  We develop a theory of the exchange interaction between ferromagnetic (FM)
metallic grains embedded into insulating matrix by taking into account the
Coulomb blockade effects. For bulk ferromagnets separated by the insulating
layer the exchange interaction strongly depends on the height and thickness of
the tunneling barrier created by the insulator. We show that for FM grains
embedded into insulating matrix the exchange coupling additionally depends on
the dielectric properties of this matrix due to the Coulomb blockade effects.
In particular, the FM coupling decreases with decreasing the dielectric
permittivity of insulating matrix. We find that the change in the exchange
interaction due to the Coulomb blockade effects can be a few tens of percent.
Also, we study dependence of the intergrain exchange interaction on the grain
size and other parameters of the system.
