Download Frustrated S = 1 On A Diamond Lattice

Frustrated S = 1 On A Diamond Lattice
J. R. Chamorro1,2 and T. M. McQueen1,2,3,4
1
Department of Chemistry, 2Institute for Quantum Matter, 3Department of Physics and Astronomy, and 4Department
of Materials Science and Engineering; The Johns Hopkins University, Baltimore MD 21218
We report the discovery of an S = 1 diamond lattice in NiRh2O4. This spinel undergoes a cubic to
tetragonal phase transition at T = 440 K that leaves all nearest neighbor interactions equivalent. In
the tetragonal phase, magnetization measurements show a Ni2+ effective moment of peff = 3.3(1) and
dominant antiferromagnetic interactions with θCW = -10.0(7) K. No phase transition to a long range
magnetically ordered state is observed by specific heat measurements down to T = 0.1 K. Thus
NiRh2O4 provides a platform on which to explore the rich physics of integer spin on the diamond
lattice, and is the first candidate topological paramagnet.
The realization that not all insulators are equivalent, i.e. that there are multiple classes of insulators not
adiabatically connected to each other and are thus topologically distinct, has resulted in numerous
discoveries. These include 2D and 3D topological insulators [1-4], topological crystalline insulators [5],
Dirac semimetals [6-7], Weyl semimetals [8-9], candidate Majorana fermions [10], and candidate
topological superconductors [11-13]. This, in turn, has spurred significant theoretical efforts to apply the
tools of topological classification to other areas.
Competing magnetic interactions between ion spins in a structure can lead to geometric magnetic
frustration, due to the inability of the system to satisfy all pairwise interactions. Since frustration prevents
the emergence of a single low energy ground state, it enables a variety of exotic states of matter, such as
valence bond solids, spin liquids, and chiral spin and spin-ice materials [14 – 21]. Recently, there have been
several concrete predictions of novel topological states in materials of greater than one dimension in which
electron correlations are the dominant interaction, including topological magnons [22-23] and the
topological paramagnet [24].
The physics of one-dimensional half-integer spin chains has been extensively explored, and these
systems are known to have no magnetic excitation gaps [25]. In contrast, integer spin chains, so called
Haldane chains, do indeed possess excitation gaps and also have topological character manifested at either
ends of the chain [26-27]. These chains are, therefore, realizations of systems that harbor both topologically
non-trivial and correlated electron behaviors. Recent work has suggested that a diamond lattice made up of
ions carrying S = 1 would result in a structure containing fluctuating and interconnected Haldane chains,
where non-trivial, topological states would arise at the ends of the chains [24]. Such an arrangement may
give rise to a topological state not electronic in nature, but rather magnetic: a topological paramagnet. While
other frustrated three-dimensional S = 1 materials are known [28-29], no materials with S = 1 on the
diamond lattice are known to date. Just as in one dimension, there must exist strongly correlated behavior
in the S = 1 diamond lattice material in order to ensure the emergence of a topologically non-trivial state.
The aforementioned work argues that the material must also show geometric magnetic frustration.
The basic building block of geometric frustration is to have spins laid out on a lattice where all
interactions cannot be simultaneously satisfied, such as those containing triangles or tetrahedra. The AB2X4
spinel structure contains two lattices primed to host geometrically frustrated magnetism: a diamond lattice
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of A-site ions and a pyrochlore lattice of B-site ions, as shown in Fig. 1a. The A-site diamond lattice is
bipartite, composed of two interlacing fcc sublattices, and can be viewed as the three-dimensional analogue
of a honeycomb lattice. There are four nearest neighbor (NN) interactions between adjacent magnetic ions
in separate fcc sublattices, and twelve next nearest neighbor (NNN) interactions between adjacent magnetic
ions within each fcc sublattice. As with the honeycomb lattice, a Néel ground state is expected in the
presence of solely NN Heisenberg interactions. However, the Néel state is destabilized in the presence of
NNN Heisenberg interactions that are at least 1/8th as strong as the NN interactions [30].
