Ferroelectric order and nonlinear optical response in Hexagonal-HoMnO3

In this work, first-principles calculations have been performed, to elucidate the electronic, structural, optical, and ferroelectric properties of h-HoMnO${}_3$, making emphasis on its polar and shift current response. The results confirm a spontaneous polarization along the c-axis driven by the hybridization of the Mn-O orbitals, and the concomitant shift of the Ho ion in the same direction. Shift current calculations reveal a significant anisotropic response with a stronger current generation along the polar axis, demonstrating a direct correlation between ferroelectricity and nonlinear optical effects. These results position the h-HoMnO${}_3$ as a promising candidate for optoelectronic and energy harvesting applications without conventional $p$-$n$ junctions.