The D'yakonov-Perel' (DP) spin-relaxation mechanism has traditionally been associated with either relativistic spin-orbit coupling, which breaks space-inversion symmetry, or inhomogeneous magnetization, which breaks both time-reversal and translational symmetries. Here, we investigate a spin-relaxation mechanism in altermagnetic systems which possess novel magnetic states characterized by sublattices connected through crystal-rotation symmetries and opposite spins with zero overall net magnetization and absence of spin-orbit coupling. We find that altermagnetic states exhibit DP-type spin relaxations in both strong- and weak-scattering regimes, with the spin-relaxation rate decreasing to zero as the temperature approaches the critical temperature of the altermagnetic phase transition. Although the overall scattering strength governs both spin and momentum relaxation, the spin relaxation is controlled by a distinct correlation time that arises from the dephasing of spin precession, which involves a high-order angular factor rather than the backscattering factor. Moreover, using a kinetic approach incorporating rigorous microscopic scattering, we also study the spin Hall current and demonstrate that this signal is highly anisotropic and proportional to the degree of altermagnetic order.

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• Spin Hall effect
• Spin current
• Spin relaxation
• Altermagnets