Disentangling Shear and Compression Phonons: Route to Anomalous Magnetothermal Transport

Abstract

Magnetothermal transport in various frustrated magnets exhibits striking field-dependent anomalies that deviate from conventional magnon or phonon transport. Here we show that symmetry-constrained spin-lattice coupling naturally leads to mode-selective spin-phonon interactions that control heat transport. In the strong spin-orbit coupling limit, we derive an effective spin-phonon Hamiltonian in which phonons with different polarizations couple selectively to distinct spin operators. As a result, compression and shear phonon modes contribute to spin heat current across different magnetic-field regimes. Using a Landauer transport framework combined with exact diagonalization of spin chains coupled to a phonon bath, we show that this mechanism produces a characteristic peak-dip-peak structure in the field dependence of heat current, providing a microscopic explanation for field-induced transport anomalies in spin-orbit-coupled Mott insulators.

Figures (3)

• Figure 1: Schematic of the spin heat transport setup. A spin system (top) with an unperturbed temperature $T_S$ is coupled to a phonon bath (bottom) with a local temperature $T_{B,i}$ via the spin-phonon interaction $H_{I,i}$. An external magnetic field $\vb{h}\parallel \hat{z}$ is applied to the system, which induces the spin-phonon coupling. A spatial temperature gradient in the phonon bath creates a local temperature difference, driving a steady-state longitudinal spin heat current $\langle\hat{\mathcal{J} }_{S}^{\Gamma_a}\rangle$ at the central bond. The spin system absorbs energy at the hot end (red) and emits energy at the cold end (blue).
• Figure 2: Schematic of the field-induced spin-lattice coupling in an edge-sharing octahedral structure. Under an external magnetic field $h_z$, distinct lattice distortions (orange arrows) selectively couple to different spin components of the central magnetic ion $\vb{s}_i$ (black arrows). (a) The shear mode ($\epsilon_{zx}$) couples to the transverse spin $s_i^x$. (b) The compression mode ($\epsilon_{z^2}$) couples to the field-aligned spin $s_i^z$.
• Figure 3: Field dependence of the spin heat current in the 1D XXZ chain in unit of the heat current scale $\mathcal{J}_0$ (see the definition and estimation in the SM). The total heat current (black curve) is decomposed into contributions from the compression strain mode ($\epsilon_{z^2}$, red) and the two shear modes ($\epsilon_{zx}, \epsilon_{yz}$, blue). The vertical gray dashed lines indicate the critical fields ($h_{c1}, h_{c2}$) separating the dimer, Luttinger liquid (LL), and polarized phases. Notably, whereas the LL phase involves contributions from all strain channels, the compression mode vanishes in the polarized regime, giving rise to the characteristic non-monotonic field dependence.