First order phase transition in ferromagnetic semiconductors in external electric and magnetic fields (on the example of La$_{1-x}$Ca$_x$MnO$_3$)

It is shown that during a first-order phase transition in ferromagnetic semiconductors based on lanthanum manganites, along with the semiconductor phase of s-electrons, a phase arises with fluctuation short-range order associated with a change in the sign of the intermode interaction parameter in the system of d-electrons. The phase separation region is characterized by fluctuations of local magnetization depending on temperature and external magnetic field. In this case, the temperature of the first order phase transition, above which phase separation arises, is appreciably affected by double exchange. Due to self-heating, the phase separation is significantly affected by the electric field, which leads to N-shaped current-voltage characteristics. Using La$_{1-x}$Ca$_x$MnO$_3$ as an example, it is shown that the switching on of electric and magnetic fields during a first-order phase transition in ferromagnetic semiconductors is accompanied by the appearance of self-oscillations of the electric current and magnetization.