Dual Nature of Improper Ferroelectricity in a Magnetoelectric Multiferroic

Using first-principles calculations, we study the microscopic origin of ferroelectricity (FE) induced by magnetic order in the orthorhombic ${\mathrm{HoMnO}}_3$. We obtain the largest ferroelectric polarization observed in the whole class of improper magnetic ferroelectrics to date. We find that the two proposed mechanisms for FE in multiferroics, lattice and electronic based, are simultaneously active in this compound: a large portion of the ferroelectric polarization arises due to quantum-mechanical effects of electron orbital polarization, in addition to the conventional polar atomic displacements. An interesting mechanism for switching the magnetoelectric domains by an electric field via a 180° coherent rotation of Mn spins is also proposed.

Figure 1

(a) In-plane arrangement of Mn and O atoms. Arrows denote the direction of spins and AFM-coupled zigzag spin chains are highlighted by shaded areas. Structural parameters reported in Table  are shown. (b) Arrows show the directions of the ionic displacements for Mn (left) and O (right) in AFM-$E$. The thick arrows at the bottom show the direction of the resulting displacements of Mn and O sublattices and $\mathbf{P}$.

Figure 2

(a) Mn-O-Mn angles (in degrees), ${\alpha }_p$ and ${\alpha }_{\mathrm{ap}}$, vs $U$. (b) $P_{\mathrm{PCM}}$ and ${\alpha }_p-{\alpha }_{\mathrm{ap}}$ vs $U$ in AFM-$E$.

Figure 3

(a) TE vs the orientation of the central spins (see gray highlighted regions in the central $\perp$ spin-configuration) with respect to the spin of the Mn in the origin. (b) $P$ calculated via PCM [empty (blue) diamonds], via DFT-BP [filled (red) diamonds] and via DFT-BP for CSP [triangles (pink); see text]. The lines are fits to $P\propto -\cos \varphi$ with constant coefficients.

Figure 4

The $ac$-plane charge density isosurface plot in the energy range $[-0.8:0]\mathrm{eV}$ (top of valence band set as zero of the energy scale) for relaxed positions in AFM $E_1$.