Ferromagnetism in the Kondo-lattice model

We propose a modified Rudermann, Kittel, Kasuya, Yosida (RKKY) technique to evaluate the magnetic properties of the ferromagnetic Kondo-lattice model. Together with a previously developed self-energy approach to the conduction-electron part of the model, we obtain a closed system of equations which can be solved self-consistently. The results allow us to study the conditions for ferromagnetism with respect to the band occupation n, the interband exchange coupling J, and the temperature T. Ferromagnetism appears for relatively low electron (hole) densities, while it is excluded around half-filling $\mathrm{}(n=1\mathrm{}).$ For small J the conventional RKKY theory $\left(\sim J^2\right)$ is reproduced, but with strong deviations for very moderate exchange couplings. For not-too-small n a critical $J_c$ is needed to produce ferromagnetism with a finite Curie temperature $T_C,$ which increases with J, then running into a kind of saturation, in order to fall off again and disappear above an upper critical exchange J. Spin waves show a uniform softening with rising temperature, and a nonuniform behavior as functions of n and J. The disappearance of ferromagnetism when varying T, J, and n is uniquely connected to the stiffness constant D becoming negative.