Abstract
We theoretically investigate the microscopic mechanism of conversion between the electron spin and the microscopic local rotation of atoms in crystals. In phonon modes with angular momenta, the atoms microscopically rotate around their equilibrium positions in crystals. In a simple toy model with phonons, we calculate the spin expectation value by using the adiabatic series expansion. We show that the time-averaged spin magnetization is generated by the microscopic local rotation of atoms via the spin-orbit interaction. On the other hand, in the system with a simple vibration of atoms, time-averaged spin magnetization becomes zero due to the time-reversal symmetry. Moreover, the magnitude of the time-averaged spin magnetization depends on the inverse of the difference of instantaneous eigenenergy, and we show that it becomes smaller in band insulators with a larger gap.
Highlights
The conversion between magnetization and mechanical rotation, such as the Einstein–de Haas effect [1] and the Barnett effect [2], has been known for more than a hundred years, and it has been focused on in spintronics recently
We have theoretically shown that a microscopic local rotation of atoms induces electron spins in the system with Rashba spin-orbit interaction
Using our toy model, which is a two-dimensional tight-binding model on the honeycomb lattice with Rashba spin-orbit interaction and phonons, we calculate the time-averaged spin magnetization using the adiabatic approximation, which is valid because the phonon frequency is much smaller than the frequency scale from the electron bandwidth
Summary
The conversion between magnetization and mechanical rotation, such as the Einstein–de Haas effect [1] and the Barnett effect [2], has been known for more than a hundred years, and it has been focused on in spintronics recently. Methods of generation of the phonon angular momentum have been proposed, such as a magnetic field [9,23], a Coriolis force in a rotating frame [24,25], circularly polarized light [21,22], infrared excitation [18,26], a temperature gradient in the system without inversion symmetry [27], and an electric field in the magnetic insulator [28].
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