Microscopic theory of spin fluctuations in itinerant-electron ferromagnets. I. Paramagnetic phase

Abstract

In microscopic theories of phase transitions occurring in itinerant-electron systems, physical phenomena are generally considered in the random-phase (RPA) or mean-particle-field approximation. We describe here a many-body theoretical method of calculating the appropriate order-parameter susceptibility function Χ(q,ω⁺) which goes beyond the RPA. A diagrammatic analysis of the equation of motion for a quantity related to Χ(q,ω⁺) is made, and it is shown how one can systematically and self-consistently include the effect of order-parameter fluctuations on Χ(q,ω⁺). The method is applied here to the paramagnetic phase of an itinerant-electron ferromagnet. A mean-fluctuation-field approximation (MFFA) which includes the contribution of one internal spin fluctuation to Χ(q,ω⁺) is discussed in detail. Its temperature-dependent contribution to Χ^-1 goes roughly as (k_BTρ_εF)^4/3. A self-consistent solution of the MFFA equation for Χ(0,0) leads to a Curie-Weiss-like behavior for it. We make an explicit comparison of our results with experimental values for Ni, and find good agreement in the range 0.1≤(T-T_c)/T_c=ε≤0.6. In the Stoner or RPA theory the Curie-Weiss law is ascribed to the T² part of the particle-field term -U∫f'(E)ρ(E)dE. This is smaller than the MFF term by a factor (k_BTρ_εF)^-2/3, and for Ni, is only 5% of the latter. The Curie-Weiss-like law observed in metallic paramagnets is therefore due to the mean spin-fluctuation field, as also realized by Murata and Doniach, and by Moriya and Kawabata. Going beyond the MFFA, we calculate the contribution of the simplest spin-fluctuation correlation diagram. The contribution of this diverges logarithmically as ε→ 0. When this term becomes comparable to the MFFA, we are well in the critical regime which cannot be conveniently discussed by this method. This criterion is used to provide a first-principles estimate of the static and dynamic critical regimes in Ni. The former obtains for ε≲ 0.05 and the latter for e≲ 0.06(q/k_F). We show how spin fluctuations suppress ferromagnetism in a two-dimensional system and plot Χ_2d(0,0) vs T for a Ni-like film in the MFFA. The method developed here can be applied to discuss fluctuation effects in the ferromagnetic phase, in superconductivity, and in itinerant-electron antiferromagnetism.