Modelling domain-wall orientation in antiferromagnets driven by magnetoelastic interactions and volume variations

In this paper, we build the mathematical framework to describe the physical phenomenon behind the equilibrium configuration joining two orthogonal antiferromagnetic domains that are simultaneously subject to magnetoelastic interactions and volume variations. To achieve this goal, we firstly define the total energy of the system and deduce the governing equations by minimizing it with respect to the field variables. Then, in order to deduce the angular dependence of elastic and magnetoelastic energies, we solve the resulting system of nonlinear PDEs together with proper boundary conditions. Results of our analytical investigations and numerical simulations allow to identify the optimal setup in which the overall energy is minimized.