Magnetic Orders of LaTiO$3$ and YTiO$3$ Under Epitaxial Strain: a First-Principles study

Perovskite $R$TiO$_3$ family is a typical Mott-insulator with localized $3$d electrons. In this work, the epitaxial strain effects on the ground magnetic orders of LaTiO$_3$ and YTiO$_3$ films have been studied using the first-principles density-functional theory. For the YTiO$_3$ films, A-type antiferromagnetic order emerges against the original ferromagnetic order under the in-plane compressive strain by LaAlO$_3$ ($001$) substrate, although the A-type antiferromagnetic order does not exist in any $R$TiO$_3$ bulks. Then, for the LaTiO$_3$ films under the compressive strain, e.g. LaTiO$_3$ films grown on LaAlO$_3$, LaGaO$_3$, and SrTiO$_3$ substrates, undergo a phase transition from the original G-type antiferromagnetism to A-type antiferromagnetism. While under the tensile strain, e.g. grown on the BaTiO$_3$ and LaScO$_3$ substrate, LaTiO$_3$ films show a tendency to transit to the C-type antiferromagnetism. Furthermore, our calculations find that the magnetic transitions under epitaxial strain do not change the insulating fact of LaTiO$_3$ and YTiO$_3$.