There are many known spinel structures with magnetic A-ions that exhibit geometric magnetic
frustration, but none are S = 1 [31-36]. There are, however, known spinels with integer spin on the A-site,
such as FeSc2S4. This material is of particular interest due to a Jahn-Teller (JT) active hole in the low energy
e orbitals, which enables frustration of orbital degrees of freedom. In combination with the spin frustration
enabled by the diamond lattice, FeSc2S4 was predicted and found to be close to or a realization of a spinorbital liquid [31, 37]. Ni2+ (d8) on the A-site should also yield curious spin orbital physics as there is an
orbital degree of freedom arising from the t2 orbitals, but closer to the quantum limit, as S = 1 instead of S
= 2. However, putting Ni2+ on the A site of a spinel is exceptionally difficult: crystal field stabilization
energies strongly favor Ni2+ on the B-site, which has octahedral coordination. Thus, virtually all nickel
spinels are in fact inverse spinels, such as in Ga(Ni0.5Ga0.5)2O4 (NiGa2O4) [38].
An exception to this pattern is NiRh2O4, which contains Ni2+ on the A site in a diamond lattice. Ni2+
is forced onto the A-site by the very large octahedral crystal field stabilization energy gained by putting
non-magnetic, low spin Rh3+ (d6) on the octahedrally-coordinated B-site. Previous reports on the synthesis
and physical properties of NiRh2O4 are scant. They suggest that, at elevated temperatures, NiRh2O4 adopts
the ideal cubic spinel structure, but that at T ~ 380 K it undergoes a cubic-to-tetragonal phase transition
[39], possibly associated with a JT distortion around the Ni2+ ions [40]. There is possible antiferromagnetic
order at TN = 18 K [41], although the rollover in the susceptibility is broad, and the local hyperfine field
measured by 61Ni Mössbauer is very small, μ0H = 2.5 T [42]. These observations suggest that either only a
small portion of the total moment is ordered, or that the entirely of the moment remains fluxional, similar
to the behavior found for FeSc2S4 [31, 37]. Though the NN interactions (JNN) remain equivalent across this
transition, NNN interactions split into a set of four interactions within a plane (JNNN1) and a set of eight
interactions out of that plane (JNNN2). The superexchange pathways for all three interactions are shown in
Fig. 1b, shown in a √2 × √2 expanded representation of the tetragonal unit cell of NiRh2O4. The NN and
NNN interactions are both mediated by -O-Rh-O- pathways, implying that NN and NNN interactions can
be of similar magnitude.
Here we report x-ray diffraction, magnetization, and specific heat measurements on NiRh2O4, along
with band structure calculation results. We show that this S = 1 diamond lattice material shows no signs of
a phase transition to long range magnetic order down to T = 0.1 K, and instead a gradual loss of entropy
over a wide temperature range. Magnetization data indicate a peff = 3.26(14) and a θCW = -10.0(7) K. The
frustration parameter, used as a qualitative measure of frustration in magnetic systems and defined as f =
|𝜃𝑊 |
𝑇𝑁
, is at least f ≥ 100 in this system, which is large in comparison to other known frustrated A-site spinel
systems [43-44]. High resolution x-ray diffraction data confirm the complete occupancy of the A-site by
Ni2+ and thus confirm NiRh2O4 as the first S = 1 diamond lattice material and concomitantly the first
candidate topological paramagnet.
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Polycrystalline NiRh2O4 was synthesized by sintering a stoichiometric mixture of green NiO
(99.998%) and Rh2O3 (99.99%) in air at 1323 K for six days. The sample was reground thrice to ensure
homogeneity. High resolution synchrotron x-ray diffraction data was collected at the Argonne National
Laboratory 11-BM Advanced Photon Source at temperatures T = 100, 160, 200, 295, 360, and 460 K.
