Abstract
With large spinorbit coupling, the electron configuration in dmetal oxides is prone to highly anisotropic exchange interactions and exotic magnetic properties. In 5d^{5} iridates, given the existing variety of crystal structures, the magnetic anisotropy can be tuned from antisymmetric to symmetric Kitaevtype, with interaction strengths that outsize the isotropic terms. By manybody electronicstructure calculations we here address the nature of the magnetic exchange and the intriguing spinglass behavior of Li_{2}RhO_{3}, a 4d^{5} honeycomb oxide. For pristine crystals without RhLi site inversion, we predict a dimerized ground state as in the isostructural 5d^{5} iridate Li_{2}IrO_{3}, with triplet spin dimers effectively placed on a frustrated triangular lattice. With RhLi antisite disorder, we explain the observed spinglass phase as a superposition of different, nearly degenerate symmetrybroken configurations.
Introduction
For dmetal compounds with localized magnetic moments, basic guidelines to soothsay the sign of the nearestneighbor (NN) magnetic exchange interactions, i. e., the AndersonGoodenoughKanamori rules^{1,2,3}, were laid down back in the 1950’s. With one single bridging anion and halffilled d states these rules safely predict antiferromagnetic (AF) exchange interactions, as is indeed encountered in numerous magnetic Mott insulators. It is however much harder to anticipate the sign of the couplings for geometries with two bridging ligands and bond angles close to 90°. Illustrative recent examples are the 5d honeycomb systems Na_{2}IrO_{3} and Li_{2}IrO_{3}. The signs of the NN Heisenberg J and of the additional symmetric Kitaev anisotropy K are intensely debated in these iridates, with both J < 0, K > 0^{4,5,6} and J > 0, K < 0^{7,8,9,10,11,12} sets of parameters being used to explain the available experimental data.
The sizable Kitaev interactions, that is, uniaxial symmetric terms that cyclically permute on the bonds of a particular hexagonal ring^{13,14,15}, are associated to strong frustration effects and unconventional magnetic ground states displaying, for example, noncollinear order, incommensurability, or spinliquid behavior^{4,5,6,7,8,11,12,15,16,17}. Obviously, in the context of electronicstructure computational methods, such features cannot be thoroughly addressed by periodic totalenergy calculations for a given set of predetermined spin configurations. A much more effective strategy is to first focus on individual pairs of NN dmetal sites and obtain reliable values for the associated effective magnetic couplings by using ab initio manybody quantum chemistry (QC) machinery (for a recent review, see ref. 18). The computed exchange parameters can be subsequently fed to effective spin Hamiltonians to be solved for larger sets of magnetically active lattice sites. Such an approach, earlier, allowed us to establish the signs plus the relative strengths of the Heisenberg and Kitaev interactions in both Na_{2}IrO_{3} and Li_{2}IrO_{3} and to additionally rationalize the qualitatively different types of AF orders in these two 5d^{5} honeycomb iridates^{16,17}.
The related 4d^{5} honeycomb compound Li_{2}RhO_{3} is even more puzzling because it features no sign of longrange magnetic order. Instead, an experimental study suggests the presence of a spinglass ground state^{19}. While the spinorbit couplings (SOC’s) are still sizable for the 4d shell and may in principle give rise on the honeycomb lattice to compelling Kitaev physics, to date no conclusive evidence is in this respect available for Li_{2}RhO_{3}. To shed light on the nature of the essential exchange interactions in Li_{2}RhO_{3} we here carry out detailed ab initio QC calculations. We show that large trigonal splittings within the Rh t_{2g} shell, comparable with the strength of the SOC, dismiss a simple picture based on j_{eff} = 1/2 and j_{eff} = 3/2 effective states^{14,20,21,22}. The magnetic properties of the system can still be described, however, in terms of pseudospins. The calculations earmark Li_{2}RhO_{3} as a 4delectron system with remarkably large anisotropic magnetic couplings, in particular, FM Kitaev interactions of up to 10–15 meV. The isotropic Heisenberg exchange, on the other hand, features opposite signs on the two sets of structurally distinct links of Rh NN’s. This sign modulation of the NN Heisenberg interactions, with strong ferromagnetic (FM) J’s for one type of RhRh bonds and weaker AF couplings for the other pairs of adjacent Rh sites, enables the initial hexagonal network to be mapped onto an effective model of spin1 dimers on a frustrated triangular lattice. We further address the issue of RhLi antisite disorder in samples of Li_{2}RhO_{3}. By exactdiagonalization (ED) calculations for an extended spin model that also includes second and third neighbor couplings, we show that the experimentally observed spinglass behavior can be rationalized as a superposition of different nearlydegenerate symmetrybroken states arising at finite concentration of inplane spin vacancies.
