The effect of dilute magnetic doping of a topological insulator on the surface states

Spin-dependent electronic properties are theoretically investigated in a diluted magnetic topological insulator (DMTI) with out-of-plane magnetization using a quantum theory based on self-consistent mean-field theory, including the spin-splitting effect in the presence of warped surface states. The effects of magnetic dopant concentration, carrier density, temperature, and external magnetic field are discussed on the surface of Bi2−xFexTe3 magnetically TI-doped sample. The parameters in the carrier-mediated magnetic mechanism are in excellent qualitative agreement with the experimentally observed magnetization. The numerical results showed that (i) the Dirac cone can shift in momentum space by the considered factors, (ii) the equal-energy contours of the DMTI deform for several different Fermi energies, (iii) an energy gap induces at surface state by doping of a small number of magnetic atoms, (iv) the spin-splitting energy becomes more when exchange interaction is included, and (v) more difference between equal-energy contours of two spin carriers with increasing the ratio of dopant density to carrier density and the spin-splitting energy. The origin of the large surface state gap will be discussed below. Moreover, the fermion spin polarization (FSP) energy ratios more than 17% are obtained in the momentum space on the surface state of Bi1.96Fe0.04Te3 compound for a density ratio of nc∕ni=0.1 at a fixed temperature T=0.2TC. Also, the FSP energy ratio reduces monotonically with decreasing the band-gap opening between the upper and lower Dirac cones at the Dirac point. The numerical results may shed light on the next applications of the magnetic topological insulator and make them convenient for future spintronics and magnetoelectric devices.