Magnetism, spin-wave relaxation and spiral exchange in a trilayer magnetic junction

We study the non-collinear exchange coupling across a trilayer magnetic junction consisting of two ferromagnets separated by a thin dilute magnetic semiconductor containing itinerant carriers with finite spin relaxation. It is remarkable that, by increasing the spin relaxation, the critical temperature is substantially enhanced and the shape of the magnetization curve becomes more mean-field like. We attribute these interesting changes to the broken time-reversal symmetry which suppresses the oscillatory Ruderman-Kittel-Kasuya-Yosida interaction. Our argument is further strengthened by the emergence of the non-collinear spiral exchange coupling across the trilayer magnetic junction with finite spin relaxation.