Collective relaxation eigenmodes and anisotropic magnon thermal transport in $α$-MnTe
The intrinsic magnon thermal transport in the altermagnet $α$-MnTe is studied by solving the three-dimensional linearized Boltzmann transport equation with the four-magnon collision matrix. Diagonalizing the collision matrix gives direct access to the relaxation eigenmodes beyond the relaxation-time approximation. We show that Umklapp scattering lifts the momentum-related zero modes of the Normal-only collision operator and substantially modifies the low-lying relaxation spectrum. Using the same collision matrix, we compute the magnon thermal conductivity tensor. The full linearized Boltzmann transport equation result exceeds the relaxation-time approximation by more than an order of magnitude at low temperature and reveals a strong transport anisotropy, with the out-of-plane thermal conductivity remaining larger than the in-plane component over the studied temperature range. A mode-resolved analysis shows that the dominant heat-carrying modes retain momentum-like character inherited from the Normal-only zero modes, and that the larger out-of-plane conductivity mainly originates from the stronger out-of-plane group-velocity contribution, rather than from a large difference in relaxation lifetimes.