Competition of magneto-dipole, anisotropy and exchange interactions in composite multiferroics

We study the competition of magneto-dipole, anisotropy and exchange interactions in composite three dimensional multiferroics. Using Monte Carlo simulations we show that magneto-dipole interaction does not suppress the ferromagnetic state caused by the interaction of the ferroelectric matrix and magnetic subsystem. However, the presence of magneto-dipole interaction influences the order-disorder transition: depending on the strength of magneto-dipole interaction the transition from the ferromagnetic to the superparamagnetic state is accompanied either by creation of vortices or domains of opposite magnetization. We show that the temperature hysteresis loop occurs due to non-monotonic behavior of exchange interaction versus temperature. The origin of this hysteresis is related to the presence of stable magnetic domains which are robust against thermal fluctuations.

Phenomenological theory of magneto-electric coupling in granular multiferroics

We study coupling between the ferroelectric polarization and magnetization of granular ferromagnetic film using a phenomenological model of combined multiferroic system consisting of granular ferromagnetic film placed above the ferroelectric (FE) layer. The coupling is due to screening of Coulomb interaction in the granular film by the FE layer. Below the FE Curie temperature the magnetization has hysteresis as a function of electric field. Below the magnetic ordering temperature the polarization has hysteresis as a function of magnetic field. We study the magneto-electric coupling for weak and strong spatial dispersion of the FE layer. The effect of mutual influence decreases with increasing the spatial dispersion of the FE layer. For weak dispersion the strongest coupling occurs in the vicinity of the ferroelectric-paraelectric phase transition. For strong dispersion the situation is the opposite. We study the magneto-electric coupling as a function of distance between the FE layer and the granular film. For large distances the coupling decays exponentially due to the exponential decrease of electric field produced by the oscillating charges in the granular ferromagnetic film.