Equal-spin and oblique-spin crossed Andreev reflections in ferromagnet/Ising superconductor/ferromagnet junction

Abstract

We study the subgap transport through a ferromagnet/Ising superconductor/ferromagnet (F/ISC/F) junction by solving the Bogoliubov--de Gennes equations. It is found that the crossed Andreev reflection (CAR) and local Andreev reflection (LAR) depend strongly on the spin-polarized F, the magnetization direction, and the Ising superconducting phase. For the same magnetization directions of the two F leads, the equal-spin CAR could take place due to the spin-flip mechanism induced by the Ising spin-orbit coupling and equal-spin-triplet pairing. Both equal-spin CAR and equal-spin LAR exhibit a remarkable magnetoanisotropy with period $\ensuremath{\pi}$ and show oscillatory behavior with a chemical potential. The equal-spin CAR is more prominent for half-metal F and double-band ISC while the normal CAR is completely suppressed. When the magnetization directions of the two F leads are different, the oblique-spin CAR occurs and its magnetoanisotropic period generally becomes $2\ensuremath{\pi}$ instead of $\ensuremath{\pi}$. In the oblique-spin CAR process, the spins of the electron and hole are neither parallel nor antiparallel. Furthermore, the property of oblique-spin CAR is very sensitive to the spin and valley degrees of freedom. The spin- and valley-polarized CAR can be achieved and controlled by the chemical potentials and the magnetization directions.