Strain-Controlled Magnetic Phase Transitions through Anisotropic Exchange Interactions: A Combined DFT and Monte Carlo Study

Epitaxial strain provides a powerful, non-chemical route to tune the properties of functional materials by manipulating the coupling between spin, charge, and lattice degrees of freedom. Using density functional theory (DFT) calculations and $\rm BiFeO_3$ as a model system, we first demonstrate how epitaxial strain exactly leads to anisotropic magnetic interactions where the exchange coupling along the $c$-axis differs from that in the $ab$-plane. We show that subtle structural modifications, specifically the distortion from a cubic to a tetragonal lattice, drive a magnetic phase transition from a G-type to a C-type antiferromagnetic (AF) phase. The anisotropy in magnetic interactions, which becomes prominent in the lower symmetry tetragonal phase, provides a direct link between the structural distortion and the potential change in magnetic ordering. For a more comprehensive study, we next investigate the role of strain in driving magnetic phase transitions within a half-filled one-band Hubbard model in three dimensions. In this framework, strain is introduced through anisotropic hopping processes between nearest- and next-nearest-neighbor sites, inspired by the DFT calculations. Using a semiclassical Monte Carlo (s-MC) approach, we construct ground state phase diagrams in the nonperturbative regime, which show how uniaxial strain stabilizes distinct magnetic ground states: Compressive strain drives a transition from a G-type to a C-type AF insulator, whereas tensile strain suppresses the C-type AF order, favoring an A-type AF phase. Overall, our combined DFT and s-MC calculations highlight that strain is a powerful tuning parameter for controlling competing magnetic phases by governing exchange coupling mechanisms in correlated systems, offering valuable insights for the design of strain-controlled materials.