Low-temperature magnetoresistance of Nb-doped transparent conducting films

The magnetoresistance of two anatase Nb-doped TiO2 films has been measured. The samples reveal both negative and positive magnetoresistance component at all measuring temperatures. It is indicated that the Lorentz force effect based on a two-band model can describe the positive magnetoresistance contribution well. Rather than weak localization or Kondo effect, the negative magnetoresistance behaviors follow a semiempirical expression considering the effect of localized magnetic moments. This expression, due to Khosla and Fischer in a paper published 40 years ago [R.P. Khosla, J.R. Fischer, Phys. Rev. B 2 (1970) 4084], is deduced from the s–d exchange Hamiltonian by considering the third-order perturbation. The field dependence of the magnetization curves for both samples reveals ferromagnetic characteristics, which proves the existence of localized magnetic moment in Ti1−xNbxO2 compounds.