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

Abstract

A unified approach is presented for investigating coupled spin-orbital fluctuations within a realistic three-orbital model for strongly spin-orbit coupled systems with electron fillings n = 3, 4, 5 in the t 2g sector of d yz , d xz , d xy orbitals. A generalized fluctuation propagator is constructed which is consistent with the generalized self-consistent Hartree-Fock approximation where all Coulomb interaction contributions involving orbital diagonal and off-diagonal spin and charge condensates are included. Besides the low-energy magnon, intermediate-energy orbiton and spin-orbiton, and high-energy spin-orbit exciton modes, the generalized spectral function also shows other high-energy excitations such as the Hund's coupling induced gapped magnon modes. We relate the characteristic features of the coupled spin-orbital excitations to the complex magnetic behavior resulting from the interplay between electronic bands, spin-orbit coupling, Coulomb interactions, and structural distortion effects, as realized in the compounds NaOsO 3 , Ca 2 RuO 4 , and Sr 2 IrO 4 .

Orbital entangled antiferromagnetoc order and spin-orbit-distortion exciton in $\rm Sr_2VO_4$

“…This feature is exactly similar as in the Sr 2 IrO 4 compound where the easy-plane anisotropy was identified as arising due to the J H induced spin-rotation-symmetry breaking in the pseudo spin-orbital basis. 21,24 With one electron in Sr 2 VO 4 and one hole in Sr 2 IrO 4 , the above similarity reflects the particle-hole symmetry at play.…”

“…The generalized self consistent approach including all orbital diagonal and off-diagonal spin and charge condensates has been applied recently to the NaOsO 3 , Ca 2 RuO 4 , and Sr 2 IrO 4 compounds, 17,21,22 illustrating the rich interplay between different physical elements. The coupling of orbital moments to weak orbital fields and the interaction-induced SOC renormalization highlight the role of orbital off-diagonal condensates on the emergent orbital and spin-orbital physics.…”

“…The generalized fluctuation propagator in the random phase approximation (RPA) was investigated recently for several 4d and 5d compounds with electron fillings n = 3, 4, 5 in the t 2g sector. 21 Collective excitations have also been investigated recently for the n = 2 Sr 2 CrO 4 compound, 23 which is of particular interest due to the active yz/xz orbital degree of freedom since n yz + n xz ≈ 1 in the reversed crystal field (ǫ xy ∼ −1) regime where n xy ≈ 1.…”

Spin–orbit coupling and magnetism in Sr2CrO4

“…The electron filling n = 2 in the t 2g for the chromate compound. The Hamiltonian terms and the methodology used have been discussed earlier [33][34][35] for other related compounds with n = 1, 3, 4, 5, and are briefly summarized below.…”

“…For this purpose, we will employ the generalized self consistent + fluctuations approach in which all physical elements are treated on equal footing. This approach was recently used to investigate spin-orbital fluctuations in several 4d and 5d compounds (NaOsO 3 , Ca 2 RuO 4 , Sr 2 IrO 4 ) with n = 3, 4, 5 electrons [33,34], and most recently in the 3d compound Sr 2 VO 4 with n = 1 electron [35].…”