Thermodynamics of an itinerant-electron ferromagnet at very lowTCεF

The validity of the classical Murata-Doniach model for the thermodynamic properties of weak itinerant magnets near $T_C$ is discussed in detail. An explicit perturbation expansion for the nontrivial thermodynamic properties in the model is carried out in terms of two small parameters available for very weak transitions. Furthermore, a microscopic examination of quantum corrections (the ${\omega }_n\ne 0$ modes) suggests that the classical phenomenological model with temperature-independent Ginsburg-Landau (GL) coefficients in valid as $T_C\to 0$ if the fluctuation phase space is simply restricted to the thermal population. Thus, if the excitations are paramagnons with $q^3$ damping, the fluctuations must be cut off at a momentum $q_m\sim T^{\frac{1}{3}}$. We find that the model is necessarily phenomenological in the sense that the quantum corrections enter the GL coefficients without benefit of a small parameter. However, given the coefficients, a small parameter is available for the Murata-Doniach model ($\frac{T_C}{{\epsilon }_F}$) if the phase transition happens to be weak. This difficulty should be present in the similar Moriya-Kawabata approach. The coefficients could presumably be determined by detailed fitting to itinerant magnets with $T_C$ in the 1-K region.