  Magnetoelectric multiferroic materials, particularly with the perovskite
structure, are receiving a lot of attention because of their inherent coupling
between electrical polarization and magnetic ordering. However, very few types
of direct coupling between polarization and magnetization are known, and it is
unclear whether they can be useful to the design of novel spintronic devices
exploiting the control of magnetization by electric fields. For instance, the
typical bi-quadratic coupling only allows to change the magnitude of the
magnetization by an electric field, but it does not permit an
electric-field-induced switching of the magnetization. Similarly, the so-called
Lifshitz invariants allow an electric-field control of complicated magnetic
orderings, but not of the magnetization. Here, we report the discovery of novel
direct couplings between polarization and magnetization in epitaxial perovskite
films, via the use of first-principles methods and the development of an
original Landau-type phenomenological theory. Our results feature penta-linear
interactions involving the ferromagnetic and anti-ferromagnetic vectors as well
as the polar distortions and oxygen octahedral tilting, and permit a number of
striking effects. Examples include a continuous electric-field control of the
magnetization magnitude and sign, and the discrete switching of the
magnetization magnitude. Thus, the high-order, penta-linear couplings
demonstrated in this work may open new paths towards novel magneto-electric
effects, as well as, spintronic and magnonic devices.