Rietveld refinements were performed on all data sets and reveal a cubic structure for the high temperature
phase and a tetragonal structure for the low temperature phase; select results shown in Fig. 2a and Table
1. A small (~ 0.2%) NiO impurity was found only with the high resolution x-ray diffraction measurements
at 11-BM, and is included in all Rietveld refinements. The elevated Rwp values in each fit can be ascribed
to the peak shapes generated by the synchrotron data collection, a problem which has been observed in
other materials [45]. The high temperature phase, at T = 460 K, has cubic symmetry with space group
Fd3m. This structure is in agreement with previous reports, with Ni2+ in an ideal tetrahedral coordination
by O2-. Inclusion of anti-site Ni/Rh mixing and off-stoichiometry (e.g. excess Ni on Rh site) did not improve
the quality of the refinement. This is in agreement with the synthesis, in which a 1:2 stoichiometric ratio of
Ni:Rh was used. The low temperature phase, observed at all other measured temperatures, has tetragonal
𝑐𝑡𝑒𝑡𝑟𝑎𝑔𝑜𝑛𝑎𝑙
𝑐
symmetry with space group I41/amd. The 𝑎𝑐𝑢𝑏𝑖𝑐 = √2𝑎
𝑐𝑢𝑏𝑖𝑐
𝑡𝑒𝑡𝑟𝑎𝑔𝑜𝑛𝑎𝑙
ratio, 1.05, indicates a large (~5%) departure
from cubic symmetry. Initial attempts to fit the data to the previously reported tetragonal model were
unsatisfactory and did not accurately capture the observed Bragg intensities. Further, the literature
structures retained nearly perfect tetrahedral coordination of nickel by oxygen, despite the large departure
from cubic symmetry, instead showing a large distortion around the Rh3+ ions, unexpected on chemical
grounds. As such, possible distortions of the unit cell for the tetragonal phase were explored using the online
resource ISODISTORT [46]. An adequate fit to the data was obtained using a structure in which there is a
buckling of the oxygen atoms in the (0 1 3) plane. This corresponds to a “pinching” of the NiO4 tetrahedra
along the c axis, the bond angles of which are shown in Fig. 2a. The net result of this distortion is that the
NiO4 tetrahedra become more linear with decreasing temperature. This naturally explains the observed
change in c/a ratio, in which the c axis elongates and the a and b axes contract. It is also consistent with the
previously proposed JT distortion, as the site symmetry of the Ni2+ tetrahedra changes from a point group
of Td in the cubic structure to D2d in the tetragonal one. To estimate the thermodynamic parameters of this
phase transition, differential scanning calorimetry (DSC) measurements were carried out in heating mode
using a TA instruments Q2000 DSC, as shown in Fig. 2b. The transition from cubic to tetragonal occurs at
T = 440 K, with an entropy loss of 0.13R, as shown in Fig. 2c. This loss is significantly less than the Rln(3)
that would be expected if the JT distortion completely suppresses the orbital degree of freedom. The
transition temperature is also higher than the T = 380 K previously reported, possibly due to an improvement
in sample stoichiometry.
What is the impact of this structural change on the magnetic ground state? Fig. 3 shows the
magnetic susceptibility, estimated as χ ~M/H with magnetization measured using the ACMS option of a
quantum design physical properties measurement system (PPMS) with an applied field of µ0H = 1 T, of
NiRh2O4 in the tetragonal phase. Nearly perfect Curie-Weiss behavior is observed, and these values agree
with the slopes of M(H) curves measured at T = 2 K and T = 300 K, once the 0.2% NiO contribution is
taken into account. A Curie-Weiss analysis
1
𝜒−𝜒0
1
= 𝐶𝑇−
𝜃𝑊
𝐶
from 1.8 ≤ T ≤ 300 K yields a Weiss
temperature of θCW = -10.0(7) K, indicative of net mean field antiferromagnetic interactions. A
paramagnetic moment of peff = √8𝐶 = 3.26(14) is observed. This value, which arises from the Ni 2+ ions,
agrees with previous reports [39], and is intermediate between the spin-only value of s = 2.83B and the
3
spin-orbital value of 3.67B based on Leff = 1 and S = 1. This is also in agreement with the DSC result,
suggestive of a residual orbital contribution to the effective magnetic moment of Ni2+. A 0 value of 0.0016
emu mol-1 K-1 Oe-1 was used to account for temperature-independent magnetic contributions. Further, there
are no indications of long range magnetic ordering down to T = 1.8 K.
To further understand the behavior of NiRh2O4, specific heat data was collected at constant pressure
using the PPMS heat capacity option, as well as with a dilution refrigerator. The resulting specific heat,
Fig. 4a, over a temperature from 0.1 ≤ T ≤ 300 K, shows no sharp anomalies that would be indicative of
long range magnetic ordering or other phase transitions in the tetragonal phase. To further analyze the
magnetic contributions to the specific heat, we estimated the phonon contribution to the specific heat
through measurements of the non-magnetic analogue ZnRh2O4, synthesized by sintering stoichiometric
amounts of ZnO and Rh2O3 in air at 1273 K for two days with no regrinding, and scaled by 0.97 to account
for the different in atomic mass between nickel and zinc. When the phonon contribution is subtracted, the
excess specific heat of NiRh2O4 is attained. This shows two broad peaks, one with a maximum at T = 1.77
K and the other with a maximum at T = 33.7 K. The total excess entropy is obtained by calculating the
integral of the phonon-subtracted C/T, as shown in Fig. 4b. The entropy crosses S = Rln(3) at T = 90 K,
and plateaus near S = Rln(6) at T = 250 K. This analysis is robust, with the total integrated entropy always
remaining between Rln(5) and Rln(6) independent of the scaling method for the diamagnetic ZnRh 2O4
analog. This exceeds the expected spin only entropy of Rln(3).
