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 (κ) 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 ${\mathit{k}}_{\left[\mathbf{100}\right]}/{\mathit{k}}_{\left[\mathbf{210}\right]}=21.56$ in the NM state to ${\mathit{k}}_{\left[\mathbf{00}\mathbf{1}\right]}/{\mathit{k}}_{\left[\mathbf{210}\right]}=1.87$ in the AM state. The higher $k_{\left[210\right]}$ 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.

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• Altermagnetism
• Lattice thermal conductivity
• Boltzmann theory
• Density functional calculations