Weak ferromagnetism in lightly electron-doped CaMnO$_3$

The origin of the weak ferromagnetism, that is observed in lightly electron-doped CaMnO$_3$, is studied by means of the non-collinear spin density functional theory, including the spin-orbit interaction. We show that the spin-canting in the G-type antiferromagnetic structure is realized by the electron-doping, and the canting angle becomes larger with increase of the doping amount. The estimated canting angle is in a good agreement with the experimental value of the Ce-doped CaMnO$_3$ [1] The spin-canted state is stabilized by the double-exchange interaction, and the spin-orbit interaction does not play a crucial role in this phenomenon. In addition, the spin-canted state shows metallic behavior by the double-exchange transfer that gives a reasonable interpretation for the experimental electronic transport property [2] We also clarify a possibility of the antiferromagnetic-ferromagnetic phase separation [3] that will be realized when doped-electrons are strongly localized.\\[4pt] [1] E.N. Caspi et al., Phys. Rev. B 69, 104402 (2004).\\[0pt] [2] P.-H. Xiang et al., Appl. Phys. Lett. 94, 062109 (2009).\\[0pt] [3] E. Dagotto et al., Phys.Rep. 344, 1 (2001).