Indirect exchange in (Ga,Mn)As bilayers via the spin-polarized inhomogeneous hole gas: Monte Carlo simulation

The magnetic order resulting from an indirect exchange between magnetic moments provided by the spin-polarized hole gas in the metallic phase of a ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x\mathrm{As}$ double layer structure is studied via Monte Carlo simulation. The exchange is calculated to the second order of perturbation of the interaction between the magnetic moments and carriers (holes). We take into account a possible polarization of the hole gas due to the existence of an average magnetization in the magnetic layers, establishing, in this way, a self-consistency between the magnetic order and the electronic structure. That interaction leads to an internal ferromagnetic order inside each layer, and a parallel arrangement between their magnetizations, even in the case of thin layers. This fact is analyzed in terms of the interlayer and intralayer interactions.