Metamagnetic transition in the two $f$ orbitals Kondo lattice model

In this work, we study the effects of a transverse magnetic field in a Kondo lattice model with two $f$ orbitals interacting with the conduction electrons. The $f$ electrons that are present on the same site interact through Hund's coupling, while on neighboring sites they interact through intersite exchange. We consider here that part of $f$ electrons are localized (orbital 1) while another part (orbital 2) are delocalized, as it is frequent in uranium systems. Then, only electrons in the localized orbital 1 interact through exchange interaction with the neighboring ones, while electrons in orbital 2 are coupled with conduction electrons through a Kondo interaction. We obtain a solution where ferromagnetism and Kondo effect coexist for small values of an applied transverse magnetic field for $T\rightarrow0$. Increasing the transverse field, two situations can be obtained when Kondo coupling vanishes: first, a metamagnetic transition occurs just before or at the same time of the fully polarized state, and second, a metamagnetic transition occurs when the spins are already pointing out along the magnetic field.