Ginzburg-Landau theory for the conical cycloid state in multiferroics: applications to CoCr$_2$O$_4$

TL;DR

This paper develops a Ginzburg-Landau theoretical framework to explain the emergence of conical cycloid magnetic order in multiferroics like CoCr$_2$O$_4$, highlighting the conditions for its coexistence with ferromagnetism and implications for electric polarization reversal.

Contribution

It introduces a Ginzburg-Landau model for conical cycloid states in multiferroics, explaining their formation without anisotropies and their transition characteristics.

Findings

Cycloidal order can occur without spin and lattice anisotropies.

The transition to the conical cycloid state from ferromagnetism is first order.

Reversal of magnetization can reverse electric polarization without toroidal moments.

Abstract

We show that the cycloidal magnetic order of a multiferroic can arise in the absence of spin and lattice anisotropies, for e.g., in a cubic material, and this explains the occurrence of such a state in CoCr$_2$O$_4$. We discuss the case when this order coexists with ferromagnetism in a so called `conical cycloid' state, and show that a direct transition to this state from the ferromagnet is necessarily first order. On quite general grounds, the reversal of the direction of the uniform magnetization in this state can lead to the reversal of the electric polarization as well, without the need to invoke `toroidal moment' as the order parameter.