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arXiv:1905.12139 · Physical review. B./Physical review. B

Antiferromagnetic Kitaev interactions in polar spin-orbit Mott insulators

Yusuke Sugita, Yasuyuki Kato, Yukitoshi Motome

Published Mar 31, 2020• 20 citations
arXivHTMLPDF

Abstract

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, $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuH}}_{3/2}{X}_{3/2}$ ($X=\text{Cl}$ 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.

DOI
10.1103/physrevb.101.100410

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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, \ensuremathα\ensuremath-RuH3/2X3/2\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuH}}_{3/2}{X}_{3/2}\ensuremathα\ensuremath-RuH3/2​X3/2​ (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.
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.
The Kitaev model, characterized by bond-dependent Ising spin interactions among spin-orbit entangled dipole moments in Mott insulators, offered a new approach to quantum spin liquids. Motivated by another type of bond-dependent interaction among quadrupole moments in 5d25{d}^{2}5d2 Mott insulators, we provide a microscopic route to uncover the Kitaev multipolar liquid, featuring fractionalized excitations out of non-Kramers doublets carrying multipole moments. The key ingredient is the magnetic field that allows for bond-anisotropic quadrupole-octupole interactions via mixing with the excited triplet states. The conditions to realize signatures of this phase in real materials are also discussed.
The current efforts to find the materials hosting Kitaev model physics have been focused on Mott insulators of d5{d}^{5}d5 pseudospin-1/2 ions Ir4+{\mathrm{Ir}}^{4+}Ir4+ and Ru3+{\mathrm{Ru}}^{3+}Ru3+ with t2g5(S=1/2,L=1){t}_{2g}^{5}(S=1/2,L=1)t2g5​(S=1/2,L=1) electronic configuration. Here we propose that the Kitaev model can be realized in materials based on d7{d}^{7}d7 ions with t2g5eg2(S=3/2,L=1){t}_{2g}^{5}{e}_{g}^{2}(S=3/2,L=1)t2g5​eg2​(S=3/2,L=1) configuration such as Co2+{\mathrm{Co}}^{2+}Co2+, which also host the pseudospin-1/2 magnetism. Considering possible exchange processes, we have derived the d7{d}^{7}d7 pseudospin-1/2 interactions in ${90}^{\ensuremath{\circ}}$ bonding geometry. The obtained Hamiltonian comprises the bond-directional Kitaev KKK and isotropic Heisenberg JJJ interactions as in the case of d5{d}^{5}d5 ions. However, we find that the presence of additional spin-active eg{e}_{g}eg​ electrons radically changes the balance between Kitaev and Heisenberg couplings. Most remarkably, we show that the exchange processes involving eg{e}_{g}eg​ spins are highly sensitive to whether the system is in Mott ($U<\mathrm{\ensuremath{\Delta}}$) or charge-transfer ($U>\mathrm{\ensuremath{\Delta}}$) insulating regime. In the latter case, to which many cobalt compounds do actually belong, the antiferromagnetic Heisenberg coupling JJJ is strongly suppressed and spin-liquid phase can be stabilized. The results suggest cobalt-based materials as promising candidates for the realization of the Kitaev model.
Can we realize Kitaev quantum spin liquids in the Jeff=1/2J_\text{eff}=1/2Jeff​=1/2 honeycomb cobaltates?
The quest for Kitaev quantum spin liquids has led to great interest in honeycomb quantum magnets with strong spin-orbit coupling. It has been recently proposed that even Mott insulators with 3d3d3d transition metal ions, having nominally weak spin-orbit coupling, can realize such exotic physics. Motivated by this, we study the rhombohedral honeycomb cobaltates CoTiO3_33​, BaCo2_22​(PO4_44​)2_22​, and BaCo2_22​(AsO4_44​)2_22​, using ab initio\textit{ab initio}ab initio density functional theory, which takes into account realistic crystal field distortions and chemical information, in conjunction with exact diagonalization numerics. We show that these Co2+^{2+}2+ magnets host jeff=1/2j_\text{eff}=1/2jeff​=1/2 local moments with highly anisotropic ggg-factors, and we extract their full spin Hamiltonians including longer-range and anisotropic exchange couplings. For CoTiO3_33​, we find a nearest-neighbor easy-plane ferromagnetic XXZXXZXXZ model with additional bond-dependent anisotropies and interlayer exchange, which supports three-dimensional (3D) Dirac nodal line magnons. In contrast, for BaCo2_22​(PO4_44​)2_22​ and BaCo2_22​(AsO4_44​)2_22​, we find a strongly suppressed interlayer coupling, and significant frustration from additional third-neighbor antiferromagnetic exchange mediated by P/As. Such bond-anisotropic J1J_1J1​-J3J_3J3​ spin models can support collinear zig-zag or coplanar spiral ground states; we discuss their dynamical spin correlations which reveal a gapped Goldstone mode, and argue that the effective parameters of these pseudospin-1/21/21/2 models may be strongly renormalized by coupling to a low energy spin-exciton. Our results call for re-examining proposals for realizing Kitaev spin liquids in the honeycomb cobaltates.
We study a spin model on honeycomb lattice with two types of Heisenberg exchange couplings, JJJ and $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{J}$, where JJJ is for the conventional spin and $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{J}$ is for rotated spin. When J=0J=0J=0, the system is either in a stripy antiferromagnetic order ($\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{J}<0$, ferromagnetic for rotated spin) or a zigzag antiferromagnetic order ($\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{J}>0$, antiferromagnetic for rotated spin). The competition between two ferromagnetic orders or between two antiferromagnetic orders induces Kitaev's spin liquid phase, characterized by the exactly solvable Kitaev model ($J=\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{J}$). Our model can be applied to layered Mott insulators AAA2{}_{2}2​IrO3{}_{3}3​ (A=LiA=\text{Li}A=Li, Na). For a monolayer of Li2{}_{2}2​IrO3{}_{3}3​, we show that it is possible to tune the controlling parameter into the Kitaev spin liquid regime by a link-dependent Rashba spin-orbital coupling.
The spin S=1/2 Kitaev honeycomb model has attracted significant attention since emerging candidate materials have provided a playground to test non-Abelian anyons. The Kitaev model with higher spins has also been theoretically studied, as it may offer another path to a quantum spin liquid. However, a microscopic route to achieve higher spin Kitaev models in solid state materials has not been rigorously derived. Here we present a theory of the spin S=1 Kitaev interaction in two-dimensional edge-shared octahedral systems. Essential ingredients are strong spin-orbit coupling in anions and strong Hund's coupling in transition metal cations. The S=1 Kitaev and ferromagnetic Heisenberg interactions are generated from superexchange paths. Taking into account the antiferromagnetic Heisenberg term from direct-exchange paths, the Kitaev interaction dominates the physics of the S=1 system. Using an exact diagonalization technique, we show a finite regime of S=1 spin liquid in the presence of the Heisenberg interaction. Candidate materials are proposed, and generalization to higher spins is discussed.