Kitaev-Heisenberg Hamiltonian for High-Spin $d^7$ Mott Insulators

Abstract

In the search for quantum spin liquids, candidate materials for the Kitaev model and its extensions have been intensively explored during the past decade, as the models realize the exact quantum spin liquids in the ground state. Thus far, insulating magnets in the low-spin $d^5$ electron configuration under the strong spin-orbit coupling have been studied for realizing the Kitaev-type bond-dependent anisotropic interactions between the spin-orbital entangled Kramers doublets. To extend the candidates, here we investigate the systems in a high-spin $d^7$ electron configuration, whose ground state is described by the spin-orbital entangled Kramers doublet. By the second- order perturbation in terms of the $t_{2g}$-$t_{2g}$ and $t_{2g}$-$e_g$ hoppings, we show that the effective spin model possesses the anisotropic Kitaev interactions as well as the isotropic Heisenberg ones. While the Kitaev interaction is always ferromagnetic, the Heisenberg interaction can become either ferromagnetic or antiferromagnetic depending on the Coulomb interactions and the crystalline electric fields. We also derive the effective model for the low-spin $d^5$ electron configuration within the same perturbation scheme, in which the Kitaev interaction becomes both ferromagnetic and antiferromagnetic, while the Heisenberg one always ferromagnetic. Referring to the previous study for the Kitaev-Heisenberg model, we find that the quantum spin liquid phase exists in the reasonable parameter region in both $d^7$ and $d^5$ cases, while the former has a richer structure of the phase diagram. We discuss the advantages of the $d^7$ case in comparison with the $d^5$ case. Our results indicate that the high-spin $d^7$ state provides another platform for the Kitaev-type quantum spin liquid.

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Cited by in corpus (162)

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• Kitaev Spin Liquid in 3d Transition Metal Compounds
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• Spin-orbit-entangled electronic phases in 4$d$ and 5$d$ transition-metal compounds
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• Antiferromagnetic Kitaev interaction in $J_\rm{eff}=1/2$ cobalt honeycomb materials Na${}_3$Co${}_2$SbO${}_6$ and Na${}_2$Co${}_2$TeO${}_6$
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• Materials design of Kitaev spin liquids beyond the Jackeli-Khaliullin mechanism
• Ferrimagnetism and anisotropic phase tunability by magnetic fields in Na${}_2$Co${}_2$TeO${}_6$
• Spin-orbit phase behaviors of Na2Co2TeO6 at low temperatures
• Honeycomb Layered Oxides: Structure, Energy Storage, Transport, Topology and Relevant Insights
• Proximate ferromagnetic state in the Kitaev model material $\alpha$-RuCl${}_3$
• Magnetic order in single crystals of Na3Co2SbO6 with a honeycomb arrangement of 3d${}^7$ Co${}^{2+}$ ions
• Order-by-Disorder from Bond-Dependent Exchange and Intensity Signature of Nodal Quasiparticles in a Honeycomb Cobaltate
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• Geometrical frustration versus Kitaev interactions in BaCo${}_2$(AsO${}_4$)${}_2$
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• Selective measurements of intertwined multipolar orders: non-Kramers doublets on a triangular lattice
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• Unveiling the S=3/2 Kitaev Honeycomb Spin Liquids
• Towards Kitaev Spin Liquid in 3d Transition Metal Compounds
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• Competing Antiferromagnetic-Ferromagnetic States in $d^7$ Kitaev Honeycomb Magnet
• Modified Curie-Weiss Law for $j_{\mathrm{eff}}$ Magnets
• Magnetic excitations of the field induced states in BaCo2(AsO4)2 probed by time-domain terahertz spectroscopy
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• Computational design of $f$-electron Kitaev magnets: honeycomb and hyperhoneycomb compounds $A_2$PrO${}_3$ ($A=$ alkali metals)
• Collective excitations in the tetravalent lanthanide honeycomb antiferromagnet, Na2PrO3
• Thermal Transport of Fractionalized Antiferromagnetic and Field Induced States in the Kitaev Material Na${}_2$Co${}_2$TeO${}_6$
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• Multiflavor Mott insulators in quantum materials and ultracold atoms
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• Quantum and classical behavior of spin-$S$ Kitaev models in an anisotropic limit
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• Planar thermal Hall effect from phonons in a Kitaev candidate material
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• Theoretical evidence of spin-orbital-entangled $J_{\mathbf{eff}}$=1/2 state in the 3$d$ transition metal oxide CuAl${}_2$O${}_4$
• Kitaev Spin Liquid Candidate OsxCl3 Comprised of Honeycomb Nano-Domains
• Field evolution of magnetic phases and spin dynamics in the honeycomb lattice magnet Na2Co2TeO6: 23Na NMR study
• Phononic-magnetic dichotomy of the thermal Hall effect in the Kitaev-Heisenberg candidate material Na${}_2$Co${}_2$TeO${}_6$
• Perfect kagome-lattice antiferromagnets with J${}_{eff}$ = 1/2: The Co${}^{2+}$-analogs of copper minerals volborthite and vesignieite
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• Orbital Magnetic Field Effects in Mott Insulators with Strong Spin-Orbit Coupling
• Suppression of the antiferromagnetic order by Zn doping in a possible Kitaev material Na${}_2$Co${}_2$TeO${}_6$
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• Topological phase diagrams of in-plane field polarized Kitaev magnets
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• Ferromagnetic Ferroelectricity due to Orbital Ordering
• Anisotropic magnetoelastic coupling in the honeycomb magnet Na${}_3$Co${}_2$SbO${}_6$
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