Effects of biaxial strain on the improper multiferroicity inh−LuFeO3films studied using the restrained thermal expansion method

Elastic strain is potentially an important approach in tuning the properties of the improperly multiferroic hexagonal ferrites, the details of which, however, have been elusive due to experimental difficulties. Employing the method of restrained thermal expansion, we have studied the effect of isothermal biaxial strain in the basal plane of $h\ensuremath{-}\mathrm{LuFe}{\mathrm{O}}₃$ (001) films. The results indicate that a compressive biaxial strain significantly enhances the ${K}₃$ structural distortion (the order parameter of the improper ferroelectricity), and the effect is larger at higher temperatures. The compressive biaxial strain and the enhanced ${K}₃$ structural distortion together cause an increase in the electric polarization and a reduction in the canting of the weak ferromagnetic moments in $h\ensuremath{-}\mathrm{LuFe}{\mathrm{O}}₃$, according to our first principles calculations. These findings are important for understanding the strain effect as well as the coupling between the lattice and the improper multiferroicity in $h\ensuremath{-}\mathrm{LuFe}{\mathrm{O}}₃$. The experimental elucidation of the strain effect in $h\ensuremath{-}\mathrm{LuFe}{\mathrm{O}}₃$ films also suggests that the restrained thermal expansion can be a viable method to unravel the strain effect in many other thin film materials.