Excitation spectrum of multiferroics at finite temperatures

Abstract

A systematic microscopic theory of the magnetoelectric (ME) effect in multiferroic materials with well-separated phase-transition temperatures is presented. Whereas the ferroelectric subsystem is described by an Ising model in a transverse field, the magnetic one is characterized by the Heisenberg model with Dzyaloshinski-Moriya interaction (DMI). The symmetry-allowed quartic coupling between both subsystems, and the application of a Green's function technique in a dynamical mean-field approximation, exhibit the calculation of the elementary excitations analytically, which are mutually influenced by the respective other subsystem. The magnetic excitation is a Goldstone mode, while the ferroelectric dispersion relation shows a soft-mode-like behavior. We find the macroscopic polarization and the transverse magnetization in a broad temperature interval up to the corresponding phase-transition temperatures (type-I multiferroics). Due to the DMI, the system offers different spiral structures, which are incorporated into the model by using a transformation of the underlying spin operators into a representation without a fixed quantization axis. The polarization increases at the magnetic phase-transition temperature, and is also enhanced by increasing the ME coupling strength as well as the DMI. We demonstrate likewise the variation of the spin-wave dispersion relation with the ME coupling strength and the DMI. As a consequence, the macroscopic magnetization is enhanced with increasing coupling.