Temperature dependence of the spin susceptibility of nearly ferromagnetic Fermi systems

Abstract

The spin susceptibility of nearly ferromagnetic Fermi systems, e.g., liquid ³He, Pd, Ni₃Ga is large (X₀X_Pauli⁻¹=α₀⁻¹≫1) and varies strongly with temperature on a scale much smaller than the Fermi temperature. A theory for this is presented here. Using a functional transformation, the thermodynamic potential of the fermion system is converted to that of interacting spin fluctuations (a vector-boson field). The parameters of the latter are determined by the fermion system. The susceptibility is related to the spinfluctuation self-energy Σ. From a diagrammatic analysis of Σ , we show that there exists a convergent expansion for its temperature-dependent part, in terms of the number of correlated internal thermal spin fluctuations. The leading terms have one or two internal spin fluctuations: the three-spin-fluctuation term is of higher order in Τ/α₀ (for Τ≪ α₀) and in Τ (for α₀≲ Τ≪ 1). (Here Τ=T/T_F⁰.) Thus a calculation of X⁻¹(Τ)X_P=α (Τ) is possible in the entire degenerate range Τ≪ 1, and not merely the paramagnon range Τ≪ α ₀. α(Τ) is shown to go as α₀+A(Τ²/α₀) for Τ≪ α₀ and as α₀+BΤ for α₀≲Τ≪ 1, and interpolates smoothly between these two limits. (A and B are constants.) The former is the paramagnon-theory result and the latter is the result for "classical" spin fluctuations. As an illustration, we calculate, with one adjustable parameter, α(Τ) for liquid ³He in the temperature range 0<Τ≲0.2. The agreement with experiment is very good.