The Coulomb based magneto-electric coupling in multiferroic tunnel junctions and granular multiferroics

We study magneto-electric effect in two systems: i) multiferroic tunnel junction (MFTJ) - magnetic tunnel junction with ferroelectric barrier and ii) granular multiferroic (GMF) in which ferromagnetic (FM) metallic grains embedded into ferroelectric matrix. We show that the Coulomb interaction influences the magnetic state of the system in several ways: i) through the spin-dependent part of the Coulomb interaction; ii) due to the Coulomb blockade effect suppressing electron hopping and therefore reducing magnetic coupling; and iii) through image forces and polarization screening that modify the barrier for electrons in MFTJ and GMF. We show that in the absence of spin-orbit or strain-mediated coupling magneto-electric effect appears in GMF and MFTJ. The Coulomb interaction depends on the dielectric properties of the system. For GMF it depends on the dielectric constant of FE matrix and for MFTJ on the dielectric constant of the FE barrier. Applying external electric field one can tune the dielectric constant and the Coulomb interaction. Thus, one can control magnetic state with electric field.