Canted-spin-caused electric dipoles: A local symmetry theory

Abstract

A pair of magnetic atoms with canted spins Sa, S b can give rise to an electric dipole moment P. Several forms for the behavior of such a moment have appeared in the theoretical literature, some of which have been invoked to explain experimental results found in various multiferroic materials. The forms that require canting of the spins are P1 ∝ R × (Sa × S b ), P2 ∝ Sa × S b , and P3 ∝ SaR · Sa − S b R · S b , where R is the relative position of the atoms and Sa, S b are unit vectors. To unify and generalize these various forms we consider P as the most general quadratic function of the spin components that vanishes whenever Sa and S b are collinear, i.e. we consider the most general expressions that require spin canting. The study reveals new forms. We generalize to the vector P, Moriya's symmetry considerations regarding the (scalar) Dzyaloshinskii-Moriya energy D · Sa × S b (which led to restrictions on D). This provides a rigorous symmetry argument which shows that P1 is allowed no matter how high the symmetry of the atoms plus environment, and gives restrictions for all other contributions. The analysis leads to the suggestion of terms omitted in the existing microscopic models, suggests a new mechanism behind the ferroelectricity found in the 'proper screw structure' of CuXO2, X=Fe,Cr, and predicts an unusual antiferroelectric ordering in the antiferromagnetically and ferroelectrically ordered phase of RbFe(MoO4)2.

Magnetic control of transverse electric polarization in BiFeO3

“…where d ab is a coupling between spin and electric polarization 30,31 . For example, the cycloidal screw state with Q 2 have finite ( Supplementary Fig.…”

“…where d is a tensor and non-zero components of it are determined by a local symmetry of the bonds 30,31 . In fact, all the tensor components of d are allowed on nearest-neighbour bonds in BiFeO 3 , which induce the coupling between the transverse component of the electric polarization and cycloidal spin structure.…”

Symmetry analysis for the Ruddlesden-Popper systems Ca3Mn2O7and CaHarris1 2011Phys. Rev. B

“…From the work of Mostovoy, 42 magnetically induced polarization was not expected to have P q, although P q, was found experimentally 43 and explained from general symmetry arguments. 43,44 Equation (9) indicates that a polarization will be induced parallel to q along one of the four (1,1,0) directions according to the signs of the OP's as indicated by Eq. (9).…”

Multiferroic Materials: Physics and Properties

“…Here, there is an additional orthogonal term in the Dzyaloshinskii vector that was previously not taken into account, as pointed out by Kaplan and Mahanti. 94 The inverse Dzyaloshinskii-Moriya effect is also active here, analogous to the cycloidal spin spiral.…”

“…92 The observed polarization in these proper screw magnets can be explained in terms of a spin-dependent metal-ligand p-d hybridization 78,79,93 mechanism. Alternatively, Kaplan et al proposed an extension of the inverse Dzyaloshinskii-Moriya mechanism 94 with a polarization proportional to the spin twist S i x S j . Here, there is an additional orthogonal term in the Dzyaloshinskii vector that was previously not taken into account, as pointed out by Kaplan and Mahanti.…”