``Giant'' magneto-elastic effect, antiferromagnetic domains and topological defects in hexagonal YMnO₃

We construct a model Hamiltonian to capture the low energy physics of coupled spins and phonons of hexagonal YMnO₃ derived from first-principles density functional theory, and determine its temperature dependent behaviour using Monte Carlo simulations. We demonstrate a first-order Néel transition accompanied by a giant magnetoelastic effect seen experimentally in YMnO₃, which is shown here to originate from the coupling between the ordering of spins in the basal plane with Γ₃ symmetry and Γ₁ phonon. We studied two distinct types of antiferromagnetic domain walls: (a) 180°: antiferromagnetic domains within one structural domain and (b) 60°: structurally locked antiferromagnetic domains. We show that the spins at a 180° antiferromagnetic domain wall within one structural domain order locally with Γ₁ symmetry, and consequently give rise to a local linear magneto-electric coupling. Finally, we show that topologically protected magnetic vortices are stabilized along a line of the intersection of six 60° antiferromagnetic domain walls.