Interplay of many-body and single-particle interactions in iridates and rhodates

Abstract

Motivated by recent experiments exploring the spin-orbit-coupled magnetism in $4d$- and $5d$-band transition metal oxides, we study magnetic interactions in Ir- and Rh-based compounds. In these systems, the comparable strength of spin-orbit coupling (SOC), crystal field splitting (CF) and Coulomb and Hund's coupling leads to a rich variety of magnetic exchange interactions, leading to new types of ground states. Using a strong coupling approach, we derive effective low-energy super-exchange Hamiltonians from the multi-orbital Hubbard model by taking full account of the Coulomb and Hund's interactions in the intermediate states. We find that in the presence of strong SOC and lattice distortions the super-exchange Hamiltonian contains various kinds of magnetic anisotropies. Here we are primarily interested in the magnetic properties of Sr${}_2$IrO${}_4$ and Sr${}_2$Ir${}_{1-x}$Rh${}_x$O${}_4$ compounds. We perform a systematic study of how magnetic interactions in these systems depend on the microscopic parameters and provide a thorough analysis of the resulting magnetic phase diagram. Comparison of our results with experimental data shows good agreement. Finally, we discuss the parameter space in which the spin-flop transition in Sr${}_2$IrO${}_4$, experimentally observed under pressure, can be realized.

15 pages, 6 figures

References in corpus (15)

• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• Novel Jeff = 1/2 Mott State Induced by Relativistic Spin-Orbit Coupling in Sr2IrO4
• Spin-Liquid State in the S = 1/2 Hyperkagome Antiferromagnet Na4Ir3O8
• Twisted Hubbard Model for Sr2IrO4: Magnetism and Possible High Temperature Superconductivity
• Quantum spin Hall effect in a transition metal oxide Na2IrO3
• Long range magnetic ordering in Na${}_2$IrO${}_3$
• Dimensionality Driven Spin-Flop Transition in Layered Iridates
• Critical properties of the Kitaev-Heisenberg model
• Robustness of basal-plane antiferromagnetic order and the $J_{eff}=1/2$ state in single-layer iridate spin-orbit Mott insulators
• Spin-orbit tuned metal-insulator transitions in single-crystal Sr2Ir1-xRhxO4 (0\leqx\leq1)
• Topological spin liquid on the hyper-kagome lattice of Na_4Ir_3O_8
• Magnetic couplings, optical spectra, and spin-orbit exciton in 5d electron Mott insulator Sr2IrO4
• Ab initio determination of excitation energies and magnetic couplings in correlated, quasi two-dimensional iridates
• Li${}_2$RhO${}_3$: A spin-glassy relativistic Mott insulator
• Magnetic excitation spectra in pyrochlore iridates

Cited by in corpus (36)

• Proximate Kitaev Quantum Spin Liquid Behaviour in α-RuCl${}_3$
• Importance of anisotropic exchange interactions in honeycomb iridates. Minimal model for zigzag antiferromagnetic order in Na${}_2$IrO${}_3$
• Mixing of $t_{2g}$-$e_g$ orbitals in 4d and 5d transition metal oxides
• A structural distortion induced magneto-elastic locking in Sr${}_2$IrO${}_4$ revealed through nonlinear optical harmonic generation
• Anisotropic Magnetic Couplings and Structure-Driven Canted to Collinear Transitions in Spin-orbit Coupled Sr2IrO4
• Orbital reconstruction in nonpolar tetravalent transition-metal oxide layers
• Tuning Magnetic Coupling in Sr${}_2$IrO${}_4$ Thin Films with Epitaxial Strain
• Structure symmetry determination and magnetic evolution in $\mathrm{S}{\mathrm{r}}_2\mathrm{I}{\mathrm{r}}_{1-\mathrm{x}}\mathrm{R}{\mathrm{h}}_{\mathrm{x}}{\mathrm{O}}_4$
• Mechanism of basal-plane antiferromagnetism in the spin-orbit driven iridate Ba2IrO4
• Validity and limitations of the superexchange model for the magnetic properties of Sr2IrO4 and Ba2IrO4 mediated by the strong spin-orbit coupling
• Correlation effects and hidden spin-orbit entangled electronic order in parent and electron-doped iridates Sr${}_2$IrO${}_4$
• Novel chiral quantum spin liquids in Kitaev magnets
• The magnetic ground state of Sr2IrO4 and implications for second-harmonic generation
• Microscopic theory of electric polarization induced by skyrmionic order in GaV${}_4$S${}_8$
• Heavy-mass magnetic modes in pyrochlore iridates due to dominant Dzyaloshinskii-Moriya interaction
• Mechanism for subgap optical conductivity in honeycomb Kitaev materials
• Spin-orbit coupling and strong electronic correlations in cyclic molecules
• Theory of electronic magnetoelectric coupling in $d^5$ Mott insulators
• Possibility to realize spin-orbit-induced correlated physics in iridium fluorides
• Magnetization density distribution of Sr${}_2$IrO${}_4$: Deviation from a local $j_{\text{eff}}=1/2$ picture
• Heisenberg and Dzyaloshinskii-Moriya interactions controlled by molecular packing in tri-nuclear organometallic clusters
• Strain-induced topological transition in SrRu${}_2$O${}_6$ and CaOs${}_2$O${}_6$
• Quasimolecular electronic structure of the spin-liquid candidate Ba${}_3$InIr${}_2$O${}_9$
• Quasimolecular $J_{\mathrm{tet}}$=3/2 moments in the cluster Mott insulator GaTa${}_4$Se${}_8$
• Analysis of resonant inelastic x-ray scattering from Sr${}_2$IrO${}_4$ in an itinerant-electron approach
• Low-Energy Model and Electron-Hole Doping Asymmetry of Single-Layer Ruddlesden-Popper Iridates
• Topological quantum phase transition driven by anisotropic spin-orbit coupling in trinuclear organometallic coordination crystals
• Effects of anisotropy in spin molecular-orbital coupling on effective spin models of trinuclear organometallic complexes
• Direct observation of oxygen polarization in Sr${}_2$IrO${}_4$ by O $K$-edge x-ray magnetic circular dichroism
• Strain-induced superconductivity in Sr2IrO4
• Modeling multiorbital effects in Sr2IrO4 under strain and a Zeeman field
• Pseudo-spin rotation symmetry breaking by Coulomb interaction terms in spin-orbit coupled systems
• Quasimolecular electronic structure of the trimer iridate Ba${}_4$NbIr${}_3$O${}_{12}$
• The rich phase diagram of the prototypical iridate Ba${}_2$IrO${}_4$: Effective low-energy models and metal-insulator transition
• The free energy of anisotropic quantum spin systems: Functional integral representation
• Non-Loudon-Fleury Raman scattering in spin-orbit coupled Mott insulators