Kittel law in BiFeO₃ ultrathin films: a first-principles-based study.

A first-principles-based effective Hamiltonian is used to investigate the thickness dependency of the size of straight-walled domains in ultrathin films made of the multiferroic BiFeO₃ (BFO) material. It is found that the Kittel law is followed, as in ferroelectric or ferromagnetic films. However, an original real-space decomposition of the different energetic terms of this effective Hamiltonian allows the discovery that the microscopic origins of such a law in BFO films dramatically differ from those in ferroelectric or ferromagnetic films. In particular, interactions between tilting of oxygen octahedra around the domain walls and magnetoelectric couplings near the surface (and away from the domain walls) play an important role in the observance of the Kittel law in the studied BFO films.