Results
Rh^{4+} 4d^{5} electronic structure
The tetravalent rhodium ions in Li_{2}RhO_{3} display a 4d^{5} valence electron configuration, octahedral ligand coordination and bonding through two bridging ligands. In the simplest picture, i.e., for sufficiently large Rh t_{2g} − e_{g} splittings and degenerate t_{2g} levels, the groundstate electron configuration at each site is a effective j_{eff} = 1/2 spinorbit doublet^{14,20,21,22}. For 5d^{5} ions in a variety of threedimensional, layered and chainlike oxides, ab initio QC electronicstructure calculations yield excitation energies of 0.6–0.9 eV for the transitions between the j ≈ 1/2 and split j ≈ 3/2 levels^{23,24,25,26} and indicate values of 0.45–0.5 eV for the strength of the SOC λ, in agreement with earlier estimates^{27}. Sharp features in the range of 0.6–0.9 eV are indeed found in the resonant xray scattering spectra^{23,24,25,28}.
The validity of the j_{eff} = 1/2 approximation for the ground state of Li_{2}RhO_{3} is however questionable since the SOC is substantially weaker for 4d elements. Indeed our QC calculations (see Table 1) indicate Rh t_{2g} splittings δ ≈ 0.11 eV, close to values of 0.14–0.16 eV estimated for λ in various Rh^{4+} oxides^{26,29}. For the ab initio QC investigation we employed multiconfiguration completeactivespace selfconsistentfield (CASSCF) and multireference configurationinteraction (MRCI) calculations^{30}, see Supplemental Material (SM) and refs 23,26. With δ and λ parameters of similar size, the j_{eff} = 1/2 and j_{eff} = 3/2 states are strongly admixed, as discussed in earlier work^{20,31} and illustrated in Table 1. In particular, for the relativistic groundstate wave function the t_{2g} hole is not equally distributed among the three Rh t_{2g} levels as for the “true” j_{eff} = 1/2 ground state^{20,21} but displays predominant d_{xy} character, close to 60%.
Magnetic couplings between two adjacent Rh^{4+} ions
Interestingly, while the results for the onsite 4d^{5} excitations are quite different as compared to the 5d^{5} excitation energies^{23}, the computed intersite effective interactions are qualitatively similar to those obtained for the 5d^{5} honeycomb iridate Li_{2}IrO_{3}^{17}. The intersite exchange couplings were estimated by MRCI + SOC calculations for embedded fragments having two edgesharing IrO_{6} octahedra in the active region. As described in earlier work^{16,17,32} and in SM, the ab initio QC data for the lowest four spinorbit states describing the magnetic spectrum of two NN octahedra is mapped in our scheme onto an effective spin Hamiltonian including both isotropic Heisenberg exchange and symmetric anisotropy. Yet the spinorbit calculations, CASSCF or MRCI, incorporate all nine triplet and nine singlet states that arise from the twosite configuration.
For onsite Kramersdoublet configurations, the most general symmetryallowed form of the effective spin Hamiltonian, for a pair of NN ions, is
where , are 1/2 pseudospin operators, J is the isotropic Heisenberg interaction, K the Kitaev coupling and the coefficients are offdiagonal elements of the symmetric anisotropic exchange matrix with . The antisymmetric anisotropic term vanishes since the crystallographic data reported in ref. 33 indicate overall C_{2 h} pointgroup symmetry for one block of NN RhO_{6} octahedra, green (B1) bonds in Fig. 1 and only slight deviations from C_{2 h} for the other type of NN’s, blue (B2 and B3) bonds in Fig. 1. For C_{2 h} symmetry of the RhRh link, . We note that in (1) α and β stand for components in the local, Kitaev bond reference frame. The z axis is here perpendicular to the Rh_{2}O_{2} plaquette (see SM and refs 14,16,17).
