Study of switching phenomenon of weak magnetoelectric coupling in proper multiferroics using Landau theory

The Landau-Khalatnikov theory is used to study the switching phenomenon of weak magnetoelectric (ME) coupling in proper multiferroics. We investigate two different types of ME multiferroics: one with a bare magnetic transition temperature below the Curie temperature of ferroelectricity, and the other type is when the Curie temperature of ferroelectricity is below the bare magnetic transition temperature. We adopt a fourth-order potential for ferromagnetics and sixth-order potential of ferroelectrics in the Landau free energy based on experimental reports. We found that the electric field alone cannot switch the magnetization and that the magnetic field alone cannot switch the polarization in weak ME multiferroics. Some interesting results were found: at a normalized transition temperature, the magnetization drops abruptly. Two switching current peaks appear when magnetic and electric fields are simultaneously applied to the system.