Spin-orbit coupling induced magnetic anisotropy and large spin wave gap in NaOsO₃

Abstract

The role of spin-orbit coupling and Hund's rule coupling on magnetic ordering, anisotropy, and excitations are investigated within a minimal three-orbital model for the 5d 3 compound NaOsO 3 . Small asymmetry between the magnetic moments for the xy and xz, yz orbitals, arising from the hopping asymmetry generated by OsO 6 octahedral tilting and rotation, together with the weak correlation effect, are shown to be crucial for the large SOC induced magnetic anisotropy and spin wave gap observed in this compound. Due to the intrinsic SOC-induced changes in the electronic densities under rotation of the staggered field, their coupling with the orbital energy offset is also found to contribute significantly to the magnetic anisotropy energy.

Coupled spin–orbital fluctuations in a three orbital model for 4d and 5d oxides with electron fillings n = 3, 4, 5—application to NaOsO3, Ca2RuO4 and Sr2IrO4

“…Two different mechanisms contributing to SOC-induced easy-plane anisotropy and large magnon gap for out-of-plane fluctuation modes were identified for the weakly correlated 5d 3 compound NaOsO 3 in terms of a simplified picture involving only the normal spin and charge densities [14,15]. Both essential ingredients-(i) small moment disparity between yz, xz and xy orbitals and (ii) spin-charge coupling effect in presence of tetragonal splitting-are intrinsically present in the considered three-orbital model on the square lattice.…”

“…Various mechanisms, such as Slater-like, magnetic Lifshitz transition, and AFM band insulator have been proposed to explain this unusual and intriguing nature of the MIT [8,[11][12][13][14]. Interplay of electronic correlations, Hund's coupling, and octahedral tilting and rotation induced band narrowing near the Fermi level in this weakly correlated compound results in the weakly insulating state with G-type AFM order, with magnetic anisotropy and large magnon gap resulting from interplay of SOC, band structure, and the tetragonal splitting [14,15]. The Os L 3 resonant edge RIXS measurements at room temperature show four inelastic peak features below 1.5 eV, which have been interpreted to correspond to the strongly gapped (∼58 meV) dispersive magnon excitations with bandwidth ∼100 meV, excitations (centered at ∼1 eV) within the t 2g manifold, and excitations from t 2g to e g states and ligand-to-metal charge transfer for the remaining two higher-energy peaks [13,16,17].…”

Aberrant electronic and structural alterations in pressure tuned perovskite NaOsO3

“…We note that such sluggish process of metallization during compression among 5d systems (especially iridates) is common with the presence of strong SOC, which usually sustains a rigid band gap [27][28][29][30][31] . In NaOsO 3 with the t 3 2g electronic configuration, the SOC formally should not play a dominant role because the resulting L eff = 0 state yields a vanishing orbital moment, yet it is found to be responsible for the weakening of the electron-electron correlation 7 , magnetic anisotropy, and large spin wave gap formation 32 . As the MIT is considered to be the SOC-driven for the most part, its evolution during compression is likely governed by the same source.…”

Doping-induced insulator-metal transition in the Lifshitz magnetic insulator NaOsO3

“…There are two additional peculiar aspects of the MIT in NaOsO 3 . First, despite being in a nominally t 3 2g configuration the ordered moment is only 1 µ B [13] due to an high degree of p − d hybridization which place the system close to an (electronic and magnetic) itinerant limit [14,16,25]; in additional even though the orbital moment is formally quenched (L eff = 0, nominally 5d 3 configuration [26]), spinorbit coupling effects are surprisingly important as they cause a renormalization (weakening) of the electron-electron correlation [16] and a large magnetic anisotropy energy [27].…”