Relative energies for the four lowlying states describing the magnetic spectrum of two NN octahedra and the resulting effective coupling constants are listed in Table 2. For the effective picture of pseudospins assumed in Eq. (1), the set of four eigenfunctions contains the singlet and the triplet components , , . In C_{2 h} symmetry, the “full” spinorbit wave functions associated to , , and transform according to the A_{g}, B_{u}, B_{u} and A_{u} irreducible representations, respectively. Since two of the triplet terms may interact, the most compact way to express the eigenstates of (1) is then , , and . The angle parametrizes the amount of mixing, related to finite offdiagonal couplings. This degree of admixture is determined by analysis of the full QC spinorbit wave functions. The effective parameters provided in Table 2 are obtained for each type of RhRh link by using the E_{1}, E_{2}, E_{3}, E_{S} MRCI relative energies and the mixing coefficients (see SM).
For B1 links, we find that both J and K are FM. While by MRCI calculations K always comes FM in spinorbit coupled honeycomb systems^{16,17}, the FM J for the B1 bonds has much to do with the peculiar kind of dependence on the amount of trigonal squashing of the oxygen octahedra and consequently on the variation of the RhORh angles of the Rh_{2}O_{2} plaquette. The latter increase to values larger than 90° for finite trigonal compression. This dependence of the NN J on the RhORh bond angles is illustrated in Fig. 2 for a simplified structural model of Li_{2}RhO_{3} where the RhO bond lengths are all the same, set to the average bond length in the experimental crystal structure^{33}. It is seen that J displays a parabolic behavior, with a minimum of about −5 meV in the interval 92–93° and a change of sign to AF couplings around 96°. For the B1 RhRh links, the RhORh bond angle is 93.4°, close to the value that defines the minimum in Fig. 2. The difference between the ≈ − 5 meV minimum of Fig. 2 and the ≈ − 10 meV result listed in Table 2 comes from additional distortions of the O octahedra in the actual structure (see the footnotes in Table 2 and ref. 33), not included in the idealized model considered for the plot in Fig. 2. An even stronger FM J was computed for the B1 type bonds in the related compound Li_{2}IrO_{3}^{17}. In Na_{2}IrO_{3}, on the other hand, the IrOIr bond angles are >97° and the NN J turns AF on all short IrIr links^{16}.
For the B2 and B3 links, we derive a FM Kitaev term and an AF Heisenberg interaction, again qualitatively similar to the QC data for Li_{2}IrO_{3}^{17}. We assign the AF value of the NN J on the B2/B3 units to the slightly larger RhORh bond angle, which as shown in Fig. 2 pulls the J towards a positive value and most importantly to additional distortions that shift the bridging ligands on the RhO_{2}Rh B2/B3 plaquettes in opposite senses parallel to the RhRh axis^{33}. The role of these additional distortions on the B2/B3 units was analyzed in detail in ref. 16 and shown to enhance as well the AF component to the intersite exchange.
Effect of longerrange exchange interactions and occurence of spinglass ground state
For further insights into the magnetic properties of Li_{2}RhO_{3}, we carried out ED calculations for an extended spin Hamiltonian that in addition to the NN terms of Eq. (1) incorporates longerrange second and thirdneighbor Heisenberg interactions J_{2} and J_{3}^{5,7,8,9}. We used clusters of 24 sites with periodic boundary conditions^{4,16,17} and the quantum chemically derived NN coupling constants listed in Table 2. The static spinstructure factor was calculated as function of variable J_{2} and J_{3} parameters. For a given set of J_{2} and J_{3} values, the dominant order is determined according to the wave number Q = Q_{max} providing a maximum value of S(Q). The resulting phase diagram is shown in Fig. 3(a). Given the similar structure of the NN magnetic interactions, it is somewhat similar to that obtained in our previous study on Li_{2}IrO_{3}^{17}. Six different regions can be identified for meV: FM, Néel, Kitaev spin liquid, stripy, diagonal zigzag and incommensurate Q (ICx) phases. The Kitaev spin liquid, stripy and incommensurate phases in strongly spinorbit coupled honeycomb 5d^{5} systems were analyzed in a number of earlier studies^{4,6,7,8,16}. The detailed nature of the diagonal zigzag and incommensurate ICx ground states for large FM J on one set of NN links was described in ref. 17. Remarkably, for J(B1) much larger than K(B1) and J(B2), the initial hexagonal lattice can be mapped onto an effective triangular model of triplet dimers on the B1 bonds^{17}.
