Theory of magneto-electric susceptibility in multiferroic chiral magnets

We present a theoretical examination of the magneto-electric response in the recently discovered multiferroic insulator Cu$_2$OSeO$_3$. Combining Monte Carlo simulation and Ginzburg-Landau analysis we predict the response in each of the magnetic phases, including helical, conical, ferromagnetic and Skyrmion crystal phases, both for thin film and bulk systems. A common feature for all non-collinear phases is that the magneto-electric susceptibility increases linearly with the applied magnetic field. Being both calculable and measurable, the magneto-electric susceptibility can serve as a new powerful probe to detect and investigate magnetic phases and phase transitions in multiferroic chiral magnets in general.