The entropy is not recovered uniformly, however. There are three ranges: a low temperature hump
that has a maxima at T = 1.77 K, a higher temperature hump at T = 33.7 K, and a higher temperature
continuum from 120 ≤ T ≤ 300 K. The hump at T = 1.77 K recovers an entropy of ΔS = 0.051R. This small
amount, equivalent to ~1% of free S=1/2 spins, likely originates from vacancies, defect sites, or surface
states. This is further supported by a field dependence at a level commensurate with isolated spins (not
shown). The hump at T = 33.7 K can be semi-quantitatively modeled as a two-level Schottky anomaly,
given by:
𝐶𝑆𝑐ℎ𝑜𝑡𝑡𝑘𝑦
Δ 2
= 𝑂𝑆𝐹 ∙ ( )
𝑇
𝑇
Δ
𝑒𝑇
[1
Δ 2
+ 𝑒𝑇]
∙ 𝑇 −1
Where the difference between the two energy levels Δ = 116(3) K and an overall scale factor OSF = 1.87(7),
which corresponds to an entropy of ΔS = 1.87(7)·Rln(2). This anomaly corresponds to a recovery of ΔS =
1.3R, which is ~75% of the total excess entropy, leaving ~22% (0.4R) in the broad continuum from T =
120 to 300 K. The ΔS = 1.3R entropy contained in the T = 33.7 K hump is somewhat larger than the ΔS =
Rln(2S+1) = Rln(3) = 1.1R spin entropy expected for S = 1 in the absence of orbital degrees of freedom.
This is even excluding the excess entropy in the T = 120 – 300 K range, and indicates a contribution from
either orbital or phonon degrees of freedom (or both).
A possible reconciliation of these observations comes from consideration of the structure, single
ion effects, and first principles DFT calculations. In the tetragonal phase, the magnetic Hamiltonian,
considering antiferromagnetic Heisenberg NN and NNN interactions, can be written as:
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ℋ = 𝐽𝑁𝑁 ∑ 𝑆𝑖 ∙ 𝑆𝑗 + 𝐽𝑁𝑁𝑁1 ∑ 𝑆𝑖 ∙ 𝑆𝑗 + 𝐽𝑁𝑁𝑁2 ∑ 𝑆𝑖 ∙ 𝑆𝑗
〈𝑖𝑗〉
〈〈𝑖𝑗〉〉
〈〈〈𝑖𝑗〉〉〉
Where JNN are the NN interactions, and JNNN1 and JNNN2 are the two distinct NNN interactions. To
estimate the relative magnitude of these exchange interactions, band structure calculations were performed
on tetragonal NiRh2O4 using density functional theory (DFT) with the local density approximation (LDA)
utilizing the Elk all-electron full-potential linearized augmented plane-wave plus local orbitals (FPLAPW+lo) code, with a Hubbard U [47] and spin orbit coupling. The U value was set to 5 eV, typical for
Ni2+ in extended oxides, with a Slater determinant of 0.1 U [48]. The large band gap opened by inclusion
of a U value can be seen in Fig. 5. A minimal supercell with four independent Ni sites was constructed
from the crystallographic structure. Based on this supercell, calculations of the total energy were performed
with eight unique spin configurations. These configurations were set by having local magnetic fields
applied, either up or down, to individual Ni sites in a direction parallel to each local z-axis. The total
energies were converged to < 0.1 meV on a 24 × 24 × 18 k-point mesh. In this case, the calculated per cell
energy differences between different configurations is 25-75 meV, values that are close to the limiting
uncertainties typically associated with DFT, implying that multiple magnetic configurations are all close in
energy in this material. If we take the calculated values for the different spin configurations as accurate, the
J values obtained from this fit are JNN = 2.2 meV, JNNN1 = 1.6 meV, and JNNN2 = – 2.0 meV, where the JNN
and JNNN1 interactions are antiferromagnetic, and JNNN2 is ferromagnetic. The total interaction strength of the
system is – JTOTAL = 4JNN + 4JNNN1 + 8JNNN2 = – 0.8 meV = 9 K. This value is very similar to the Weiss
temperature of -10.0(7) K obtained experimentally, and would imply significant frustration due to
competing nearest neighbor and next nearest neighbor interactions; future inelastic scattering measurements
will provide more accurate parameters from experiment.
