Current-driven domain wall motion in ferrimagnetic nanowires

Current-driven DW motion in a ferrimagnetic (FiM) nanowire through spin transfer torques (STTs) is explained by the energy-work principle. An adiabatic STT (a-STT) can be incorporated into the Lagrangian as an energy functional and tends to twist DW planes. DWs in homogeneous FiM nanowires can resist an a-STT from moving below a critical value proportional to the maximal transverse anisotropic field. Second, a nonadiabatic STT (na-STT) cannot be included in the Lagrangian and can enter the spin dynamics through the Rayleigh functional. A static DW cannot exist under a na-STT such that a DW in a homogeneous FiM nanowire must propagate under an arbitrarily small na-STT. Third, STTs do positive work on a DW which must compensate by energy dissipated by moving spins inside the DW through damping. Below the Walker breakdown current, the na-STT does positive work and the a-STT does no work. Above the Walker breakdown, a DW starts to precess around the wire axis during its propagation along the axis. Whether the a-STT does a negative or a positive work depends on the direction of the DW precession, while the na-STT still does a positive work. Last, a DW velocity formula is obtained, which agrees with simulations both below and above the Walker breakdown current. In the vicinity of the angular momentum compensation point, the precession frequency of a DW reaches its maximum, and the DW structure is distorted. The DW distortion and spin wave emission modify the DW motion, which deviates from its linear dependence on current density. This theory explains well the observed DW mobility near the angular momentum compensation point of FiM nanowires and resolves the puzzle of the unphysical negative na-STT problem.