  We revisit the non-collinear exchange coupling across the trilayer magnetic
junction mediated by the diluted-magnetic-semiconductor thin film. By numerical
approaches, we investigate the spiral angle between the ferromagnetic layers
extensively in the parameter space. In contrast to previous study, we
discovered the important role of spin relaxation, which tends to favor spiral
exchange over the oscillatory Ruderman-Kittel-Kasuya-Yosida interaction.
Finally, we discuss the physics origins of these two types of magnetic
interactions.
