Green's function approach to ferromagnetism on the Kondo lattice

Abstract

Kondo compounds exhibit a rich phase diagram, which involves different types of magnetic ordering and superconductivity, depending on temperature, pressure and electron concentration. In the Kondo lattice model, we develop the chain of equations of motion generated by the conduction electron Green's function G ij σ ( ω ) ≡ 〈 〈 c i σ ; c j σ † 〉 〉 and by spin Green's function χ ij σ ( ω ) = 〈 〈 S i σ ¯ ; S j σ 〉 〉 . The third generation Green's functions are approximated as combinations of the lower-order Green's functions. The method allows the evaluation of the f electron and conduction-electron magnetizations 〈 S i z 〉 and 〈 s i z 〉 and the local spin correlations 〈 S i z s i z 〉 and 〈 S i + s i - 〉 as self-consistent parameters. We investigate in particular the stability of the ferromagnetic phase on a cubic lattice. The magnetizations and local correlations are calculated as a function of temperature for fixed values of the Kondo exchange J and the conduction electron concentration n.