Magnetic Excitations in Spin-Orbit Coupled $d^4$ Mott Insulator on Square Lattice

Abstract

We study the magnetic order and excitations in strong spin-orbit coupled, Van Vleck-type, $d^4$ Mott insulators on a square lattice. Extending the previous work, we include the tetragonal crystal field splitting and explore its effects on magnetic phase diagram and magnon spectra. Two different ordered phases, with in-plane and out-of-plane orientation of the staggered moments, are found for the higher and lower values of the crystal field splitting, respectively. The magnetic excitation spectra for paramagnetic and magnetically ordered phases are calculated and discussed in the context of a candidate spin-orbit $d^4$ Mott insulator Ca${}_2$RuO${}_4$.

arXiv comment7 pages, 6 figures; to appear in PRB

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• Highly anisotropic magnon dispersion in Ca2RuO4: evidence for strong spin orbit coupling
• Spin-Orbital Excitations in Ca${}_2$RuO${}_4$ Revealed by Resonant Inelastic X-ray Scattering
• Doping-Induced Ferromagnetism and Possible Triplet Pairing in d4 Mott Insulators
• Spin-orbit coupled systems in the "atomic" limit: rhenates, osmates, iridates
• Spin-Orbital Order Modified by Orbital Dilution in Transition Metal Oxides: From Spin Defects to Frustrated Spins Polarizing Host Orbitals
• Orbital and spin order in spin-orbit coupled $d^1$ and $d^2$ double perovskites
• A New Era of Excitonic Insulators
• Magnon dispersion in Ca2RuO4: impact of spin-orbit coupling and oxygen moments
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• Possible quadrupole order in tetragonal Ba2CdReO6 and chemical trend in the ground states of 5d1 double perovskites
• The Curious Case of NiRh${}_2$O${}_4$: A Spin-Orbit Entangled Diamond Lattice Paramagnet
• Quantum entanglement in the one-dimensional spin-orbital SU(2)$\otimes XXZ$ model
• Enhancement of magnetodielectric coupling in 6H-perovskites Ba3RRu2O9 for heavier rare earth cations (R=Ho,Tb)
• Upper branch magnetism in quantum magnets: Collapses of excited levels and emergent selection rules
• Spin-orbital excitons and their potential condensation in pentavalent iridates
• Decomposing imaginary time Feynman diagrams using separable basis functions: Anderson impurity model strong coupling expansion
• Magnetic reorientation transition in a three orbital model for $\mathrm{C}{\mathrm{a}}_2\mathrm{Ru}{\mathrm{O}}_4$ -- Interplay of spin-orbit coupling, tetragonal distortion, and Coulomb interactions
• Charge transfer model for the electronic structure of layered ruthenates
• Electronic excitations in $5d^4$ J=0 Os${}^{4+}$ halides studied by RIXS and optical spectroscopy
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• Photoemission Spectrum of Ca2RuO4: Spin Polaron Physics in an S=1 Antiferromagnet with Anisotropies
• Magnetic phases for two $t_{2g}$ holes with spin-orbit coupling and crystal field
• Emergence of pure spin current in doped excitonic magnets
• Role of orbital off-diagonal spin and charge condensates in a three orbital model for $\mathrm{C}{\mathrm{a}}_2\mathrm{Ru}{\mathrm{O}}_4$ -- Coulomb renormalized spin-orbit coupling, orbital moment, and tunable magnetic order
• Competition of three-dimensional magnetic phases in Ca${}_2$Ru${}_{1-x}$Fe${}_x$O${}_4$: A structural perspective
• Coupled spin-orbital fluctuations in a three orbital model for $4d$ and $5d$ oxides with electron fillings $n=3,4,5$ -- Application to $\mathrm{NaOs}{\mathrm{O}}_3$, $\mathrm{C}{\mathrm{a}}_2\mathrm{Ru}{\mathrm{O}}_4$, and $\mathrm{S}{\mathrm{r}}_2\mathrm{Ir}{\mathrm{O}}_4$
• Spin and charge order in doped spin-orbit coupled Mott insulators
• Collective mode excitations and simulated $L$-edge resonant-inelastic x-ray scattering spectra in antiferromagnetic Ca${}_2$RuO${}_4$
• Critical magnetic fluctuations in the layered ruthenates Ca${}_2$RuO${}_4$ and Ca${}_3$Ru${}_2$O${}_7$
• Magnetic polarons due to spin-length fluctuations in ${\mathbf{d}}^4$ spin-orbit Mott systems