  We study the properties of heterostructures formed by two layers of diluted
magnetic semiconductor separated by a nonmagnetic semiconductor layer. We find
that there is a RKKY-type exchange coupling between the magnetic layers that
oscilles between ferromagnetic and antiferromagnetic as a function of the
different parameters in the problem. The different transport properties of
these phases make that this heterostructure presents strong magnetoresistive
effects. The coupling can be also modified by an electric field. We propose
that it is possible to alter dramatically the electrical resistance of the
heterostructure by applying an electric field. Our results indicate that in a
single gated sample the magnetoresistance could be modulated by with an
electrical bias voltage.
