Surface multiferroics in silicon enabled by hole-carrier doping

We predict a coexistence of magnetic and electric orders on clean Si(0 0 1) surfaces by first-principles calculations. Upon hole-carrier doping, the Si surfaces can be ferromagnetic, with polarized spins concentrated in an atom-thick space near the surface, due to an exchange splitting of localized s-like surface states on surface Si dimers. The surface magnetization can be controlled by reorienting the electric polarization of Si dimers, manifested as a transition from the magnetic antiferroelectric ground state to ferroelectric p(2 × 1) reconstruction that can be driven by an in-plane external electric field. The coupling between magnetic and electric orders can be further enhanced by strain silicon technology, rendering the Si surfaces as the first metal-free material displaying a multiferroic behavior.