Mechanism of Spontaneous Electric Polarization Flop in TbMnO$_{3}$

Orthorhombic perovskite TbMnO$_{3}$ is one of the typical multiferroic systems. Spontaneous electric polarization (P) along the $c$-axis which originates from the spiral configuration of Mn$^{3+}$ spins rotating in the \textit{bc}-plane appears below $T_{C}$ ($\sim $27K). P//$c$ is turned to the direction along the a-axis by applying a magnetic field along $a$- or $b$-axis. Magnetic structure analysis and a spin-polarized neutron diffraction study of $^{160}$Gd$_{0.7}$Tb$_{0.3}$MnO$_{3}$ strongly suggest that P//$a$ in TbMnO$_{3}$ in high magnetic fields also originates from spin spiral rotating in the \textit{ab}-plane as in the case of P//$c$. It has been pointed out that anisotropic Tb $f$-electron magnetic moments play an important role for the complicated electric polarization flop. In this study, we have confirmed the change of spin basal plane of TbMnO$_{3}$ from the \textit{bc-} to \textit{ab-} plane by applying a magnetic field along the $b$-axis using spin-polarized neutron diffraction technique. We observed that a magnetic fields induce a C-type antiferromagnetic structure caused by the local anisotropy of Tb magnetic moments. We have succeeded in explaining the electric polarization flop of TbMnO$_{3}$ in terms of a coupling between Mn$^{3+}$ spins and anisotropic Tb magnetic moments.