First principles study of the multiferroics BiFeO$_{3}$, Bi$_{2}$FeCrO$_{6}$, and BiCrO$_{3}$: Structure, polarization, and magnetic ordering temperature

TL;DR

This study uses ab initio density functional theory to analyze the structure, polarization, and magnetic ordering temperatures of three bismuth-based multiferroics, highlighting the importance of the LDA+U method and superexchange theory.

Contribution

It provides a detailed comparison of three multiferroics and demonstrates how to predict magnetic properties and ordering temperatures from first principles.

Findings

LDA+U is essential for accurate structural parameters of Bi2FeCrO6.

Superexchange explains the signs and magnitudes of magnetic couplings.

Predicted magnetic ordering temperatures suggest potential for room-temperature multiferroics.

Abstract

We present results of an {\it ab initio} density functional theory study of three bismuth-based multiferroics, BiFeO$_{3}$, Bi$_{2}$FeCrO$_{6}$, and BiCrO$_{3}$. We disuss differences in the crystal and electronic structure of the three systems, and we show that the application of the LDA+$U$ method is essential to obtain realistic structural parameters for Bi$_{2}$FeCrO$_{6}$. We calculate the magnetic nearest neighbor coupling constants for all three systems and show how Anderson's theory of superexchange can be applied to explain the signs and relative magnitudes of these coupling constants. From the coupling constants we then obtain a mean-field approximation for the magnetic ordering temperatures. Guided by our comparison of these three systems, we discuss the possibilities for designing a multiferroic material with large magnetization above room temperature.