Spin Current and Magnetoelectric Effect in Noncollinear Magnets

A new mechanism of the magnetoelectric effect based on the spin supercurrent is theoretically presented in terms of a microscopic electronic model for noncollinear magnets. The electric polarization ${\stackrel{\ensuremath{\rightarrow}}{P}}_{ij}$ produced between the two magnetic moments ${\stackrel{\ensuremath{\rightarrow}}{S}}_{i}$ and ${\stackrel{\ensuremath{\rightarrow}}{S}}_{j}$ is given by $\stackrel{\ensuremath{\rightarrow}}{P}\ensuremath{\propto}{\stackrel{\ensuremath{\rightarrow}}{e}}_{ij}\ifmmode\times\else\texttimes\fi{}({\stackrel{\ensuremath{\rightarrow}}{S}}_{i}\ifmmode\times\else\texttimes\fi{}{\stackrel{\ensuremath{\rightarrow}}{S}}_{j})$ with ${\stackrel{\ensuremath{\rightarrow}}{e}}_{ij}$…