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arXiv:1910.00074 · Physical review. B./Physical review. B

Highly frustrated magnetism in relativistic d 4 Mott insulators: Bosonic analog of the Kitaev honeycomb model

Jiří Chaloupka, Giniyat Khaliullin

Published Dec 16, 2019• 21 citations
arXivHTMLPDF

Abstract

We study the orbitally frustrated singlet-triplet models that emerge in the context of spin-orbit coupled Mott insulators with ${t}_{2g}^{4}$ electronic configuration. In these compounds, low-energy magnetic degrees of freedom can be cast in terms of three-flavor ``triplon'' operators describing the transitions between spin-orbit entangled $J=0$ ionic ground state and excited $J=1$ levels. In contrast to a conventional, flavor-isotropic O(3) singlet-triplet models, spin-orbit entangled triplon interactions are flavor-and-bond selective and thus highly frustrated. In a honeycomb lattice, we find close analogies with the Kitaev spin model---an infinite number of conserved quantities, no magnetic condensation, and spin correlations being strictly short-ranged. However, due to the bosonic nature of triplons, there are no emergent gapless excitations within the spin gap, and the ground state is a strongly correlated paramagnet of dense triplon pairs with no long-range entanglement. Using exact diagonalization, we study the bosonic Kitaev model and its various extensions, which break exact symmetries of the model and allow magnetic condensation of triplons. Possible implications for magnetism of ruthenium oxides are discussed.

DOI
10.1103/physrevb.100.224413

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We study the orbitally frustrated singlet-triplet models that emerge in the context of spin-orbit coupled Mott insulators with t2g4{t}_{2g}^{4}t2g4​ electronic configuration. In these compounds, low-energy magnetic degrees of freedom can be cast in terms of three-flavor ``triplon'' operators describing the transitions between spin-orbit entangled J=0J=0J=0 ionic ground state and excited J=1J=1J=1 levels. In contrast to a conventional, flavor-isotropic O(3) singlet-triplet models, spin-orbit entangled triplon interactions are flavor-and-bond selective and thus highly frustrated. In a honeycomb lattice, we find close analogies with the Kitaev spin model---an infinite number of conserved quantities, no magnetic condensation, and spin correlations being strictly short-ranged. However, due to the bosonic nature of triplons, there are no emergent gapless excitations within the spin gap, and the ground state is a strongly correlated paramagnet of dense triplon pairs with no long-range entanglement. Using exact diagonalization, we study the bosonic Kitaev model and its various extensions, which break exact symmetries of the model and allow magnetic condensation of triplons. Possible implications for magnetism of ruthenium oxides are discussed.
In this doctoral dissertation, we consider the significance of spin-orbit coupling for the phases of matter which arise for strongly correlated electrons. We explore emergent behavior in quantum many-body systems, including symmetry-breaking orders, quantum spin liquids, and unconventional superconductivity. Our study is cemented by a particular class of Mott-insulating materials, centered around a family of two- and three-dimensional iridium oxides, whose honeycomb-like lattice structure admits peculiar magnetic interactions, the so-called Kitaev exchange. By analyzing recent experiments on these compounds, we show that this unconventional exchange is the key ingredient in describing their magnetism, and then use a combination of numerical and analytical techniques to investigate the implications for the phase diagram as well as the physics of the proximate three-dimensional quantum spin liquid phases. These long-ranged-entangled fractionalized phases should exhibit special features, including finite-temperature stability as well as unconventional high-Tc superconductivity upon charge-doping, which should aid future experimental searches for spin liquid physics. Our study explores the nature of frustration and fractionalization which can arise in quantum systems in the presence of strong spin-orbit coupling.
In the field of quantum magnetism, the exactly solvable Kitaev honeycomb model serves as a paradigm for the fractionalization of spin degrees of freedom and the formation of [Formula: see text] quantum spin liquids. An intense experimental search has led to the discovery of a number of spin-orbit entangled Mott insulators that realize its characteristic bond-directional interactions and, in the presence of magnetic fields, exhibit no indications of long-range order. Here, we map out the complete phase diagram of the Kitaev model in tilted magnetic fields and report the emergence of a distinct gapless quantum spin liquid at intermediate field strengths. Analyzing a number of static, dynamical, and finite temperature quantities using numerical exact diagonalization techniques, we find strong evidence that this phase exhibits gapless fermions coupled to a massless U(1) gauge field. We discuss its stability in the presence of perturbations that naturally arise in spin-orbit entangled candidate materials.
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.
Mott-insulating transition metal oxides containing t2g4{t}_{2g}^{4}t2g4​ ions with strong spin-orbit coupling were recently demonstrated to display unusual magnetism due to a dynamical mixing of the low-energy multiplet states via exchange processes. Here we derive exchange interactions in the situation where a tetragonal or trigonal crystal field selects a single relevant excited state on top of the singlet ionic ground state, producing an effective spin-12\frac{1}{2}21​. We show that these moments universally obey antiferromagnetic transverse-field Ising model (TFIM) with an intrinsic transverse field generated by the splitting of the two ionic singlets. Using Ru4+{\mathrm{Ru}}^{4+}Ru4+ as a example ion, we provide quantitative estimates of the exchange and illustrate the emergent TFIM physics based on phase diagrams and excitation spectra obtained for several 2D lattices---square, honeycomb, as well as for the frustrated triangular lattice.
Abstract A family of spin–orbit coupled honeycomb Mott insulators offers a playground to search for quantum spin liquids (QSLs) via bond-dependent interactions. In candidate materials, a symmetric off-diagonal Γ term, close cousin of Kitaev interaction, has emerged as another source of frustration that is essential for complete understanding of these systems. However, the ground state of honeycomb Γ model remains elusive, with a suggested zigzag magnetic order. Here we attempt to resolve the puzzle by perturbing the Γ region with a staggered Heisenberg interaction which favours the zigzag ordering. Despite such favour, we find a wide disordered region inclusive of the Γ limit in the phase diagram. Further, this phase exhibits a vanishing energy gap, a collapse of excitation spectrum, and a logarithmic entanglement entropy scaling on long cylinders, indicating a gapless QSL. Other quantities such as plaquette-plaquette correlation are also discussed.
Spin-orbital generalization of Kitaev model provides a robust extension to the original Kitaev model. However, real materials often exhibit competing interactions that break exact solvability which can give rise to new phases. Motivated by recent microscopic proposals of coexisting Yao-Lee and Kitaev couplings, we investigate the fate of the ground state when two independent exactly solvable spin liquid Hamiltonians each originally formulated on different lattice geometries are combined on a common lattice environment. We first focus on the hybrid Kitaev's honeycomb and square-lattice model. Using self-consistent mean-field analysis and perturbative calculation, we show that the strong-Kitaev regime yields magnetic order in the spin sector, while the orbital sector retains its topological order. We further analyze the hybridization of the Yao-Lee and square-lattice models and find that the model exhibits a rich evolution of Majorana Dirac bands and Lifshitz transitions. Remarkably, when the Yao-Lee and square-lattice couplings are equal and opposite, the model restores its exact solvability with a single itinerant Majorana flavor. These results demonstrate that hybrid spin liquid platforms may host various emergent phases beyond conventional exactly solvable limits.