Based on the extended s-d exchange model. which includes both isotropi
c and anisotropic spin interactions between conduction electrons and l
ocal states, we have derived analytically the interlayer coupling acro
ss a semiconductor spacer with a general band structure. Both Heisenbe
rg-type and Dzyaloshinski-Moriya (DM) - type Ruderman-Kittel-Kasuya-Yo
sida-like interlayer coupling are obtained as a result of spin-orbit i
nteraction. The interlayer coupling decreases exponentially with space
r thickness and the oscillation period depends on the band structure a
nd orientation of spacers. Our result is different from previous theor
y; in particular, the DM-type interlayer exchange coupling offers a na
tural explanation to the noncollinear alignment of neighboring ferroma
gnetic layers as were observed in recent experiments on magnetic-semic
onductor multilayer structures.