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arXiv:1603.02548 · Physical review. B./Physical review. B

Challenges in design of Kitaev materials: Magnetic interactions from competing energy scales

Stephen M. Winter, Ying Li, Harald O. Jeschke, Roser Valentí

Published Jun 27, 2016• 508 citations
arXivHTMLPDF

Abstract

Much interest has emerged in the realization of materials with quantum spin liquid ground states, which would provide fertile ground for realizing exotic excitations. Three ``Kitaev'' spin liquid candidate materials have been proposed -- Na${}_{2}$IrO${}_{3}$, $\ensuremath{\alpha}$-RuCl${}_{3}$, and $\ensuremath{\alpha}$-Li${}_{2}$IrO${}_{3}$ -- and there has been many diverging proposals for the most relevant interactions. Here, the authors re-evaluate carefully the magnetic interactions in these materials, using nonperturbative exact diagonalization methods. The results clarify misconceptions in the literature and help estimate the potential for realizing the spin liquid state in real materials.

DOI
10.1103/physrevb.93.214431

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Quantum spin liquids have fascinated condensed matter physicists for decades because of their unusual properties such as spin fractionalization and long-range entanglement. Unlike conventional symmetry breaking, the topological order underlying quantum spin liquids is hard to detect experimentally. Even theoretical models are scarce for which the ground state is established to be a quantum spin liquid. The Kitaev honeycomb model and its generalizations to other tricoordinated lattices are chief counterexamples—they are exactly solvable, harbor a variety of quantum spin liquid phases, and are also relevant for certain transition metal compounds including the polymorphs of (Na,Li) 2 IrO 3 iridates and RuCl 3 . In this review, we give an overview of the rich physics of the Kitaev model, including two-dimensional and three-dimensional fractionalization as well as dynamic correlations and behavior at finite temperatures. We discuss the different materials and argue how the Kitaev model physics can be relevant even though most materials show magnetic ordering at low temperatures.
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Abstract Large anisotropic exchange in 5 d and 4 d oxides and halides open the door to new types of magnetic ground states and excitations, inconceivable a decade ago. A prominent case is the Kitaev spin liquid, host of remarkable properties such as protection of quantum information and the emergence of Majorana fermions. Here we discuss the promise for spin-liquid behavior in the 4 d 5 honeycomb halide α -RuCl 3 . From advanced electronic-structure calculations, we find that the Kitaev interaction is ferromagnetic, as in 5 d 5 iridium honeycomb oxides, and indeed defines the largest superexchange energy scale. A ferromagnetic Kitaev coupling is also supported by a detailed analysis of the field-dependent magnetization. Using exact diagonalization and density-matrix renormalization group techniques for extended Kitaev-Heisenberg spin Hamiltonians, we find indications for a transition from zigzag order to a gapped spin liquid when applying magnetic field. Our results offer a unified picture on recent magnetic and spectroscopic measurements on this material and open new perspectives on the prospect of realizing quantum spin liquids in d 5 halides and oxides in general.
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Abstract Aligning with the ongoing search for quantum spin liquids (QSLs), identifying QSLs in Kitaev magnets has attracted significant research interest during the past decade. Nevertheless, it remains a significant challenge. One of the major difficulties is that Kitaev QSL is typically fragile to competing interactions such as off-diagonal exchanges, which are ubiquitous in real materials owing to spin-orbit coupling and crystal-field effects. This, in turn, generates many intriguing field-induced novel phases and the thermal Hall effect. In this review, we focus on the interplay between the Kitaev interaction and off-diagonal Γ and Γ′ exchange from a numerical perspective. The review discusses certain representative exotic phases such as Γ spin liquid, nematic ferromagnet, spin-flop phase, and distinct chiral spin states with spontaneous time-reversal symmetry breaking. It also presents quantum phase diagrams of anisotropic Kitaev-Γ chains that exhibit kaleidoscopy for both ordered and disordered phases.
Abstract What is the correct low-energy spin Hamiltonian description of α\alphaα α -RuCl 3_{3}3​ 3 ? The material is a promising Kitaev spin liquid candidate, but is also known to order magnetically, the description of which necessitates additional interaction terms. The nature of these interactions, their magnitudes and even signs, remain an open question. In this work we systematically investigate dynamical and thermodynamic magnetic properties of proposed effective Hamiltonians. We calculate zero-temperature inelastic neutron scattering (INS) intensities using exact diagonalization, and magnetic specific heat using a thermal pure quantum states method. We find that no single current model satisfactorily explains all observed phenomena of α\alphaα α -RuCl 3_{3}3​ 3 . In particular, we find that Hamiltonians derived from first principles can capture the experimentally observed high-temperature peak in the magnetic specific heat, while overestimating the magnon energy at the zone center. In contrast, other models reproduce important features of the INS data, but do not adequately describe the magnetic specific heat. To address this discrepancy we propose a modified ab initio model that is consistent with both magnetic specific heat and low-energy features of INS data.