Thermal conductivity in noncollinear magnets

TL;DR

This work investigates intrinsic magnetic heat transport in noncollinear magnets by focusing on spin-spiral ground states in a frustrated Heisenberg model. A Bogoliubov-diagonalized quadratic magnon Hamiltonian plus cubic three-magnon terms from noncollinearity leads to a Boltzmann equation solved in the relaxon basis. The main finding is that the full relaxon solution yields dramatically higher thermal conductivity than the single-magnon approximation, with heat carried by a few dominant relaxons, including a KBN electromagnon associated relaxon. Thermal conductivity increases as spiral pitch decreases, and the results provide a blueprint for calculating magnetic thermal transport in noncollinear magnets, with implications for heat management in spintronic devices.

Abstract

Magnetic memory and logic devices, including prospective ones based on skyrmions, inevitably produce heat. Thus, controlling heat flow is essential for their performance. Here we study how non-collinear spin arrangement affects the magnon contribution to thermal conductivity. As a paradigm system, we consider the most basic non-collinear magnet with a spin spiral ground state. Spin noncollinearity leads to anharmonic terms, resulting in magnon fusion and decay processes. These processes determine the magnon lifetime, which can be used to estimate thermal conductivity in a single-mode approximation. However, by solving the full Boltzmann equation numerically, we find a much higher thermal conductivity. This signifies that heat is carried not by individual magnons but by their linear combinations -- relaxons. The thermal conductivity is found to increase with the diminishing spiral pitch, consistent with recent experiments. The results provide the blueprint for calculating magnetic thermal transport in non-collinear magnets.

Figures (2)

• Figure 1: (a) Quasi-1D spin spiral state is stabilized by competing nearest- and next-nearest neighbor exchange interactions $J_1,J_2$ and ferromagnetic interactions $J_3,J_4$. (b) Magnon dispersion along the spiral wave vector $E(k_x,k_y=0,k_z=0)$. The model parameters are $J_2=1$ meV, $Q=\frac{2\pi}{5}$, $J_1=-4J_2\cos Q$ and the strength of the easy plane anisotropy $\Delta$ is indicated in the legend. The easy plane anisotropy favors one plane for the spiral (in our case, the $xz$ plane), so the Goldstone modes associated with the continuous rotational symmetry, broken by the anisotropy, are now gapped. (c) $k_y=k_z=q_y=q_z=0$ cut of the surface in $(\bm{k,q})$ space where the energy conservation law for the scattering event $\epsilon_{\bm{k}}+\epsilon_{\bm{q}}=\epsilon_{\bm{k}+\bm{q}}$ is satisfied.
• Figure 2: (a,b) Relaxons with the largest thermal conductivity contributions (95% and 4%), obtained for $T=5$ K and $Q=1.1$. The contribution $\theta_k$ of individual magnons to the relaxon is encoded by the color of the magnon dispersion curve $\omega(k)$. The positive contribution (in red) implies that the relaxon increases the magnon occupation by $\theta_k$ with respect to the Bose-Einstein equilibrium $n_k$, while blue color indicates the reduction. (c) Contributions of individual relaxons to $\kappa$ as a function of the spiral wave vector $Q$, with $J_1$ fixed and $J_2$ varied to fulfill $\cos Q=-J_1/4J_2$. (d) The dependence of magnon thermal conductivity on the spiral wave vector $Q$ for different temperatures. (e) Temperature dependence of magnon thermal conductivity for different spiral wave vectors $Q$. (f) Comparison between the thermal conductivity, computed in the relaxon picture and using magnon single-mode approximation.