Ab initio statistical mechanics of the Néel transition in hexagonal YMnO3 : Antiferromagnetic domain walls, vortices, and local magnetoelectric coupling

Abstract

Hexagonal manganites with coexisting antiferromagnetism and ferroelectricity have driven numerous research activities uncovering their potential in novel electronic devices. An antiferromagnetic order lowers the translational symmetry of the lattice; the structure of domain walls spatially separating distinctly ordered antiferromagnetic and structural states is quite rich and needs to be understood fundamentally. Here, we construct a model Hamiltonian to capture the low energy physics of coupled spins and phonons in hexagonal multiferroic ${\mathrm{YMnO}}_{3}$ derived from first-principles density functional theory and determine its temperature dependent behavior using Monte Carlo simulations. We demonstrate a weakly first order or close to being second order N\'eel transition accompanied by a $giant$ magnetoelastic effect observed experimentally in ${\mathrm{YMnO}}_{3}$ and show how it originates from the coupling between the in-plane ordering of spins with symmetry of ${\mathrm{\ensuremath{\Gamma}}}_{3}$ irreducible representation and collective atomic displacements with symmetry of ${\mathrm{\ensuremath{\Gamma}}}_{1}$ irreducible representation. We reveal the intriguing magnetic structure with the symmetry of ${\mathrm{\ensuremath{\Gamma}}}_{1}$ irreducible representation at the ${180}^{\ensuremath{\circ}}$ antiferromagnetic domain wall and predict a linear magnetoelectric coupling which can be confirmed using the piezoresponse force microscopy. Finally, we show that a stable magnetic vortex forms along a line of intersection of six ${60}^{\ensuremath{\circ}}$ antiferromagnetic domain walls, with energy comparable to that of dislocations in metals.