Since J_{2} and J_{3} are expected to be AF in honeycomb d^{5} oxides^{8,9}, the most likely candidate for the magnetic ground state of “clean” crystals of Li_{2}RhO_{3}, according to our results, is the diagonal zigzag state (see Fig. 3) and is found to be stable in a wide region of and . Experimentally, however, a spinglass ground state was determined, with a spin freezing temperature of ~6 K^{19}. As possible cause of the observed spinglass behavior in Li_{2}RhO_{3} we here investigate the role of LiRh site intercalation. Significant disorder on the cation sublattice is a well known feature in Li_{2}MO_{3} compounds. A typical value for the degree of Li^{+} −M^{4+} site inversion in these materials is 10–15%^{34,35}. Partial substitution of the “inplane” Rh^{4+} ions by nonmagnetic Li^{+} species introduces spin defects in the honeycomb layer. On the 24site cluster employed for our ED calculations, 10–15% site inversion translates in replacing two centers by vacancies. Hereafter, we denote the two spin defects as p_{1} and p_{2}.
The effect of spin vacancies on the static spinstructure factor in the diagonal zigzag phase (J_{2} = J_{2} = 3) is shown in Fig. 3(d,e). For comparison, the static spinstructure factor is also plotted in Fig. 3(c) for the ideal case without spin defects. In the absence of “defects”, the ground state is characterized in the bulk limit by symmetrybroken longrange order with either or wave vectors. Since the two symmetrybreaking states are degenerate, the structure factor displays four peaks, at Q = Q_{1} and Q = Q_{2} [see Fig. 3(c)]. However, by introducing spin vacancies, the degeneracy may be lifted via impurity pinning effects. For example, when the two defects occupy positions 17 and 20 [(p_{1}, p_{2}) = (17, 20), see Fig. 3(b)] the spin structure defines one of the symmetrybreaking states with Q = Q_{1} [Fig. 3(d)]; likewise, defects at (p_{1}, p_{2}) = (17, 18) yield a state with Q = Q_{2} [Fig. 3(e)]. In other words, two different kinds of dominant shortrange order can be obtained with antisite disorder. The “locally” favored symmetrybreaking direction depends on the relative positions of the spin vacancies. In a macroscopic system, such “local” domains displaying different symmetrybreaking ordering directions are randomly distributed. Additional frustration is expected to arise because it is not possible to match two differently ordered domains without an emerging “string”. It is therefore likely that by creating some amount of spin defects the longrange zigzag order disappears and the resulting state is perceived as a spin glass at low temperature. A similar mechanism was proposed for the isotropic HeisenbergKitaev and J_{1}J_{2}J_{3} models^{5}.
An early well known example of frustration induced through the competition between two different, degenerate spin configurations is the twodimensional Ising model on a square lattice with randomly distributed, competing FM and AF bonds^{36}. To investigate how the diagonal zigzag state is destroyed by increasing the concentration of spin defects, we also studied a simplified Ising model with J = − ∞ for the B1 bonds, J_{2} = J_{3} and all other interactions set to zero. This is a reasonable approximation for the honeycomb layers of Li_{2}RhO_{3} since the diagonal zigzag phase essentially consists of alternating spinup and spindown chains [see sketch in Fig. 3(a)]. Spin structures obtained this way for various spindefect concentrations x are shown in Fig. 3(f–i). For x = 0 the symmetrybreaking diagonal zigzag state is realized, with degenerate Q = Q_{1} and Q = Q_{2} spin structures. At finite, low concentration x ~ 2% those two configurations are no longer degenerate since one of them features slightly lower groundstate energy. We still have in this case a “macroscopically stable” ground state. At intermediate defect concentration x ~ 7% the longrange order is in a strict sense destroyed. However, the large domain walls with either Q = Q_{1} and Q = Q_{2} seem to survive. At higher concentration x ~ 12% the longrange order disappears completely. Moreover, we can now identify a mixture of local structures with different symmetrybreaking directions [see Fig. 3(i)].
