Origin of Ferroelectricity in Orthorhombic $LuFeO_3$

In this Letter, we demonstrate that a small but finite ferroelectric polarization in orthorhombic LuFeO$_3$ is primarily of electronic origin (oriented along a-axis) driven by commensurate (k = 0) and collinear magnetic structure. The nonpolar orthorhombic lattice (space group $Pnma$) undergoes isostructural transition at the magnetic transition temperature $T_N$ ($\sim$600 K). Application of electric field, however, induces finite piezostriction via electrostriction resulting in clear domain contrast images in piezoresponse force microscopy.