Critical Properties of the Kitaev-Heisenberg Model

Abstract

We study the critical properties of the Kitaev-Heisenberg (KH) model on the honeycomb lattice at finite temperatures that might describe the physics of the quasi two-dimensional (2D) compounds, Na2IrO3 and Li2IrO3. The model undergoes two phase transitions as a function of temperature. At low temperature, thermal fluctuations induce magnetic long-range order by the order-by-disorder mechanism. This magnetically ordered state with a spontaneously broken Z6 symmetry persists up to a certain critical temperature. We find that there is an intermediate phase between the low-temperature, ordered phase and the high-temperature, disordered phase. Finite-sized scaling analysis suggests that the intermediate phase is a critical Kosterlitz-Thouless (KT) phase with continuously variable exponents. We argue that the intermediate phase has been observed above the low-temperature, magnetically ordered phase in Na2IrO3, and also likely exists in Li2IrO3.Introduction. The Ir-based transition metal oxides, in which the orbital degeneracy is accompanied by a strong relativistic spin-orbit coupling (SOC), have recently attracted a lot of theoretical and experimental attention [1][2][3][4][5][6][7][8]. This is because the strong SOC creates a different, and frequently novel, set of magnetic and orbital states due to the unusual anisotropic exchange interactions between localized moments which are in turn determined by the combination of spin and lattice symmetries. The spin-orbital models that describe the low-energy physics of iridium systems often include anisotropic terms that do not reduce to the conventional easy-plane and easy-axis anisotropies because they involve the products of different components of multiple spin operators. These terms are responsible for exotic Mott-insulating states [3], topological insulators [10,11], spin-orbital liquid states [1, 2], and non-trivial long-range magnetic orders [3,4,6].A prominent example of such an anisotropic spinorbital model is the KH model on the honeycomb lattice [12,13] which likely describes the low-energy physics of the quasi 2D compounds, Na 2 IrO 3 and Li 2 IrO 3 . In these compounds, Ir 4+ ions are in a low spin 5d 5 configuration and form weakly coupled hexagonal layers [4,6,8]. Due to strong SOC, the atomic ground state is a doublet where the spin and orbital angular momenta of Ir 4+ ions are coupled into J eff = 1/2. It was suggested [12,13] that the interactions between these effective moments can be described by a spin Hamiltonian containing two competing nearest neighbor (NN) interactions: an isotropic antiferromagnetic (AF) Heisenberg exchange interaction and a highly anisotropic ferromagnetic (FM) Kitaev exchange interaction [14]. This competition can be described with the parameter, 0 ≤ α ≤ 1, which sets the relative strength of these two interactions. At α = 0, the coupling corresponds to the AF Heisenberg interaction, and at α = 1, it corresponds to the Kitaev interaction.This model immediately attracted a lot of attention; several theoretical studies were publis...

Nature of the possible magnetic phases in a frustrated hyperkagome iridate

“…On the one hand, a comparison between preceding classical calculations 39,40 and quantum calculations 6,12 on the honeycomb iridate spin model suggests that, even for the quantum J = 1/2 case, physics discussed in this paper may hold true in those parameter regions with higher magnetic ordering temperatures. Such parameter regions cover most of the physically relevant parameter regions (3J − G > 0), including one of the 'candidate' parameter points, i.e.…”

Kitaev-Heisenberg model in a magnetic field: Order-by-disorder and commensurate-incommensurate transitions

“…On the other hand, thermal and quantum fluctuations select the collinear single-Q zigzag order. 46,47 This order-by-disorder phenomenon indicates a repulsive interaction, v ∼ v 0 + v 1 T , with v 0,1 > 0; the two terms correspond to quantum and thermal contributions, respectively. On the other hand, a finite g is allowed when time-reversal symmetry is explicitly broken by a magnetic field.…”

Finite-temperature phase diagram of the classical Kitaev-Heisenberg model

“…In our recent study, we have shown that the intermediate phase is a critical phase with two finite-temperature boundaries that correspond to Berezinskii-Kosterlitz-Thouless (BKT) phase transitions. 16 To describe the finite temperature properties of the KH model, we use a projection of the vector order parameter on the (111) plane. The vector is characterized by both the absolute value and the azimuthal angle of |m N (S) |.…”

“…Recently, Jackeli and Khaliullin 1 suggested that the Kitaev model could actually be realized within the honeycomb iridates with general formula A 2 IrO 3 , since the anisotropic part of the interactions among Ir-ions has the same form as the Kitaev coupling. This suggestion has triggered a lot of experimental [7][8][9][10][11] and theoretical [12][13][14][15][16][17][18] activity in the study of Na 2 IrO 3 and Li 2 IrO 3 compounds.…”