Discussion
In sum, we have calculated the microscopic neareastneighbor magnetic interactions between effective 1/2 spins in Li_{2}RhO_{3} and uncovered a substantial difference between the two types of bonds that are present: one is dominated by Heisenberg and the other by Kitaev types of couplings. The latter give rise to strong frustration, even if the interactions are predominantly ferromagnetic. In this setting we have additionally considered the effect of the presence of antisite disorder. Experimentally the inplane spindefect concentration in Li_{2}RhO_{3} has been estimated as x = 10–15%^{34,35}. Based on our theoretical findings it is likely that the observed spinglass behavior arises from the combination of such antisite disorder and strongly frustrating magnetic interactions, in particular, the different Kitaev/Heisenberg dominated magnetic bonds and the Isinglike physics associated with the triplet dimer formation that results from there.
Our combined ab initio and effectivemodel calculations on both Li_{2}RhO_{3} and related d^{5} honeycomb iridates^{16,17,23} indicate that a description in terms of onsite 1/2 pseudospins can well account for the diverse magnetic properties of these systems. While alternative models rely on the formation of delocalized, quasimolecular orbitals^{37,38} and for Li_{2}RhO_{3} downplay the role of spinorbit interactions^{38}, here we show that the latter give rise in Li_{2}RhO_{3} to anisotropic Kitaev interactions the same magnitude as in 5d iridates^{16,17,39}. That happens in spite of having a Rh t_{2g} splitting δ and a spinorbit coupling λ of similar magnitude, the same way similar sets of Ir δ and λ parameters in CaIrO_{3}^{40} still generate symmetric anisotropic exchange terms in the range of 10 meV (work is in progress).
Methods
The Molpro QC package was employed for all ab initio calculations^{41}. To analyze the electronic ground state and the nature of the dd excitations, a cluster consisting of one reference RhO_{6} octahedron plus three NN RhO_{6} octahedra and 15 nearby Li ions was used. The magnetic spectrum for two Rh^{4+} ions was obtained from calculations on a cluster containing two reference and four NN RhO_{6} octahedra plus the surrounding 22 Li ions, see SM for details. The farther solidstate environment was in both cases modeled as a finite array of point charges fitted to reproduce the crystal Madelung field in the cluster region. The spinorbit treatment was carried out according to the procedure described in ref. 42, using spinorbit pseudopotentials for Rh.
Additional Information
How to cite this article: Katukuri, V. M. et al. Strong magnetic frustration and antisite disorder causing spinglass behavior in honeycomb Li_{2}RhO_{3}. Sci. Rep. 5, 14718; doi: 10.1038/srep14718 (2015).
References
Goodenough, J. B. An interpretation of the magnetic properties of the perovskitetype mixed crystals La1 − xSrxCoO3 − λ . J. Phys. Chem. Sol. 6, 287–297 (1958).
Kanamori, J. Superexchange interaction and symmetry properties of electron orbitals. J. Phys. Chem. Sol. 10, 87–98 (1959).
Anderson, P. W. New approach to the theory of superexchange interactions. Phys. Rev. 115, 2 (1959).
Chaloupka, J., Jackeli, G. & Khaliullin, G. Zigzag Magnetic Order in the Iridium Oxide Na2IrO3 . Phys. Rev. Lett. 110, 097204 (2013).
Andrade, E. C. & Vojta, M. Magnetism in spin models for depleted honeycomblattice iridates: Spinglass order towards percolation. Phys. Rev. B 90, 205112 (2014).
Rau, J. G., Lee, E. K.H. & Kee, H.Y. Generic Spin Model for the Honeycomb Iridates beyond the Kitaev Limit. Phys. Rev. Lett. 112, 077204 (2014).
Kimchi, I. & You, Y.Z. KitaevHeisenbergJ2J3 model for the iridates A2IrO3 . Phys. Rev. B 84, 180407 (2011).
