Magnetic field and pressure induced valence and metal-insulator transitions in the spin-one-half Falicov–Kimball model

A combination of exact diagonalization calculations and a well-controlled approximate method is used to study valence and metal-insulator transitions in the spin-one-half Falicov–Kimball model (FKM) in the external magnetic field. It is shown that there exists a critical value of the magnetic field $$h_c$$ h c that depends on the f-level position $$E_f$$ E f , above which the spin-one-half FKM maps onto the spinless FKM. In this limit the spin-one-half FKM recovers all physics of the spinless model, including the picture of valence and metal-insulator transitions induced by changes of $$E_f$$ E f and opens the way to its experimental verification in real systems, like rare-earth compounds in the external magnetic field. In addition, we have found that the spin-one-half FKM in the external magnetic field exhibits a wide spectrum of continuous, as well as discontinuous valence, magnetic and metal-insulator transitions that can be induced by tuning directly the external magnetic field or indirectly the external pressure (via the f-level position). The experimental verification of these transitions represent also an interesting challenge, the solution of which can shed more light on the physics of valence and metal-insulator transitions in correlated d-f electron systems. Most of presented results are calculated for the one-dimensional spin-one-half FKM, but to establish connection with the behavior of real rare-earth materials we discuss also effects of the increasing system dimension and the anisotropic spin-dependent d-f interaction, which can play an important role in these materials. Graphic abstract