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We study exchange coupling due to the interelectron Coulomb interactionbetween two ferromagnetic grains embedded into insulating matrix. Thiscontribution to the exchange interaction complements the contribution due tovirtual electron hopping between the grains. We show that the Coulomb and thehopping based exchange interactions are comparable. However, for most systemparameters these contributions have opposite signs and compete with each other.In contrast to the hopping based exchange interaction the Coulomb basedexchange is inversely proportional to the dielectric constant of the insulatingmatrix $\varepsilon$. The total intergrain exchange interaction has acomplicated dependence on the dielectric permittivity of the insulating matrix.Increasing $\varepsilon$ one can observe the ferromagnet-antiferromagnet(FM-AFM) and AFM-FM transitions. For certain parameters no transition ispossible, however even in this case the exchange interaction has largevariations, changing its value by three times with increasing the matrixdielectric constant.

Competition of the Coulomb and hopping based exchange interactions in granular magnets