Ferroelectricity driven by Y $d^0$-ness with re-hybridization in YMnO$_3$

Recently multiferroicity, in which magnetism and ferroelectricity co-exist, takes much attention due to its exotic magnetoelecric (ME) phenomena. Hexagonal $R$MnO$_3$ ($R$ = Ho, Er, Tm, Yb, Lu, Y, Sc) exhibits multiferroicity with high ferroelectric and low antiferromagnetic transition temperature ($T_E >$ 600K, $T_M\sim$ 90K). The hexagonal structure ($P6_3cm$) brings out soft mode phonons required for ferroelectricity, but its driving force has been puzzled. We investigated electronic structure of hexagonal multiferroic YMnO$_3$ using the polarization dependent x-ray absorption spectroscopy (PXAS) at O $K$- and Mn $L_{2,3}$-edges. PXAS exhibits strong polarization dependence at both edges, reflecting anisotropic Mn 3$d$ orbital occupation. Moreover, the O $K$-edge spectra show that Y $4d$ states are strongly hybridized with O $2p$ ones, resulting in large anomalies in Born effective charges on off-centering Y- and O-ions. These results manifest that the Y $d^0$-ness with re-hybridization is the driving force for the ferroelectricity, and suggest a new approach to understand the multiferroicity in the hexagonal manganites.