The Microscopic Model of BiFeO$_3$

TL;DR

This paper develops a microscopic model for BiFeO3 that accounts for the anisotropy energy confining the cycloidal wavevector q to specific axes, explaining its rotation under magnetic fields.

Contribution

It introduces a refined microscopic model incorporating anisotropy energy to accurately describe q confinement and rotation in BiFeO3.

Findings

Anisotropy energy confines q to three-fold axes at low fields.

The model explains the rotation of q under magnetic fields.

Provides a basis for understanding multiferroic behavior in BiFeO3.

Abstract

Many years and great effort have been spent constructing the microscopic model for the room temperature multiferroic BiFeO3 However, earlier models implicitly assumed that the cycloidal wavevector q was confined to one of the three-fold symmetric axis in the hexagonal plane normal to the electric polarization. Because recent measurements indicate that q can be rotated by a magnetic field, it is essential to properly treat the anisotropy that confines q at low fields. We show that the anisotropy energy $-K_3 S^6 \sin^6 \theta \cos 6 \phi $ confines the wavevectors q to the three-fold axis $\phi =0$ and $+-2 \pi/3$ within the hexagonal plane with $\theta = \pi /2$.