11. May 2018

A theory for the gapless field-induced quantum spin-liquid phase of α−RuCl3

The material α−RuCl3 continues to garner attention as the current poster child for realising the Kitaev model. New work places recent experimental observations on a solid theoretical footing, and concludes that the physics of α−RuCl3 is not dominated by Kitaev interactions.

The Kitaev model on the honeycomb lattice is a fundamental paradigm for quantum spin liquids (QSLs), both of the gapped and ungapped variety. One of the canditate materials for realising Kitaev-type physics is α−RuCl3, a layered honeycomb spin-½ insulator with anisotropic magnetic interactions. Under ambient conditions α−RuCl3 has a magnetically ordered ground state, but in an applied magnetic field it undergoes a transition to a disordered one, which has the behaviour of a QSL. Despite recent experimental progress, the controversy over the gapped or gapless nature of this QSL state continues. Writing in Physical Review Letters [1], PSI theorist Bruce Normand and Zheng-Xin Liu at Renmin University of China in Beijing now present a model that reproduces behaviour found in α−RuCl3 that deviates from that expected for a pure Kitaev system.

The motivation for the study of Liu and Normand came from a nuclear magnetic resonance (NMR) investigation published last year [2], to which the two theorists also contributed. NMR is the definitive technique for detecting low-energy, low-density magnetic excitations. The 2017 experiments on α−RuCl3 are the most sensitive NMR measurements, on the best samples and at the lowest temperatures achieved to date. They revealed gapless magnetic excitations with a cone-type dispersion over a broad range of applied in-plane fields; by contrast, these excitations became gapped when the field was applied out of the plane.

The new theoretical model of Liu and Normand reproduces the most salient features of the NMR study. Because the experiments clearly indicate spin fractionalisation, the researchers introduced a spinon representation. Their model required not only a Kitaev interaction but also a stronger off-diagonal symmetric term. In their Variational Monte Carlo calculations, they observed the field-induced phase transition to a disordered phase, whose nature depends crucially on the field orientation. For specific in-plane field directions, they found a gapless Dirac spin liquid, in agreement with experiment. For a range of out-of-plane fields, they predicted the existence of a chiral spin liquid, whose unique experimental signature would be an integer-quantised thermal Hall effect. Based on their finding that the measured in-plane response is a consequence of Dirac-type spinons, rather than the Majorana type expected in a system displaying Kitaev physics, they concluded that the behaviour of α−RuCl3 is indeed dominated by the additional interaction terms.

Dr. Bruce Normand
Paul Scherrer Institute, 5232 Villigen PSI, Switzerland
Phone: +41 56 310 2297, e-mail: bruce.normand@psi.ch

Original Publications
1. Dirac and chiral quantum spin liquids on the honeycomb lattice in a magnetic field
Liu Z-X, Normand B
Physical Review Letters, 120: 187201, 2018
DOI: 10.1103/PhysRevLett.120.187201

2. Gapless spin excitations in the field-induced quantum spin liquid phase of α−RuCl3
Zheng J, Ran K, Li T, Wang J, Wang P, Liu B, Liu Z-X, Normand B, Wen J, Yu W
Physical Review Letters, 119: 227208, 2017
DOI: 10.1103/PhysRevLett.119.227208

Additional reading
The field-induced quantum spin-liquid phase of α−RuCl3 is gapless
(NUM Highlight on the work presented in Ref. 2)