On the theory of the ferromagnetic phase transition in crystalline and amorphous materials

Abstract

The ferromagnetic phase transition is determined by the interaction of spin clusters which are strongly coupled together. In the time-dependent Ginzburg–Landau theory (TDGL) this coupling is described by a nonlinear term in the equation of motion for the magnetization, and therefore the theory of phase transitions is mathematically rather complicated. We present a molecular field theory with correlations in space and time, which neglects the nonlinear coupling term, but which takes into account implicitly the effect of coupled spin clusters when constructing an appropriate linear equation of motion. The theory holds as long as the nonlinear term in the TDGL is not the dominant one, and it improves the conventional molecular field theory in a rather large range of temperatures, in which the couplings between the fluctuations are small enough but still important. It therefore may be successfully applied to the case of amorphous ferromagnets, which show deviations from the conventional molecular field behavior in a temperature range which is much larger than the range of critical behavior in crystalline Fe or Ni. Results for the critical slowing down and for the paramagnetic susceptibility are given.