Spin-induced ferroelectricity in a triangular-lattice antiferromagnet studied by magnetoelectric coupling tensors

Abstract

The spin-induced electric polarization in multiferroics with long-period modulated magnetic structure and some polar crystals is difficult to calculate directly due to the modeling limitation or the lack of a reference paraelectric phase. We propose a general method to investigate spin-induced polarization by combining symmetry arguments and first-principles calculations, and demonstrate it in the triangular-lattice delafossite structure. Two special spin models based on the four-sublattice orthorhombic supercell were used to calculate the polarization induced by spin-current and $p\text{\ensuremath{-}}d$ hybridization mechanisms, respectively. All the polarization components appearing in various spiral spin orders can be explained by the two different spin-current mechanisms through analyzing the symmetry of ${\mathbf{S}}_{a}\ifmmode\times\else\texttimes\fi{}{\mathbf{S}}_{b}$ vectors, where ${\mathbf{S}}_{a}$ and ${\mathbf{S}}_{b}$ represents the neighbor spins. We confirm that the $p\text{\ensuremath{-}}d$ hybridization mechanism only plays a minor role in the origins of polarization in addition to causing the $2q$ lattice modulation, where $q$ is the magnetic modulation wave number.