A plausible energy level analysis for Ni2+ tetrahedra in NiRh2O4 that is consistent with our
observations is shown in Fig. 6. Shown in Fig. 6a, the tetrahedral crystal field of Ni2+ results in a splitting
of the five orbitals into e and t2 sets. The t2 set then has three separate electron configurations that are well
separated from each other in energy, the lowest of which is the e4t24 single particle level. Placing eight
electrons in the single particle levels gives rise to a series of multi-electron states, the lowest of which is a
spin and orbital triplet 3T1 [49]. SOC and the JT distortion independently split this 3T1 state, as shown in
Fig. 6b. SOC splits 3T1 into four separate multi-electron states, based on their double group symmetries: Γ1,
Γ4, Γ3, and doubly degenerate Γ5 [50]. The JT distortion splits 3T1 into two separate multi-electron states, 3E
and 3A2. 3E is a threefold degenerate manifold composed of Γ5 and Γ1. 3A2 is six-fold degenerate and made
up of Γ1, Γ2, Γ3, Γ4, and Γ5. However, since the SOC and the JT distortion are on comparable energy scales,
competition between these two interactions results in a mixing of multi-electron states. Using their double
group symmetries, one arrives at a ground state manifold as shown in the box in Fig. 6b. Inside the dashed
box, one may observe a total of six states that account for the observed ΔS = Rln(6) in the magnetic specific
heat in NiRh2O4.
A time-reversal-protected three-dimensional topological paramagnetic state has recently been
predicted to emerge in frustrated spin-1 Mott insulators, specifically systems with S = 1 on a diamond
lattice. Wang, et. al., compared the spinels MnAl2O4 and CoAl2O4 and concluded that NiAl2O4 might be a
naturally good candidate. However, as the authors point out, this system is an inverted spinel where Ni 2+
goes into the B-site and forces Al3+ onto the A-site [51]. NiRh2O4, however, does not have appreciable site
mixing and has the Ni2+ ions on the A-site, which are forced there, as aforementioned, by the high octahedral
5
crystal field stabilization energy of low spin Rh3+. It is noted, however, that tetrahedral Ni2+ will have an
orbital degree of freedom that will make the simple Heisenberg spin Hamiltonian inadequate, and our data
does indeed seem to show than there remains an unquenched orbital contribution to the nickel moment.
This does not, however, preclude any novel physics from emerging, but rather emphasizes the need for a
model which includes orbital, and possibly phonon, terms. In short, NiRh2O4 is an S = 1 diamond lattice
system, and is therefore the first candidate topological paramagnet.
In conclusion, we present magnetic susceptibility, specific heat, and synchrotron powder X-ray
diffraction data on NiRh2O4 that confirm spin and orbital frustration despite undergoing a structural phase
transition onset by a JT distortion. No phase transition to long range magnetic order is observed down to T
= 0.1 K, indicating a significant degree of frustration. We have confirmed the tetragonal I41/amd structure
to be the correct structure for low temperatures, and a high temperature ordinary spinel structure with cubic
Fd3m structure. The entropy exceeds the ΔS = Rln(3) value expected for an S = 1 system, indicating a
remaining orbital or phonon contribution to the specific heat. Thus NiRh2O4 is a realization of S = 1 on the
diamond lattice and is a platform for exploring the physics of such a frustrated, three-dimensional integer
spin system, e.g. topological paramagnetism.
The authors thank W. Adam Phelan and Steve Aubuchon (TA Instruments) for assistance with the
differential scanning calorimetry measurements. The work at IQM was supported by the US Department of
Energy, office of Basic Energy Sciences, Division of Materials Sciences and Engineering under grant DEFG02-08ER46544.Use of the Advanced Photon Source at Argonne National Laboratory was supported by
the U. S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No.
DE-AC02-06CH11357.
