Noncollinear interlayer coupling across a semiconductor spacer

Based on the extended s-d exchange model. which includes both isotropic and anisotropic spin interactions between conduction electrons and local states, we have derived analytically the interlayer coupling across a semiconductor spacer with a general band structure. Both Heisenberg-type and Dzyaloshinski-Moriya (DM) - type Ruderman-Kittel-Kasuya-Yosida-like interlayer coupling are obtained as a result of spin-orbit interaction. The interlayer coupling decreases exponentially with spacer thickness and the oscillation period depends on the band structure and orientation of spacers. Our result is different from previous theory; in particular, the DM-type interlayer exchange coupling offers a natural explanation to the noncollinear alignment of neighboring ferromagnetic layers as were observed in recent experiments on magnetic-semiconductor multilayer structures.