Effects of strain on ferroelectric polarization and magnetism in orthorhombic HoMnO3

Abstract

We explore how the ferroelectric polarization of antiferromagnetic E-type orthorhombic HoMnO${}_{3}$ can be increased, by investigating the effects of in-plane strain on both the magnetic properties and the ferroelectric polarization, using combined density functional theory calculations and a model Hamiltonian technique. Our results show that the net polarization is strongly enhanced under compressive strain, due to an increase of the elec-tronic contribution to the polarization. In contrast, the ionic contribution is found to decrease. We identify the electron-lattice coupling, due to Jahn-Teller (JT) distortions, and its response to strain, to be responsible for the observed behavior. The JT-induced orbital ordering of occupied Mn-${e}_{g}^{1}$ electrons in alternating $3{x}^{2}\ensuremath{-}{r}^{2}3{y}^{2}\ensuremath{-}{r}^{2}$ orbital states in the unstrained structure, changes under in-plane compressive strain to a mixture with ${x}^{2}\ensuremath{-}{z}^{2}{y}^{2}\ensuremath{-}{z}^{2}$ states. The asymmetric hopping of ${e}_{g}$ electrons between Mn ions along zigzag spin chains (typical of the AFM-E spin configuration) is therefore enhanced under strain, explaining the large value of the polarization. Using a degenerate double-exchange model including electron-phonon interaction, we reproduce the change in the orbital ordering pattern. In this picture, the orbital ordering change is related to a change of the Berry phase of the ${e}_{g}$ electrons. This causes an increase of the electronic contribution to the polarization.