The Current-Phase Relation of Ferromagnetic Josephson Junction Between Triplet Superconductors

Abstract: We study the Josephson effect of a $\rm{T_1 F T_2}$ junction, consisting of spin-triplet superconductors (T), a weak ferromagnetic metal (F), and ferromagnetic insulating interfaces. Two types of the triplet order parameters are considered; $(k_x +ik_y)\hat{z}$ and $k_x \hat{x}+k_y\hat{y}$. We compute the current density in the ballistic limit by using the generalized quasiclassical formalism developed to take into account the interference effect of the multilayered ferromagnetic junction. We discuss in detail how the current-phase relation is affected by orientations of the d-vectors of superconductor and the magnetizations of the ferromagnetic tunneling barrier. General condition for the anomalous Josephson effect is also derived.