Scaling of Hall Resistivity in the Mixed State of MgB2 Films

The longitudinal resistivity (rho_{xx}) and transverse resistivity (rho_{xy}) of MgB2 thin films in the mixed state were studied in detail. We found that the temperature dependencies of rho_{xx} and \rho_{xy} at a fixed magnetic field (H) satisfy the scaling law of $\rho_{xy}=A\rho_{xx}^\beta$, where the exponent beta varies around 2.0 for different fields. In the low field region (below 1T), beta maintains a constant value of 2.0 due to the weak pinning strength of the vortices, mainly from the superfluid of the pi band. When H>1T, beta drops abruptly to its lowest value at about 2T because of the proliferation of quasiparticles from the pi-band and, hence, the motion of the vortices from the superfluid of the sigma-band dominates the dissipation. As the field is increased further, the vortex pinning strength is weakened and beta increases monotonically towards 2.0 at a high field. All the results presented here are in good agreement with the expectation of the vortex physics of a multi-band superconductor.