Phonon-induced spin-orbit torques from first principles

Understanding the transfer of electron spin angular momentum to the environment is paramount for the development of quantum devices. Phonons induce a dynamical magnetic field through relativistic spin-orbit coupling, applying an intrinsic torque to the electron spin angular momentum. A microscopic quantification of these torques remains an open challenge. Here we show a rigorous framework for computing phonon-induced spin-orbit torques from first principles. We apply this method to prototypical materials in each of the Laue point groups and analyze how different phonon modes contribute to the spin torque in each point group. Our results highlight fundamental differences between the same-spin / spin-flip electron-phonon matrix elements and phonon-induced spin torques, shedding light on how phonons absorb the electron spin angular momentum during relaxation. Extensions to include orbital angular momentum transfer will be described. Our work enables quantitative analysis of spin angular momentum transfer between electron spins and lattice vibrations, enabling the description of spin Hall effects and related physics in materials and devices.