Hysteresis Loops for Magnetoelectric Multiferroics Using Landau-Khalatnikov Theory

Abstract

We present a theoretical discussion of the hysteresis in magnetoelectric multiferroics with bi-quadratic magnetoelectric coupling. The calculations were performed by employing Landau-Khalatnikov equation of motion for both the ferroelectric and ferromagnetic phase, then solve it simultaneously. In magnetoelectric, we obtain four types of hysteresis: ferroelectric hysteresis, ferromagnetic hysteresis and two types of cross hysteresis (electric field versus magnetization and magnetic field versus electric polarization). The cross hysteresis has butterfly shape which agree with the result from the previous research. It can also be seen from that hysteresis, that magnetization / electric polarization can not be flipped into the opposite direction using external electric / magnetic field when the magnetoelectric coupling is bi-quadratic type. Overall, the result shows that Landau-Khalatnikov equation is able to approximate hysteresis loops in multiferroics system.