Effect of the four-sheet Fermi surface on magnetoresistivity of MgB2

Recent experimental data of anisotropic magnetoresistivity measured in MgB₂ films have shown an intriguing behaviour: the angular dependence of magnetoresistivity changes dramatically with temperature and disorder. In order to explain such phenomenology, in this work, we extend our previous analyses on multiband transverse magnetoresistivity in magnesium diboride, by calculating its analytic expression, assuming a constant anisotropic Fermi surface mass tensor. The calculation is done for arbitrary orientation of the magnetic field with respect to the crystalline axes and for the current density either perpendicular or parallel to the magnetic field. This approach allows to extract quite univocally the values of the scattering times in the σ- and π-bands by fitting experimental data with a simple analytic expression. We also extend the analysis to the magnetoresistivity of polycrystalline samples, with an arbitrary angle between the current density and the magnetic field, taking into account the anisotropy of each randomly oriented grain. Thereby, we propose magnetoresistivity as a very powerful characterization tool to explore the effect of disorder by irradiation or selective doping as well as of phonon scattering in each one of the two types of bands, in single crystals and polycrystalline samples, which is a crucial issue in the study of magnesium diboride.