The Kondo Lattice Models and Magnetism for Cerium and Uranium Systems

The interplay between the Kondo effect and magnetism is important in anomalous rare-earth and actinide systems and a brief review of the different Kondo lattice models is presented here. The first studied case is the classical Kondo lattice model with S = 1/2 spins for the 4f localized electrons, which describes the strong competition between the Kondo effect and magnetic ordering leading to small ordering temperatures less than roughly 10 K. The second reviewed case describes the underscreened Kondo lattice model with S = 1 spins for the 5f localized electrons, which can account for the coexistence of both the Kondo effect and the ferromagnetic order and, therefore, the large Curie temperatures observed in actinide compounds like UTe and $NpNiSi_2$; the question of the delocalization of the 5f electrons is also discussed here. The last case describes the competition between the "spin glass" behaviour, the Kondo effect and the magnetic ordering in disordered cerium alloys like $CeNi_{x}Cu_{1 - x}$ or $CeRh_{x}Pd_{1 - x}$ and several models used for the spin glass state are reviewed, as well as the occurrence of magnetic glass clusters.