6
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9
Fig. 1. (a) The structure of a cubic AB2X4 spinel, consisting of a corner-sharing tetrahedral network of Bions and a bipartite diamond lattice of A-ions. The diamond lattice is a 3D version of the honeycomb
network (one hexagon highlighted), and is predicted to exhibit a variety of magnetic ground states
depending on the spin of the A-ion and the magnitudes of the nearest-neighbor JNN and next-nearestneighbor JNNN interactions. (b) NiRh2O4 is a realization of S = 1 on the diamond lattice, with non-magnetic
B-ions (Rh3+, LS d6). Below T = 440 K, NiRh2O4 is tetragonal, preserving equivalent NN interactions, but
with two distinct NNN interactions. Possible superexchange pathways are shown.
10
Fig. 2. Synchrotron XRD and DSC measurements show a cubic to tetragonal phase transition in NiRh 2O4
at T = 440 K. (a) Bond angles for each NiO4 tetrahedron as a function of temperature. The phase transition
corresponds to a Jahn-Teller distortion of the local NiO4 tetrahedron breaking some of the orbital
degeneracy that was present in the cubic phase. (b) High temperature DSC measurement of NiRh2O4,
showing a phonon contribution to the specific heat at high temperature by estimation with a linear fit of the
data. (c) The entropy loss at the transition is ΔS = 0.13R, which is significantly smaller than the 1.1R
required for a fully quenched orbital degree of freedom.
11
Fig. 3. Curie-Weiss analysis of magnetization measurements done on tetrahedral NiRh2O4 under an applied
field µ0H = 1 T. The diamonds indicate data points and the line is the fit. The extracted effective moment
per Ni2+ ion is 3.26(14), greater than the spin only value of 2.83. A Weiss temperature of -10.0(7) K implies
net antiferromagnetic mean field magnetic interactions. There is no indication of magnetic ordering to T =
1.8 K.
12
Fig. 4. (a) Specific heat over temperature (squares) from T = 0.1 to 300 K measured under zero applied
magnetic field. The phonon contribution (triangles) is estimated from ZnRh2O4 to learn the magnetic
contribution (circles). No sharp anomalies that would be indicative of a phase transition are observed down
to T = 0.1 K. The Schottky anomaly fit in the magnetic specific heat is shown with a dashed line. (b)
Integration of C/T yields the entropy of the magnetic component, which far exceeds the expected Rln(3)
spin only value. The bulk of this entropy is recovered in a broad feature centered at T = 33 K, that can be
modeled as a two-level Schottky anomaly with energy difference Δ = 116(3) K and scale factor
corresponding to a contained entropy of ΔS = 1.87(7)·Rln(2).
13
Fig 5. The band structure of NiRh2O4. Applying a U of 5 eV splits the Ni d bands that cross the Fermi level,
effectively opening a gap in the material and making it insulating.
14
Fig. 6. Possible energy level analysis for Ni2+ tetrahedra in NiRh2O4 (a) Tetrahedral crystal field of Ni2+
results in a splitting of the five orbitals into e and t2 sets, with eight electrons that give rise to a multielectron spin and orbital triplet 3T1 ground state. (b) Spin orbit coupling and Jahn-Teller interactions
compete and further split the energy levels of the Td crystal field. Competition between the two interactions
lead to a set of energy levels consistent with the observed S = Rln(6) in the magnetic specific heat in the
tetragonal phase.
15
Table I. Structural analysis of cubic and tetragonal NiRh2O4.Tetrahedral (T = 100 K): I41/amd, a = b =
5.88680 (1) Å, c = 8.71541 (2) Å. Ni: 4a (1/2, 3/4, 3/8); Rh: 8d (1/2, 3/4, 3/4); O: 16h (0, y, z). Rp = 12.9;
Rwp = 15.9; χ2 = 1.3. Cubic (T = 460 K): Fd-3m, a = 8.47674 (1) Å. Ni: 8a (0, 0, 0); Rh: 16d (5/8, 5/8, 5/8);
O: 32e (x, x, x). Rp = 14.6; Rwp = 16.9; χ2 = 1.4. All occupancies were held at unity in final refinements.
Ni Biso
Rh Biso
Ox
Oy
Oz
O Biso
T = 100 K
0.0626 (1)
0.1593 (1)
0.000
0.51145(23)
-0.26682(14)
0.144 (1)
T = 460 K
0.6601 (1)
0.6143 (1)
0.38255 (11)
0.925 (1)
16