Spin excitation continuum to topological magnon crossover and thermal Hall conductivity in Kitaev magnets

TL;DR

This work investigates finite-temperature crossovers between a Kitaev spin-liquid spin-excitation continuum and field-induced topological magnons in three Kitaev-dominant models under a $[111]$ field. By combining classical molecular-dynamics simulations for the dynamical spin structure factor with linear spin-wave theory for the polarized state, the authors map out regime-specific spectral weight redistribution and highlight nonlinear effects that limit LSWT's validity near crossovers. They identify distinct crossover behaviors across FM Kitaev, AFM Kitaev, and $K\Gamma\Gamma'$ models, including an intermediate spin-liquid-like phase in the AFM case, and show that the thermal Hall conductivity can exceed or deviate from the half-quantized value in these regimes. The results offer guidance for interpreting finite-temperature experiments on Kitaev materials such as $\alpha$-RuCl$_3$ and underscore the need for theoretical frameworks that treat thermal crossover physics beyond conventional magnon pictures.

Abstract

There has been great interest in identifying a Kitaev quantum spin liquid state in frustrated magnets with bond-dependent interactions. In particular, the experimental report of a half-quantized thermal Hall conductivity in $α$-RuCl$_3$ in the presence of a magnetic field has generated excitement as it could be strong evidence for a field-induced chiral spin liquid. More recent experiments, however, provide a conflicting interpretation advocating for topological magnons in the field-polarized state as the origin of the non-quantized thermal Hall conductivity observed in their experiments. An inherent difficulty in distinguishing between the two scenarios is the phase transition between a putative two-dimensional spin liquid and the field-polarized state exists only at zero temperature, while the behaviour at finite temperature is mostly crossover phenomena. In this work, we provide insights into the finite temperature crossover behavior between the spin excitation continuum in a quantum spin liquid and topological magnons in the field-polarized state in three different theoretical models with large Kitaev interactions. These models allow for a field-induced phase transition from a spin liquid (or an intermediate field-induced spin liquid) to the field-polarized state in the quantum model. We obtain the dynamical spin structure factor as a function of magnetic field using molecular dynamics simulations and compute thermal Hall conductivity in the field-polarized regime. We demonstrate the gradual evolution of the dynamical spin structure factor exhibiting crossover behaviour near magnetic fields where zero-temperature phase transitions occur in the quantum model. We also examine nonlinear effects on topological magnons and the validity of thermal Hall conductivity computed using linear spin wave theory. We discuss the implications of our results to existing and future experiments.

Figures (10)

• Figure 1: The $x$, $y$, and $z$ bonds of the Kitaev model are coloured in blue, green, and pink, respectively. The local spin axis ($S_x,S_y,S_z$) is shown coming out of the plane of the honeycomb, and the crystallographic axis ($a,b,c$) is indicated in the basis of the spin axis. The high symmetry points of the first Brillouin zone $\Gamma$, $M$, and $K$ are denoted with pink, purple, and blue squares, respectively.
• Figure 2: Field dependence of the neutron scattering dynamical structure factor $\mathcal{S}(\mathbf{q},\omega)$ obtained from molecular dynamics simulations for $K=-1, \Gamma=0, \Gamma'=0$ at $T/|K|=0.001$. The intensities are normalized with respect to the maximum value of each plot and the colourbar is presented on a logarithmic scale. The magnon bands of the polarized phase computed with LSWT are shown below the respective molecular dynamics results in (b)-(f).
• Figure 3: Field dependence of the neutron scattering dynamical structure factor $\mathcal{S}(\mathbf{q},\omega)$ computed with molecular dynamics for $K=1, \Gamma=0, \Gamma'=0$ at $T/|K|=0.001$. The intensities are normalized with respect to the maximum value of each plot and the colourbar is presented on a logarithmic scale. The magnon bands of the polarized phase computed with LSWT are shown below the respective molecular dynamics results in (j)-(l). The lower band in (j) occurs as a flat band at $\omega=0$.
• Figure 4: Two-dimensional thermal Hall conductivity $\kappa_{xy}^{2D}/T$ as a function of temperature due to magnons in the polarized state. $\kappa_{xy}^{2D}/T$ is in units of $\pi/6$, and we set $k_B=\hbar=1$ here. (a) was computed with interaction parameters $(K,\Gamma,\Gamma')=(-1,0,0)$ and (b) with $(K,\Gamma,\Gamma')=(1,0,0)$, both under a field $\mathbf{h}=h(1,1,1)/\sqrt{3}$. The half quantized values are indicated with the grey dashed line.
• Figure 5: Field dependence of the neutron scattering dynamical structure factor $\mathcal{S}(\mathbf{q},\omega)$ computed with molecular dynamics for $K=-1, \Gamma=0.25, \Gamma'=-0.02$ at $T/|K|=0.001$. The intensities are normalized with respect to the maximum value of each plot and the colourbar is presented on a logarithmic scale. The magnon bands of the polarized phase computed with LSWT are shown under the respective molecular dynamics results in (e)-(f).