Magnetization dynamics of a ferromagnet embedded in a Josephson junction with a spin-orbit coupled element

Abstract

We investigate the free energy of Andreev bound states (ABS) in a Josephson junction containing a ferromagnet and an element where broken inversion symmetry produces Rashba spin-orbit coupling. Applying an extended Blonder-Tinkham-Klapwijk (BTK) formalism and finding static solutions for the wave function in the junction, we calculate the permissible energy levels in the Andreev regime and find the thermodynamic free energy. The free energy is found to depend on the magnetization direction of the ferromagnet in such a way that the effect of ABS in the junction on the magnet is an easy axis effective field, perpendicular to both the direction of broken inversion symmetry and the direction of propagation in the junction. Treating the dynamical time evolution of the system as an adiabatic perturbation, we find that the ABS effective field can be controlled by manipulating the superconductive phase across the junction and in an example system it can used to achieve switching of a magnetic bit.