Singh, Y. et al. Relevance of the HeisenbergKitaev Model for the Honeycomb Lattice Iridates A2IrO3 . Phys. Rev. Lett. 108, 127203 (2012).
Choi, S. K. et al. Spin Waves and Revised Crystal Structure of Honeycomb Iridate Na2IrO3 . Phys. Rev. Lett. 108, 127204 (2012).
Foyevtsova, K., Jeschke, H. O., Mazin, I. I., Khomskii, D. I. & Valenti, R. Ab initio analysis of the tightbinding parameters and magnetic interactions in Na2IrO3 . Phys. Rev. B 88, 035107 (2013).
Reuther, J., Thomale, R. & Rachel, S. Spiral order in the honeycomb iridate Li2IO3 . Phys. Rev. B 90, 100405 (2014).
Sela, E., Jiang, H.C., Gerlach, M. H. & Trebst, S. Orderbydisorder and spinorbital liquids in a distorted HeisenbergKitaev model. Phys. Rev. B 90, 035113 (2014).
Kitaev, A. Anyons in an exactly solved model and beyond. Ann. Phys. 321, 2–111 (2006).
Jackeli, G. & Khaliullin, G. Mott Insulators in the Strong SpinOrbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models. Phys. Rev. Lett. 102, 017205 (2009).
Chaloupka, J., Jackeli, G. & Khaliullin, G. KitaevHeisenberg Model on a Honeycomb Lattice: Possible Exotic Phases in Iridium Oxides A2IrO3 . Phys. Rev. Lett. 105, 027204 (2010).
Katukuri, V. M. et al. Kitaev interactions between j = 1/2 moments in honeycomb Na2IrO3 are large and ferromagnetic: insights from ab initio quantum chemistry calculations. New J. Phys. 16, 013056 (2014).
Nishimoto, S. et al. Strongly frustrated triangular spin lattice emerging from triplet dimer formation in honeycomb Li2IrO3. arXiv:1403.6698 (unpublished) (2014).
Malrieu, J. P., Caballol, R., Calzado, C. J., de Graaf, C. & Guihery, N. Magnetic Interactions in Molecules and Highly Correlated Materials: Physical Content, Analytical Derivation and Rigorous Extraction of Magnetic Hamiltonians. Chem. Rev. 114, 429 (2014).
Luo, Y. et al. Li2RhO3: A spinglassy relativistic Mott insulator. Phys. Rev. B 87, 161121 (2013).
Thornley, J. H. M. The magnetic properties of (IrX6)^{2−} complexes. J. Phys. C (Proc. Phys. Soc.) 1, 1024 (1968).
Abragam, A. & Bleaney, B. Electron Paramagnetic Resonance of Transition Ions (Clarendon Press, Oxford, 1970).
Kim, B. J. et al. Novel Jeff = 1/2 Mott State Induced by Relativistic SpinOrbit Coupling in Sr2IrO4 . Phys. Rev. Lett. 101, 076402 (2008).
Gretarsson, H. et al. CrystalField Splitting and Correlation Effect on the Electronic Structure of A2IrO3 . Phys. Rev. Lett. 110, 076402 (2013).
Liu, X. et al. Testing the Validity of the Strong SpinOrbitCoupling Limit for Octahedrally Coordinated Iridate Compounds in a Model System Sr3CuIrO6 . Phys. Rev. Lett. 109, 157401 (2012).
Hozoi, L. et al. Longerrange lattice anisotropy strongly competing with spinorbit interactions in pyrochlore iridates. Phys. Rev. B 89, 115111 (2014).
Katukuri, V. M. et al. Electronic Structure of LowDimensional 4d^{5} Oxides: Interplay of Ligand Distortions, Overall Lattice Anisotropy and SpinOrbit Interactions. Inorg. Chem. 53, 4833–4839 (2014).
Andlauer, B., Schneider, J. & Tolksdorf, W. Optical Absorption, Fluorescence and Electron Spin Resonance of Ir^{4+} on Octahedral Sites in Y3Ga5O12 . Phys. Stat. Sol. B 73, 533 (1976).
