Ferroelectricity in spiral magnets

It was recently observed that materials showing most striking multiferroic phenomena are frustrated spin-density-wave magnets. We present a simple phenomenological theory, which describes the orientation of the induced electric polarization for various incommensurate magnetic states, its dependence on temperature and magnetic field, and anomalies of dielectric susceptibility at magnetic transitions. We show that electric polarization can be induced at domain walls and that magnetic vortices carry electric charge.Comment: 4 pages, 4 figure

On the connectivity of finite subset spaces

We show that for an m-connected cell complex X the space exp_k X of non-empty subsets of X of cardinality at most k is (m + k - 2)-connectedComment: 2 page