A three-orbital-model approach for studying spin wave excitations in the strongly spin-orbit coupled layered perovskite iridates is presented which provides a unified description of magnetic excitations as well as the electronic band structure. The calculated spin wave dispersions with realistic three-band parameters are in excellent agreement with the RIXS data for iridates, including the strong AF zone boundary dispersion in the single-layer compound Sr 2 IrO 4 and the large anisotropy gap in the bilayer compound Sr 3 Ir 2 O 7 . The RIXS spin wave data is shown to provide evidence of mixing between the J = 1/2 and 3/2 sectors in both compounds.

Including the orbital off-diagonal spin and charge condensates in the self consistent determination of magnetic order within a realistic three-orbital model for the 4d4 compound Ca2RuO4, reveals a host of novel features including strong and anisotropic spin–orbit coupling (SOC) renormalization, coupling of strong orbital magnetic moments to orbital fields, and a magnetic reorientation transition. Highlighting the rich interplay between orbital geometry and overlap, SOC, Coulomb interactions, tetragonal distortion, and staggered octahedral tilting and rotation, our investigation yields a planar antiferromagnetic (AFM) order for moderate tetragonal distortion, with easy a–b plane and easy b axis anisotropies, along with small canting of the dominantly yz, xz orbital moments. With decreasing tetragonal distortion, we find a magnetic reorientation transition from the dominantly planar AFM order to a dominantly c axis ferromagnetic order with significant xy orbital moment.

Effects of the structural distortion associated with the OsO 6 octahedral rotation and tilting on the electronic band structure and magnetic anisotropy energy for the 5d 3 compound NaOsO 3 are investigated using the density functional theory (DFT) and within a three-orbital model. Comparison of the essential features of the DFT band structures with the three-orbital model for both the undistorted and distorted structures provides insight into the orbital and directional asymmetry in the electron hopping terms resulting from the structural distortion. The orbital mixing terms obtained in the transformed hopping Hamiltonian resulting from the octahedral rotations are shown to account for the fine features in the DFT band structure. Staggered magnetization and the magnetic character of states near the Fermi energy indicate weak coupling behavior.

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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 .