Spin-dependent anisotropy of lattice thermal conductivity in the altermagnetic semiconductor MnTe

The recent identification of altermagnets (AMs) and their associated physical phenomenon have drawn considerable interest in the field of spintronics. In this study, we conducted a comprehensive investigation on the vibrational and thermal transport properties of the altermagnetic semiconductor MnTe based on first-principles calculations with phonon Boltzmann transport theory. Our findings revealed that the lattice thermal conductivity (\ensuremath{\kappa}) of MnTe exhibits a unique spin-dependent anisotropy, with values along the [100], [001], and [210] directions at the magnetic transition temperature (${T}_{N}=310$ K) being 1.87, 3.05, and 1.63 W/mK, respectively. In contrast, the lattice thermal conductivity in the [100], [001], and [210] directions for nonmagnetic (NM) MnTe are 6.90, 6.78, and 0.32 W/mK at 310 K. Our phonon analysis revealed that the lowest thermal conductivity along the [210] direction in both AM and NM MnTe is a consequence of the intrinsically smallest group velocities in this crystallographic orientation. Remarkably, the [210] direction inherits the AM crystal symmetry of MnTe, and the magnetization and spin arrangement significantly weaken the directional anisotropy from ${\mathbit{k}}_{[\mathbf{100}]}/{\mathbit{k}}_{[\mathbf{210}]}=21.56$ in the NM state to ${\mathbit{k}}_{[\mathbf{00}\mathbf{1}]}/{\mathbit{k}}_{[\mathbf{210}]}=1.87$ in the AM state. The higher ${k}_{[210]}$ in the AM state compared to the NM state predominantly originates from its enhanced phonon lifetime and weaker phonon anharmonicity. These results deepen our understanding of the mechanisms driving spin-dependent anisotropic thermal transport in altermagnetic semiconductors and provide valuable insights for the design of AM based spin-caloritronic devices, spintronic memristors, and cryogenic magnetic sensors.