Coexistence of spiral magnetic state and weak ferromagnetism in a multiferroic, cross-controlled by external magnetic and electric fields

The influence of external magnetic and electric fields on the properties of a multiferroic with a helical magnetic structure is described. Thermodynamics of the phase transition from the antiferromagnetic ferroelectric to the new magnetic state is described for a multiferroic with a perovskite-type structure. In this magnetic state a spiral spin structure and weak ferromagnetism can exist simultaneously. Such a state is a result of the first-order phase transition at a certain temperature below TN when, due to the Dzyaloshinskii–Moriya effect, a helical magnetic structure occurs. In this state the vectors of electrical polarization and the helicoid of magnetic moments in perovskites are mutually perpendicular and lie in the basic (ab) plane perpendicular to the main c axis. In this case an additional electrical polarization proportional to the square of magnetization appears in the (ab) plane which reduces the common polarization of the ferroelectric. It is shown that a weak ferromagnetic moment m occurs along the c axis in an applied magnetic field in addition to a modulated magnetic structure appearing in the (ab) plane. The dependence of these phenomena on the applied electric field is considered. It is shown that a sign-alternating electric field causes a linear-in-the-field variation of the magnetic moment opposite in sign to the electric field variation (i.e., the greater is the electric field, the smaller is the magnetic moment m). The observed hysteresis phenomena determining the temperature ranges of overheating and overcooling of each phase under applied magnetic and electrical fields are explained.