Thermal Hall conductivity near field-suppressed magnetic order in a Kitaev-Heisenberg model

Abstract

We investigate thermal Hall conductivity ${\kappa }_{xy}$ of a $J$-$K$ Kitaev-Heisenberg model with a Zeeman field in the $(111)$ direction in the light of the recent debate surrounding the possible re-emergence of Ising topological order (ITO) and half-quantized ${\kappa }_{xy}/T$ upon field-suppression of long-range magnetic order in Kitaev materials. We use the purification-based finite temperature Tensor Network approach making no prior assumptions about the nature of the excitations: Majorana, visons or spin waves. For purely Kitaev interactions and fields $h/K\gtrsim 0.02$ sufficient to degrade ITO, the peak ${\kappa }_{xy}/T$ monotonously decreases from half-quantization associated with lower fields - a behavior reminiscent of vison fluctuation corrections. For higher fields $h/K\gtrsim 0.1,$ we find the results qualitatively consistent with a spin-wave treatment. In our $J$-$K$ model (with ferro-$K$ and antiferro-$J$), in the vicinity of field-suppressed magnetic order, we found ${\kappa }_{xy}/T$ to be significant, with peak magnitudes exceeding half-quantization followed by a monotonous decrease with increasing $h.$ We thus conclude that half-quantized thermal Hall effect in the vicinity of field suppressed magnetic order in our model, is a fine-tuning effect and is not associated with a Majorana Hall state with ITO.

8 pages, 9 figures

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• Formulation of spin Nernst effect for spin-nonconserving insulating magnets
• Field tuning Kitaev systems for spin fractionalization and topological order
• Microscopic theory of field-tuned topological transitions in the Kitaev honeycomb model
• Field-induced phase transitions in the Kitaev-Heisenberg model: A sign-problem-free quantum Monte Carlo study and possible application to $\alpha$-RuCl3