Theoretical study of the multiferroic properties in M-doped (M=Co, Cr, Mg) ZnO thin films

•The paper analyzes the multiferroic properties of doped ZnO thin films by a microscopic model.•The magnetization exhibits a maximum at a fixed doping concentration.•The polarization increases with growing dopant concentration.•The ferroelectric transition temperature is enhanced for increasing dopant concentration.

The origin of multiferroism is still an open problem in ZnO. We propose a microscopic model to clarify the occurrence of multiferroism in this material. Using Green׳s function technique we study the influence of ion doping and size effects on the magnetization and polarization of ZnO thin films. The calculations for magnetic Co- and Cr-ions are based on the s–d model, the transverse Ising model in terms of pseudo-spins and a biquadratic magnetoelectric coupling, whereas in case of nonmagnetic Mg-ions the model takes into account the Coulomb interaction and an indirect coupling between the pseudo-spins via the conduction electrons. We show that the magnetization M exhibits a maximum for a fixed concentration of the doping ions. Furthermore M increases with decreasing film thickness N. The polarization increases with increasing concentration of the dopant and decreasing N. The results are in good agreement with the experimental data.