Magnetoelectric coupling and spin reorientation in BiFeO 3

We have studied the electric properties of multiferroic BiFeO 3 (BFO) using the transverse Ising model in terms of pseudo‐spin variables S with S = 7/2 and the Green's function method. Mechanisms of magnetoelectric (ME) couplings and electric field‐induced spin‐reorientation (SR) transition in BFO ( 71 ∘ in‐plane and 109 ∘ out‐of‐plane switching) are examined. It is established that the spontaneous polarization P s is responsible for the origin of an incommensurate non‐collinear magnetic phase below T N . The relevance of two types of ME mechanisms is shown: the first one is quadratic with respect to the magnetic spins and the ferroelectric variables, whereas a second one defines a ME interaction which is induced from the appearance of a spontaneous polarization in BFO, called antisymmetric ME interaction. When an external magnetic field is applied they compete against each other and as a result the spontaneous polarization P s is renormalized. The extraordinary polarization below T N is numerically calculated and its dependency on the easy‐axis anisotropy K and the external magnetic field is examined. The type of magnetic SR transition under the influence of the electric field is determined. The critical values of E for different switching processes are numerically calculated.