Ferromagnetic Kitaev interaction and the origin of large magnetic anisotropy in α-RuCl3

Abstract

α-RuCl 3 is drawing much attention as a promising candidate Kitaev quantum spin liquid [1][2][3][4][5][6][7][8]. However, despite intensive research efforts, controversy remains about the form of the basic interactions governing the physics of this material. Even the sign of the Kitaev interaction (the bonddependent anisotropic interaction responsible for Kitaev physics) is still under debate, with conflicting results from theoretical and experimental studies [5,6,[9][10][11][12][13][14][15]. The significance of the symmetric off-diagonal exchange interaction (referred to as the Γ term) is another contentious question [16][17][18]. Here, we present resonant elastic x-ray scattering data that provides unambiguous experimental constraints to the two leading terms in the magnetic interaction Hamiltonian. We show that the Kitaev interaction (K) is ferromagnetic, and that the Γ term is antiferromagnetic and comparable in size to the Kitaev interaction. Our findings also provide a natural explanation for the large anisotropy of the magnetic susceptibility in α-RuCl 3 as arising from the large Γ term. We therefore provide a crucial foundation for understanding the interactions underpinning the exotic magnetic behaviours observed in α-RuCl 3 .

Identification of magnetic interactions and high-field quantum spin liquid in α-RuCl3

“…In our K - J -Γ- model of α -RuCl 3 , we see a dominating FM Kitaev interaction and a sub-leading positive Γ term (Γ > 0), which fulfill the interaction signs proposed from recent experiments 6 , 34 , 39 and agree with some ab initio studies 9 , 33 , 36 , 37 , 43 , 57 . The strong Kitaev interaction seems to play a predominant role at intermediate temperature, which leads to the fractional liquid regime and therefore naturally explains the observed proximate spin liquid behaviors 14 , 15 , 19 .…”

“…The spin-orbit magnet α -RuCl 3 , with edge-sharing RuCl 6 octahedra and a nearly perfect honeycomb plane, has been widely believed to be a correlated insulator with the Kitaev interaction 1 – 6 . The compound α -RuCl 3 , and the Kitaev materials in general, have recently raised great research interest in exploring the inherent Kitaev physics 7 – 11 , which can realize non-Abelian anyon with potential applications in topological quantum computations 12 , 13 .…”

Universal thermodynamics in the Kitaev fractional liquid

“…Therefore, the analysis in Fig. 8 suggests the FM Kitaev interactions in both compounds Na 2 IrO 3 and α-RuCl 3 , in agreement with previous theoretical [10,38,60,61] and experimental [40] estimates.…”

“…For the typical Kitaev materials Na 2 IrO 3 and α-RuCl 3 , the predominant Kitaev interactions have been widely accepted to be ferromagnetic (FM) [10,24,33,[38][39][40]. Thus, we choose K γ < 0 henceforth and set K z = −1 as the fixed energy scale.…”

Emergence of nematic paramagnet via quantum order-by-disorder and pseudo-Goldstone modes in Kitaev magnets

“…In addition to a substantial Kitaev interaction, there exist other types of spin-exchange interactions [11] in these materials, which ultimately stabilize a magnetic order instead of the desired quantum spin liquid. A paradigmatic example of Kitaev materials is α-RuCl 3 [12], which has a zigzag (ZZ) ordered ground state [13][14][15][16]. Upon applying a magnetic field, however, the ZZ order vanishes [14,[17][18][19][20][21][22], while a half-quantized thermal Hall conductivity is observed [23].…”