3.5%, implying that the empirical formula may be oxygen deficient, at Ba Y Rh Ti O (δ ≈ 0.5). The crystal structure of Ba Y Rh Ti O is shown in Figure 2a , where two RhO octahedra are face-sharing to form a Rh O dimer. In one unit cell, there are two Rh O dimers linked by YO octahedra and TiO tetrahedra. The Rh -based dimers are arranged in a triangular lattice as shown in Figure 2b . The distance between two Rh atoms within a dimer is quite short (2.60 Å) indicating strong chemical interactions between them or even a metal-metal bond. This short Rh-Rh bond length has previously been seen in Sr Rh O , which displays Rh –O chains in its crystal structure. There are two kinds of Rh-O bond lengths in the Rh O dimer in Ba Y Rh Ti O : 2.21 Å to the outer oxygens, and 2.16 Å to the oxygens between the Rh ions, consistent with the presence of strong Rh-Rh interactions, which shorten the Rh-O bonds. Thus there are likely three types of dominant magnetic interactions in Ba Y Rh Ti O , dimer-dimer in-plane interactions (d = 5.92 Å), plane to plane interactions of the dimers (d=14.75 Å, and interactions within the dimers (d = 2.60 Å) as shown in Figures 2a-c . The structural parameters determined in the refinement are summarized in
Table 1 and selected bond lengths are listed in
Table 2 . The temperature-dependent magnetic susceptibility of Ba Y Rh Ti O measured under the applied magnetic field of 2 kOe is shown in Figure 3 . By applied fields of 5 T, however (data not shown) the low temperature susceptibility appears to be lower by a factor of 2. This is due to curvature in the M vs H behavior in high fields and the definition of susceptibility as ΔM/ΔH and does not represent the intrinsic low field susceptibility of this substance. The inset in
Figure 3 shows the magnetization as a function of applied magnetic field from 0-9 T at different temperatures. The M vs. H curves are linear above 10 K, and become curved below 10 K, which agrees well with the deviation observed in the temperature-dependent magnetic susceptibility measured in fields of 2 T and higher. There is no sign of magnetic saturation up to 9 T at temperatures down to 1.8 K. igure 4 shows the magnetic susceptibility of Ba Y Rh Ti O from 1.8-300 K in a 2 kOe applied magnetic field. Above 200 K, the magnetic susceptibility almost reaches zero. Curie-Weiss fitting from 10-50 K results in the Curie-Weiss temperature of -2.8 K and an effective moment of 0.76 μ B /mol-Rh as seen in the inset of Figure 4 . The small negative Curie-Weiss temperature implies the dominance of weak anti-ferromagnetic interactions and the relatively low moment observed compared to that expected in an ionic picture for isolated Rh spin ½ ions (1.73 μ B ) will be of interest in the theoretical treatment of this material. In comparison, in Ba Rh O , the fact that the magnetic susceptibility does not follow the Curie-Weiss law has been attributed to the presence of non-magnetic Rh ions that interrupt the exchange interactions between Rh ions, resulting the disruption in magnetic interactions within a chain . In the rhodate family, Sr RhO known to be the first magnetically ordered Rh compound has the antiferromagnetic transition temperature at 7 K and the effective moment of 1.71 μ B /mol-Rh, as expected for moment of spin ½. Although both Ba Y Rh Ti O and Sr RhO compounds have Rh oxidation state (S = ½), Ba Y Rh Ti O has much smaller Curie-Weiss temperature and effective moment, this implies a delocalization of the moment among the Rh and O in the dimers. The inset in Figure 4 shows the FC/ZFC dc susceptibility in an applied field of 100 Oe. At low field, there is no bifurcation in ZFC/FC susceptibility down to 1.8 K, indicating that there is no spin glass state or structural disorder in Ba Y Rh Ti O . This confirms that there is no mixing between Rh and Ti in the crystal structure. The transmittance data for Ba Y Rh Ti O powder were converted using the Kubelka-Munk method. Fitting to indirect band gap does not produce a reasonable, flat baseline, and thus the fit is done to the direct gap equation. The direct optical band gap is determined from this data o be 0.17 eV by extrapolating the linear absorption region until it intersects with the baseline of the absorption as seen in Figure 5 . The resistivity of Ba Y Rh Ti O is plotted as a function of reciprocal temperature in the inset of Figure 5 . The activation energy of 0.15 eV obtained by fitting the Arrhenius equation, which must be from or to defect states associated with the valence or conduction band, together with the optical data, show that Ba Y Rh Ti O is a semiconductor. Figure 6a shows the heat capacity of Ba Y Rh Ti O from 0.35 to 14 K measured in magnetic fields of 0, 1, 2, 4, 5, 6 and 9 T. An upturn is seen below 3 K that is dramatically influenced in an applied magnetic field. A broad hump typical of the