Ferromagnetic Systems The Exchange Interaction And The Band Splitting Interaction Theory

In crystal, when there is overlap between the electrons, the system forms the electronic band. In the magnetic system, there is a exchange interaction between sites, which results the splitting of the band into spin-up and spin-down, respectively. The system is as a transition element magnetic metal model, in which the electrons play roles of both itineracy and consisting of local spins. When hopping strengths spin-up t↑and spin-down t↓are different, the shape, the width and the vertex of two sub-bands are different. We study with Green's Function Method to research the effects of temperature and magnetic field on energy band of this system, and the system which is with the splitting of the band and the exchange interaction. With the increase of temperature, the band gap of two sub-band decreases, magnetization intensity drops. At Curie point, the two sub-bands become identical, magnetization intensity is zero. The change and overlapping of two sub-bands'distance make out the transition between insular, semiconductor and metal qualitatively with temperature increasing.We use the 3d transition element magnetic metal, in which the electrons play roles of both itineracy and consisting of local spins. In the paper, we use model Hamiltonian and Green's function method to study the change condition of DOS in different transition probability of two spins, and we talk about the influencing factors of the splitting of the band with the exchange interaction.