Electronic Structure of Low-Dimensional 4d⁵ Oxides: Interplay of Ligand Distortions, Overall Lattice Anisotropy, and Spin–Orbit Interactions

Abstract

The electronic structure of the low-dimensional 4d 5 oxides Sr 2 RhO 4 and Ca 3 CoRhO 6 is herein investigated by embedded-cluster quantum chemistry calculations. A negative tetragonal-like t 2g splitting is computed in Sr 2 RhO 4 and a negative trigonal-like splitting is predicted for Ca 3 CoRhO 6 , in spite of having positive tetragonal distortions in the former material and cubic oxygen octahedra in the latter. Our findings bring to the foreground the role of longerrange crystalline anisotropy in generating noncubic potentials that compete with local distortions of the ligand cage, an issue not addressed in standard textbooks on crystal-field theory. We also show that sizable t 2g 5 −t 2g 4 e g 1 couplings via spin− orbit interactions produce in Sr 2 RhO 4 ⟨ ⟩ = ⟨∑ · ⟩ l s i i i ground-state expectation values significantly larger than 1, quite similar to theoretical and experimental data for 5d 5 spin−orbit-driven oxides such as Sr 2 IrO 4 . On the other hand, in Ca 3 CoRhO 6 , the ⟨ ⟩ values are lower because of larger t 2g −e g splittings. Future X-ray magnetic circular dichroism experiments on these 4d oxides will constitute a direct test for the ⟨ ⟩ values that we predict here, the importance of many-body t 2g −e g couplings mediated by spin−orbit interactions, and the role of low-symmetry fields associated with the extended surroundings. ■ INTRODUCTIONOne of the most difficult problems in electronic structure theory is the correct description of correlated d and f electrons in solid-state compounds. Although density functional theory (DFT) provides results in reasonably good agreement with the experiment for weakly and moderately correlated electron systems, there are many materials, in particular, d-and felectron oxides, whose electronic structures cannot be properly treated within the canonical DFT framework. Extensions of DFT by dynamical mean-field theory (DMFT) led to DFT +DMFT schemes and allowed one to overcome some of the intrinsic limitations of DFT.1,2 Yet the accuracy and predictive power of the DFT+DMFT calculations is to some extent restricted by the use of parametrizations such as the on-site Coulomb repulsion U. It is therefore desirable to explore complementary techniques, e.g., wave-function-based quantum chemistry methods. While early attempts and the first encouraging results go back as early as the 1970s, with the work of Wachters, Bagus, and others, 3,4 the tremendous progress in computer technology nowadays makes possible many-body quantum chemistry calculations on larger and larger embedded clusters with remarkably good results for quantities such as the d-level splittings and intersite spin interactions; see, e.g., refs 5−34.Most of the investigations have been focused on 3d transition-metal compounds 3−24 and very recently, because of novel physics arising from strong spin−orbit coupling (SOC), on 5d oxides. 25−29 The 4d materials, on the other hand, received little attention in this context. Here we investigate with the help of ab initio quantum chemistry methods the...

Iridates from the molecular side

“…Although their local structures are obviously comparable, the electronic resemblance between these compounds should be discussed here. The branching ratios extracted from XAS (0.85; Table 1) are identical for 1 and 2 , and very close to the values found for oxido-iridates, for example, 0.87 for Sr 2 IrO 4 and 0.85 for Y 2 Ir 2 O 7 (refs 31, 32). In addition, the L 2 / L 3 XMCD intensity ratio of 4.7% for 2 is almost identical to the value determined for Sr 2 IrO 4 (∼5%) (ref.…”

Kitaev exchange and field-induced quantum spin-liquid states in honeycomb α-RuCl3

“…20). The quantum chemistry g factors are consistent with a ratio δ / λ  ~ 0.5, i.e., t 2 g splittings of ≈70 meV (see the data in Tables 1 and 2) for a 4 d SOC in the range of 120–150 meV242736. Electron spin resonance measurements of the g factors might provide more detailed experimental information that can be directly compared to our calculations.…”

Covalency and vibronic couplings make a nonmagnetic j=3/2 ion magnetic

“…For example, test CASSCF calculations in which the size of the point charges placed at the 12 Os and 6 alkaline-ion nearest-neighbor sites are modified from the formal ionic values 7+ and 1+ (12 × 7 + 6 × 1 = 90) to 5+ and 5+ (12 × 5 + 6 × 5 = 90) show a reduction of about 2 eV of the t 2g -e g level splitting. Similar effects, with relative shifts and even inversion of the d-electron energy levels due to charge imbalance at nearby cation sites, were recently evidenced in Sr 2 RhO 4 and Sr 2 IrO 4 [8,26], the rare-earth 227 iridates R 2 Ir 2 O 7 [34] and Cd 2 Os 2 O 7 [35]. The mechanism has not been thoroughly explored so far experimentally but seems to hold much potential in the context of orbital engineering in TM compounds.…”