Landau Fermi-liquid theory for heavy-fermion compounds. I. Thermodynamics

Abstract

We generalize the Landau Fermi-liquid theory for describing electrons in heavyfermion compounds. The theory gives resuIts in good agreement with microscopic mean-field approaches. We study the low-temperamre magnetic properties of the compounds and the competition between ferromagnetism and the coherent Kondo state, taking into a m u t the RKKY interaction.

Landau Fermi-liquid theory for heavy-fermion compounds: II. Collective modes

“…In the present paper we derive a description of dynamic phenomena in heavy-fermion compounds within the generalized Landau Fermi-liquid theory proposed in our previous paper [11] where we have shown that the phenomenological approach gives a detailed description of the low-temperature thermodynamic properties of the heavy-fermion ground state in agreement with microscopic approaches [8,9]. Moreover the Landau-like approach has enabled us to study the ferromagnetic phase transition stimulated by the RKKY interaction.…”

“…It is important to note that in the general case the local effective energy of f electrons (ε f (r, t) = εf +ε f 1 (r, t)) depends on r and t. In accordance with the Landau-like approach to heavy fermion systems [11] the value of ε f (r, t) is determined by the constraint that the number N f of f electrons does not depend on r and t in low-frequency processes, i.e.…”

“…In accordance with the generalized Landau Fermi-liquid theory proposed in [11] an equilibrium distribution of the conduction and f electrons in the system is described by a distribution matrix N ab 0αβ (k) with the band indices a, b = c, f and spin indices α and β for s = 1 2 spins. It is convenient to present the matrix in the block form…”

“…If we take into account only the exchange interaction between conduction and f electrons and neglect the potential interactions between electrons, then, in the equilibrium state, elements of the quasi-particle energy matrix are given by (2.4) where h c 0 (k) and h f 0 (k) are the equilibrium effective magnetic fields which affect conduction and f electrons, respectively [11]. These fields and the function b(k) that characterizes the formation of the coherent state are related to the equilibrium distribution matrix N 0 :…”

“…where k = E 2k − E 1k is the direct energy gap between the bands (3.4), λ ≡ ω/qv F and ϕ 0 is the term with l = 0 in the expansion of the interaction function ϕ(k, p) in the Legendre polynomials. According to [11], for the heavy-fermion system the parameter ϕ 0 must be negative. ρ 0 is the density of states in the conduction band ε(k) near the Fermi surface.…”