We have investigated the magnetic structure and ferroelectricity in $\mathrm{RbFe}\left(\mathrm{MoO}{}_4\right){}_2$ via first-principles calculations. Phenomenological analyses have shown that ferroelectricity may arise due to both the triangular chirality of the magnetic structure and through coupling between the magnetic helicity and the ferroaxial structural distortion. Indeed, it was recently proposed that the structural distortion plays a key role in stabilizing the chiral magnetic structure itself. We have determined the relative contribution of the two mechanisms via ab initio calculations. Whilst the structural axiality does induce the magnetic helix by modulating the symmetric exchange interactions, the electric polarization is largely due to the in-plane spin triangular chirality, with both electronic and ionic contributions being of relativistic origin. At the microscopic level, we interpret the polarization as a secondary steric consequence of the inverse Dzyaloshinskii-Moriya mechanism and accordingly explain why the ferroaxial component of the electric polarization must be small.

• Received 19 July 2013
• Revised 25 April 2014

DOI:https://doi.org/10.1103/PhysRevB.90.024402