Electric polarization reversal in multiferroic TbMnO$_{3}$ with rotating magnetic field direction.

Recent extensive studies of magneto-electric multiferroics have revealed that the magnitude and direction of electric polarization can be considerably modified by the application of a magnetic field. TbMnO$_{3}$ is a prototypical multiferroic which shows the electric polarization flop from $P$//$c$ to $P$//$a$ by the application of magnetic field along the $b$ or $a$ axis. We have found that the direction of the magnetic-field induced polarization along the $a$-axis ($P_{a})$ is memorized even in the zero field where $P_{a}$ is absent. The polarization direction can be reversed by rotating the magnetic field direction in the \textit{ab} plane. For the memory application of the multiferroic material, such a bistability in zero field and a switching between the bistable states with some noneverlasting stimulus are essential.