Magnetocaloric effect in the ferromagnetic Kondo lattice model

The Kondo lattice model describes a lattice of localized spins SiSi interacting with the conduction electrons via a local exchange coupling J  . Assuming a ferromagnetic Hund's rule coupling J>0J>0, the model can be used to describe some itinerant magnetocaloric materials such as Gd(SixGe1-x)4Gd(SixGe1-x)4, La(Fe1-xSix)13La(Fe1-xSix)13, and LaCa1-xMnxO3LaCa1-xMnxO3, which are important for magnetic refrigeration near room temperature. The localized magnetic moments are described in the model Hamiltonian by spin operators, and the conduction electrons by fermionic operators. To study the magnetocaloric effect, a uniform external magnetic field is added through a Zeeman term. By averaging the fermionic degrees of freedom, one obtains an indirect exchange coupling J^ij between spins at sites i and j  , which corresponds to the RKKY interaction. The self-consistent mean value 〈Siz〉 is evaluated in the effective Heisenberg Hamiltonian within the random phase approximation (RPA). The conduction electron magnetization for a given value of 〈Siz〉 is obtained from the corresponding Green's functions through the equation of motion method. The pressure and doping dependence of the Curie temperature are taken into account in the evaluation of J^ij. The magnetocaloric effect is characterized by the isothermal entropy change ΔSΔS and the adiabatic temperature change ΔTadΔTad upon magnetic field variations in the neighborhood of the ferromagnetic phase transition. The results are obtained for S=72 and compared to measurements with Gd compounds.