Kim, J. et al. Magnetic Excitation Spectra of Sr2IrO4 Probed by Resonant Inelastic XRay Scattering: Establishing Links to Cuprate Superconductors. Phys. Rev. Lett. 108, 177003 (2012).
Haverkort, M. W., Elfimov, I. S., Tjeng, L. H., Sawatzky, G. A. & Damascelli, A. Strong SpinOrbit Coupling Effects on the Fermi Surface of Sr2RuO4 and Sr2RhO4 . Phys. Rev. Lett. 101, 026406 (2008).
Helgaker, T., Jørgensen, P. & Olsen, J. Molecular ElectronicStructure Theory (Wiley, Chichester, 2000).
Hill, N. J. Electron paramagnetic resonance of osmiumdoped trichlorotris(diethylphenylphosphine)rhodium(III). J. Chem. Soc., Faraday Trans. 2 68, 427–434 (1972).
Katukuri, V. M. et al. Mechanism of basalplane antiferromagnetism in the spinorbit driven iridate Ba2IrO4 . Phys. Rev. X 4, 021051 (2014).
Todorova, V. & Jansen, M. Synthesis, Structural Characterization and Physical Properties of a New Member of Ternary Lithium Layered Compounds—Li2RhO3 . Z. Anorg. Allg. Chem. 637, 37 (2011).
Kobayashi, H. et al. Structure and lithium deintercalation of Li2 − xRuO3 . Solid State Ionics 82, 25–31 (1995).
Kobayashi, H., Tabuchi, M., Shikano, M., Kageyama, H. & Kanno, R. Structure and magnetic and electrochemical properties of layered oxides, Li2IrO3 . J. Mater. Chem. 13, 957–962 (2003).
Vannimenusi, J. & Toulouse, G. Theory of the frustration effect: II. Ising spins on a square lattice. J. Phys. Solid State Phys. 10, L537–L542 (1977).
Mazin, I. I., Jeschke, H. O., Foyevtsova, K., Valent, R. & Khomskii, D. I. Na2IrO3 as a Molecular Orbital Crystal. Phys. Rev. Lett. 109, 197201 (2012).
Mazin, I. I. et al. Origin of the insulating state in honeycomb iridates and rhodates. Phys. Rev. B 88, 035115 (2013).
Gretarsson, H. et al. Magnetic excitation spectrum of Na2IrO3 probed with resonant inelastic xray scattering. Phys. Rev. B 87, 220407 (2013).
Bogdanov, N. A., Katukuri, V. M., Stoll, H., van den Brink, J. & Hozoi, L. Postperovskite CaIrO3: A j = 1/2 quasionedimensional antiferromagnet. Phys. Rev. B 85, 235147 (2012).
Werner, H.J., Knowles, P. J., Knizia, G., Manby, F. R. & Schütz, M. Molpro: a generalpurpose quantum chemistry program package. WIREs Comput Mol Sci 2, 242–253 (2012).
Berning, A., Schweizer, M., Werner, H.J., Knowles, P. J. & Palmieri, P. Spinorbit matrix elements for internally contracted multireference configuration interaction wavefunctions. Mol. Phys. 98, 1823–1833 (2000).
Acknowledgements
We thank V.Yushankhai, Y. Singh, N.A. Bogdanov and U.K. Rößler for useful discussions. L. H. acknowledges financial support from the German Research Foundation (Deutsche Forschungsgemeinschaft, DFG). This work is supported by SFB 1143 of the Deutsche Forschungsgemeinschaft.
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V.M.K. carried out the ab initio calculations and subsequent mapping of the ab initio results onto the effective spin Hamiltonian, with assistance from L.H., H.S. and I.R. S.N. performed the exactdiagonalization calculations. V.M.K., S.N., J.V.D.B. and L.H. analyzed the data and wrote the paper, with contributions from all other coauthors.
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Katukuri, V., Nishimoto, S., Rousochatzakis, I. et al. Strong magnetic frustration and antisite disorder causing spinglass behavior in honeycomb Li_{2}RhO_{3}. Sci Rep 5, 14718 (2015). https://doi.org/10.1038/srep14718
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DOI: https://doi.org/10.1038/srep14718
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