Schottky effect was observed at around 1 K under zero applied magnetic field . A similar upturn feature at the lowest temperatures, suppressed applied magnetic fields, has been observed in some QSL candidates . The low temperature heat capacity approximately obeys a universal scaling law, as shown in Figure 6b . Similar to reported QSL candidates, the heat capacity data of Ba Y Rh Ti O collapse at the critical point of around 0.35 K/T . The power law fitting of heat capacity data in Ba Y Rh Ti O results in the power of 0.57 ( Figure 6c) . This is in contrast to what is seen in conventional magnetic insulators, whose heat capacity is proportional to T . We can rule out the possibility that the nuclear spins of the constituent atoms are the origin of the low temperature heat capacity behavior because the heat capacity of Ba Y Ti O obeys the T -behavior below 7 K and does not show the upturn and ( Figure 6d ). Moreover, the heat capacity values at low temperatures of TiO , Y O , BaO and RhO are many orders of magnitude smaller than that of Ba Y Rh Ti O
17 45–48 . On subtraction of the phonon contribution, the measured heat capacity data under zero applied magnetic field can be used to calculate the magnetic entropy in Ba Y Rh Ti O , as shown in Figure 7 . The heat capacity of Ba Y Ti O up to 12 K (where the heat capacity data for both a Y Rh Ti O and Ba Y Ti O intersect) accounts for the phonon contribution. Surprisingly, the magnetic entropy only reaches 0.32 Rln2 by 12 K. This indicates that a tremendous amount of magnetic entropy is present at lower temperatures in this material. In the inset of Figure 7 , C/T as function of T at zero applied magnetic field results in a Sommerfeld constant of 166 mJ/mol f.u-K (or 83 mJ/mol Rh-K ). This large value implies that heavy mass quasiparticles are present in this material. Compared to the heavy fermion superconductor Sr RuO (γ = 39 mJ/mol Ru-K ) or the Sr Rh O layer perovskite (γ = 16 mJ/mol Rh-K ) or Sr Rh O (γ = 30 mJ/mol-K ) , Ba Y Rh Ti O , which is an electrical insulator, has a much larger Sommerfeld constant. This could be an interesting result for physicists and theorists to investigate. CONCLUSIONS Ba Y Rh Ti O , synthesized by a solid state method in air at ambient pressure crystallizes in a hexagonal perovskite unit cell in the P / mmc space group. The material has a small effective moment, 0.76 μ B /mol-Rh, or 1.5 μ B /dimer, compared to 1.73 μ B /mol-Rh expected for a purely ionic Rh (spin ½) system. The small negative Curie-Weiss temperature may be due to a competition between antiferromagnetic and ferromagnetic interactions, but it may alternatively indicate the dominance of very weak antiferromagnetic interactions in the material. The magnetic susceptibility and heat capacity measurements indicate that magnetic ordering is absent down to 0.35 K. The large Sommerfeld constant observed may come from the presence of a high density of low energy states, which may be due to the presence of strong magnetic fluctuations at very low temperature. The heat capacity shows an upturn under zero field at the lowest temperatures measured that is suppressed by applied fields larger than 2 T, a significant characteristic of QSL candidates. The approximate data collapse in scaled heat capacity curves further suggests that Ba Y Rh Ti O may host a spin liquid ground state. Thus growing crystals of this material will e of interest for thermal conductivity and inelastic magnetic neutron scattering experiments, as will µSR studies. Furthermore, the possible presence of oxygen vacancies, which will significantly impact the number of electrons on the dimers, and thus the magnetism, will be investigated by powder neutron diffraction, and the results will be reported elsewhere. ACKNOWLEDGMENTS
The authors acknowledge the use of Princeton’s Imaging and Analysis Center, which is partially supported by the Princeton Center for Complex Materials, a National Science Foundation (NSF)-MRSEC program (DMR-1420541). All of the research reported here was supported by the Institute of Quantum Matter, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences under Award No. DE-SC0019331.
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Ba1 4f 1 ⅓ ⅔ 0.18094(6) 0.0091(6) Ba2 4f 1 ⅓ ⅔ 0.58950(6) 0.0124(6) Ba3 2a 1 0 0 0 0.0435(14) Ba4 2b 1 0 0 ¼ 0.0119(10) Rh 4f 1 ⅓ ⅔ 0.70592(10) 0.0455(10) Ti 4f 1 ⅓ ⅔ 0.05146(24) 0.0218(20) Y 4e 1 0 0 0.12544(10) 0.0067(10) O1 12k 1 0.1930(10) 0.3861(19) 0.42554(31) 0.0311(20) O2 12k 1 0.1629(10) 0.3258(21) 0.83969(31) 0.0311(20) O3 6h 1 0.4982(11) -0.0035(22) ¼ 0.0311(20) O4 4f 1 ⅓ ⅔ 0.5072(6) 0.0311(20) a = b = 5.920426(20) Å, c = 29.49740(18) Å, V = 895.407(5) Å , α = β = 90 ° , γ = 120 ° . χ = 3.71, R wp = 11.18%, R p = 7.91%, R F2 = 8.91% able 2 : Selected interatomic distances (Å) for Ba Y Rh Ti O at 300 K. Interatomic distance (Å)