Effective magnetic interactions in spin-orbit coupled $d^4$ Mott insulators

Abstract

Transition metal compounds with the $(t_{2g}{)}^4$ electronic configuration are expected to be nonmagnetic atomic singlets both in the weakly interacting regime due to spin-orbit coupling, as well as in the Coulomb dominated regime with oppositely aligned $L=1$ and $S=1$ angular momenta. However, starting with the full multi-orbital electronic Hamiltonian, we show the low energy effective magnetic Hamiltonian contains isotropic superexchange spin interactions but anisotropic orbital interactions. By tuning the ratio of superexchange to spin-orbit coupling $J_{\mathrm{SE}}/\lambda$, we obtain a phase transition from nonmagnetic atomic singlets to novel magnetic phases depending on the strength of Hund's coupling, the crystal structure and the number of active orbitals. Spin-orbit coupling plays a non-trivial role in generating a triplon condensate of weakly interacting excitations at antiferromagnetic ordering vector $\vec{k}=\vec{\pi }$, regardless of whether the local spin interactions are ferromagnetic or antiferromagnetic. In the large $J_{\mathrm{SE}}/\lambda$ regime, the localized spin and orbital moments produce anisotropic orbital interactions that are frustrated or constrained even in the absence of geometric frustration. Orbital frustration leads to frustration in the spin channel opening up the possibility of spin-orbital liquids with both spin and orbital entanglement.

11 pages, 9 figures; supplement: 4 pages and 1 figure

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Cited by in corpus (41)

• The Challenge of Spin-Orbit-Tuned Ground States in Iridates
• Nature of the magnetism of iridium in the double perovskite Sr2CoIrO6
• Mixing of $t_{2g}$-$e_g$ orbitals in 4d and 5d transition metal oxides
• Octupolar vs Néel Order in Cubic 5$d^2$ double perovskites
• Determination of Hund's coupling in 5d Oxides using Resonant Inelastic X-ray Scattering
• Octupolar order in d-orbital Mott insulators
• New Evidence for a Low-Temperature Magnetic Ground State in Double-Perovskite Iridates with Ir5+(5d4) Ions
• Unraveling the nature of magnetism of the 5${\mathbf{d}}^4$ double perovskite Ba${}_2$YIrO${}_6$
• Multipolar magnetism in d-orbital systems: Crystal field levels, octupolar order, and orbital loop currents
• Origin of magnetic moments and presence of a resonating valence bond state in Ba${}_2$YIrO${}_6$
• Spin-orbit coupled systems in the "atomic" limit: rhenates, osmates, iridates
• Floquet engineering of Kitaev quantum magnets
• Density matrix renormalization group study of a three-orbital Hubbard model with spin-orbit coupling in one dimension
• Unconventional magnetism in the 4d${}^4$ based ($S=1$) honeycomb system Ag${}_3$LiRu${}_2$O${}_6$
• Probing the $J_{eff}=0$ ground state and the Van Vleck paramagnetism of the Ir${}^{5+}$ ions in the layered Sr${}_2$Co${}_{0.5}$Ir${}_{0.5}$O${}_4$
• Octupolar order and Ising quantum criticality tuned by strain and dimensionality: Application to $d$-orbital Mott insulators
• Possible quadrupole order in tetragonal Ba2CdReO6 and chemical trend in the ground states of 5d1 double perovskites
• Spin-orbit effects in pentavalent Iridates: Models and materials
• Structural, thermodynamic, and local probe investigations of a honeycomb material Ag${}_3$LiMn${}_2$O${}_6$
• How spin-orbital entanglement depends on the spin-orbit coupling in a Mott insulator
• Spin-Orbital Entangled Excitonic Insulators in $(t_{2g}{)}^4$ Correlated Electron Systems
• The Curious Case of NiRh${}_2$O${}_4$: A Spin-Orbit Entangled Diamond Lattice Paramagnet
• Van Vleck excitons in Ca${}_2$RuO${}_4$
• BCS-BEC crossover in a $(t_{2g}{)}^4$ Excitonic Magnet
• Gapless to gapless phase transitions in quantum spin chains
• Orbiton-Phonon coupling in Ir5+(5d4) double perovskite Ba2YIrO6
• Magnetic phase transitions in quantum spin-orbital liquids
• Correlated Paramagnetism and Interplay of Magnetic and Phononic Degrees of Freedom in 3d-5d Coupled La2CuIrO6
• Magnetization dynamics fingerprints of an excitonic condensate $t_{2g}^4$ magnet
• Correlated electron metal properties of the honeycomb ruthenate Na${}_2$RuO${}_3$
• Spin-orbit excitons and electronic configuration of the $5d^4$ insulator Sr${}_3$Ir${}_2$O${}_7$F${}_2$
• Novel Block Excitonic Condensate at $n=3.5$ in a Spin-Orbit Coupled $t_{2g}$ Multiorbital Hubbard Model
• On the electronic ground state of two non-magnetic pentavalent honeycomb iridates
• Magnetic phases for two $t_{2g}$ holes with spin-orbit coupling and crystal field
• J = 0 nonmagnetic insulating state in K${}_2$Os$X_6$ (X = F, Cl and Br)
• Multipolar multiferroics in $4d^2$/$5d^2$ Mott insulators
• Evolution of Spin-Orbital Entanglement with Increasing Ising Spin-Orbit Coupling
• A Novel ground state in a new dimer iridate Ba13Ir6O30 with Ir6+(5d3) Ions
• Collective mode excitations and simulated $L$-edge resonant-inelastic x-ray scattering spectra in antiferromagnetic Ca${}_2$RuO${}_4$
• Magnetic ordering in the $J_{\mathrm{eff}}$ = 0 Nickelate NiRh${}_2$O${}_4$ prepared via a solid-state metathesis
• Localized-itinerant dichotomy and unconventional magnetism in SrRu${}_2$O${}_6$