The induced magnetic and electric fields’ paradox leading to multicaloric effects in multiferroics

Magneto-electric effect in multiferroics implies that an applied magnetic field induces an electric polarization change in a multiferroic solid and vice versa, an applied electric field modifies its magnetization. The magneto-electric effect is a powerful feature of multiferroics and has attracted huge interest due to potential technological applications. One such possible application is the multicaloric effect in multiferroics. However, a closer examination of this effect and its derivation leads to a paradox, in which the predicted changes in one of the order phase at a constant applied field are due to the excitation by the same field. Here this apparent paradox is first explained in detailed and then solved. Understanding how electric and magnetic fields can be induced in multiferroic materials is an essential tool enabling their theoretical modelling as well as facilitating the introduction of future applications.