Spin Hall Current and Spin-transfer Torque in Ferromagnetic Metal

We theoretically examine the spin-transfer torque in the presence of spin-orbit interaction (SOI) at impurities in a ferromagnetic metal on the basis of linear response theory. We obtained, in addition to the usual spin-transfer torque, a new contributioin $\sim {\bm j}_{\rm SH}^{\phantom{\dagger}} \cdot \nabla {\bm n}$ in the first order in SOI, where ${\bm j}_{\rm SH}^{\phantom{\dagger}}$ is the spin Hall current driven by an external electric field. This is a reaction to inverse spin Hall effect driven by spin motive force in a ferromagnet.Comment: 4 pages, Proceedings of the International Conference on Magnetism, submitted to J. Phys: Conference Serie

The boundary of the moduli space of stable cubic fivefolds

By GIT theory due to Mumford, the moduli space of stable cubic fivefolds is compactified by adding non stable semi-stable (i.e. strictly semi-stable) locus. In this paper, we prove that this locus consists of 19 components. Moreover, we give a description of equation and singularity of cubic fivefold corresponding to the generic point in each component.Comment: 14 page