Effect of the quadratic magnetoelectric coupling and Dzyaloshinski-Moriya interaction on domain walls in hexagonal manganites

Abstract

Considering the quadratic magnetoelectric coupling and Dzyaloshinski-Moriya interaction in hexagonal manganites, we solve self-consistently equations describing the profiles of ferroelectric and antiferromagnetic domain walls. Our numerical calculations show that both the quadratic magnetoelectric coupling and Dzyaloshinski-Moriya interaction are responsible for the mobility and clamping of ferroelectric and antiferromagnetic domain walls although they less affect the profiles of domain walls. The direction of the movement of domain walls depends on the signs of coefficients of them. The centers of ferroelectric and antiferromagnetic domain walls move to a new position as the temperature passes through ${T}_{N}$. This procedure, which costs extra energy and lowers the total energy of the system, leads to the dielectric anomaly at its N\'eel temperature ${T}_{N}$ in hexagonal $R{\mathrm{MnO}}_{3}$.