Multiferroicity of BiMnO$_3$ reexamined from first principles.

BiMnO$_3$ is believed to show both ferromagnetic and ferroelectric orders. In contrast to its robustly confirmed ferromagnetism, only one experimental group has succeeded in observing ferroelectric hysteresis loop[1]. Another group has reported small magnetocapacitance effect around the ferromagnetic Curie temperature[2]. Using first-principles scalar-relativistic full-potential linear augmented plane wave (FLAPW) method and adopting the experimental lattice data, we have given several significant insights on physical properties of BiMnO$_3$[3]. Further extended results will be shown in this talk. With including spin-orbit interaction, possible directional coupling between the polarization and magnetization will be discussed together with magnetocrystalline anisotropy. Results of structual optimization based on the first-principles atomic forces will be presented to verify its ferroelectricity. Possible doping effect will also be explored. [1] A.~Moreira dos Santos {\it et al.}, Solid State Commun.\ {\bf 122} 49 (2002). [2] T.~Kimura {\it et al.}, Phys.\ Rev.\ B {\bf 67} 180401(R) (2003). [3] T.~Shishidou, N.~Mikamo, Y.~Uratani, F.~Ishii, and T.~Oguchi, J.\ Phys.: Condens.\ Matter {\bf 16} S5677 (2004).