Microscopic theory of the Coulomb based exchange coupling in magnetic tunnel junctions

Abstract

We study interlayer exchange coupling based on the many-body Coulomb interaction between conduction electrons in magnetic tunnel junction. This mechanism complements the known interaction between magnetic layers based on virtual electron hopping (or spin currents). We find that these two mechanisms have different behavior on system parameters. The Coulomb based coupling may exceed the hopping based exchange. We show that the Coulomb based exchange interaction, in contrast to the hopping based coupling, depends strongly on the dielectric constant of the insulating layer. The dependence of the interlayer exchange interaction on the dielectric properties of the insulating layer in magnetic tunnel junction is similar to magnetoelectric effect where electric and magnetic degrees of freedom are coupled. We calculate the interlayer coupling as a function of temperature and electric field for magnetic tunnel junction with ferroelectric layer and show that the exchange interaction between magnetic leads has a sharp decrease in the vicinity of the ferroelectric phase transition and varies strongly with external electric field.

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

“…Recently the exchange interaction between magnetic grains was considered using the Hamiltonian Ĥ0 + ĤdC [27]. However, later it was shown [31] that the indirect Coulomb interaction may also lead to magnetic coupling between the FM contacts. In particular, this was demonstrated for MTJ with infinite leads.…”

“…The Coulomb based exchange coupling between infinite magnetic leads was considered in Ref. [31], where it was shown that the Coulomb interaction inside the FM leads also contributes to the total interlayer exchange coupling. However, for infinite leads the last three terms in Eq.…”

“…To calculate the contribution to the exchange interaction due to the insulating region we will follow the approach of Ref. [31] where exchange coupling was calculated for MTJ. In this approach the electric field E ij 1,2 created by effective charges ρ (1,2) ij inside the insulating region was calculated by taking into account the screening produced by the FM leads.…”

“…However, it is known that the manybody Coulomb interaction also leads to the magnetic exchange interaction [29 and 30]. Recently, the Coulomb based exchange interaction was considered in MTJ [31]. It was shown that this contribution to the magnetic interaction between magnetic leads separated by the insulating layer is comparable and even larger than the hopping based exchange coupling.…”

“…In Ref. [31] it was shown that the Coulomb based coupling strongly depends on the insulator dielectric constant. For granular system both the hopping and the Coulomb based exchange depends on the matrix dielectric susceptibility.…”