Theoretical study of the epitaxial strain effect on the structural and magnetic properties of a YFeO$_{3}$ thin film on a SrTiO$_3$ substrate

The electronic structure and magnetic properties of a YFeO$_3$ thin film deposited on a SrTiO$_3$ substrate are studied using the GGA+U method. It is shown that the epitaxial strain in the YFeO$_3$/SrTiO$_3$ thin film significantly changes the crystal structure and displaces iron atoms located at the film surface from the plane formed by the nearest oxygen atoms. These distortions lead to a change in the type of long-range magnetic ordering from the G-type antiferromagnetic ordering observed in stoichiometric YFeO$_3$ to ferrimagnetic ordering close to the A-type antiferromagnetism and to the transition from the insulating state to metallic one. The complete relaxation of atomic positions gives rise to a “breathing mode” distortion in the film bulk, which is accompanied by the electric polarization of 15.1 $\mu$C/cm$^2$. The latter is in agreement with the experiment. The distortion of oxygen octahedra surrounding iron atoms leads to the transition from the high-spin state to the intermediate-spin state and to a stepwise decrease in local magnetic moments.