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arXiv:1905.13683 · Physical review. B./Physical review. B

Orbital magnetic field effects in Mott insulators with strong spin-orbit coupling

W. M. H. Natori, Roderich Moessner, Johannes Knolle

Published Oct 2, 2019• 8 citations
arXivHTMLPDF

Abstract

We study the effect of a magnetic field on the low-energy description of Mott insulators with strong spin-orbit (SO) coupling. In contrast to the standard case of the Hubbard model without SO coupling, we show that Peierls phases can modulate the magnetic exchange at leading order in the interaction. Our mechanism crucially depends on the existence of distinct exchange paths between neighboring magnetic ions enclosing a well-defined area. Thus it will generically be present in any solid state realization of the Kitaev model and its extensions. We explicitly calculate the variation of the exchange constants of the so-called $JK\mathrm{\ensuremath{\Gamma}}$ model as a function of the magnetic flux. We discuss experimental implications of our findings for various settings of candidate Kitaev spin liquids.

DOI
10.1103/physrevb.100.144403

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We study the effect of a magnetic field on the low-energy description of Mott insulators with strong spin-orbit (SO) coupling. In contrast to the standard case of the Hubbard model without SO coupling, we show that Peierls phases can modulate the magnetic exchange at leading order in the interaction. Our mechanism crucially depends on the existence of distinct exchange paths between neighboring magnetic ions enclosing a well-defined area. Thus it will generically be present in any solid state realization of the Kitaev model and its extensions. We explicitly calculate the variation of the exchange constants of the so-called JK\ensuremathΓJK\mathrm{\ensuremath{\Gamma}}JK\ensuremathΓ model as a function of the magnetic flux. We discuss experimental implications of our findings for various settings of candidate Kitaev spin liquids.
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 d5{d}^{5}d5 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 d7{d}^{7}d7 electron configuration, whose ground state is described by the spin-orbital entangled Kramers doublet. By the second-order perturbation in terms of the ${t}_{2g}\ensuremath{-}{t}_{2g}$ and ${t}_{2g}\ensuremath{-}{e}_{g}$ 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 d5{d}^{5}d5 electron configuration within the same perturbation scheme, in which the Kitaev interaction becomes both ferromagnetic and antiferromagnetic, while the Heisenberg one is 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 d7{d}^{7}d7 and d5{d}^{5}d5 cases, while the former has a richer structure of the phase diagram. We discuss the advantages of the d7{d}^{7}d7 case in comparison with the d5{d}^{5}d5 case. Our results indicate that the high-spin d7{d}^{7}d7 state provides another platform for the Kitaev-type quantum spin liquid.
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A bond-directional anisotropic exchange interaction, called the Kitaev interaction, is a promising route to realize quantum spin liquids. The Kitaev interactions were found in Mott insulators with the strong spin-orbit coupling, in the presence of quantum interference between indirect electron transfers. Here we theoretically propose a different scenario by introducing a polar structural asymmetry that unbalances the quantum interference. We show that the imbalance activates additional exchange processes and gives rise to a dominant antiferromagnetic Kitaev interaction, in stark contrast to the conventional ferromagnetic ones. We demonstrate by ab initio calculations that polar Ru trihalides with multiple anions, $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuH}}_{3/2}{X}_{3/2}$ (X=ClX=\text{Cl}X=Cl and Br), exhibit dominant antiferromagnetic Kitaev interactions by this mechanism. Our proposal opens the way for materializing the Kitaev spin liquids in unexplored parameter regions.
We study the effective spin-orbital model for honeycomb-layered transition metal compounds, applying the second-order perturbation theory to the three-orbital Hubbard model with the anisotropic hoppings. This model is reduced to the Kitaev model in the strong spin-orbit coupling limit. Combining the cluster mean-field approximations with the exact diagonalization, we treat the Kugel-Khomskii type superexchange interaction and spin-orbit coupling on an equal footing to discuss ground-state properties. We find that a zigzag ordered state is realized in the model within nearest-neighbor interactions. We clarify how the ordered state competes with the nonmagnetic state, which is adiabatically connected to the quantum spin liquid state realized in a strong spin-orbit coupling limit. Thermodynamic properties are also addressed. The present paper should provide another route to account for the Kitaev-based magnetic properties in candidate materials.
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