Hall effect and magnetoresistance in single crystals of NdFeAsO$_{1-x}$F$_{x}$

Hall effect and magnetoresistance have been measured on single crystals of $NdFeAsO_{1-x}F_{x}$ with x = 0 ($T_c$ = 0 $ $K) and x = 0.18 ($T_c$ = 50 $ $K). For the undoped samples, strong Hall effect and magnetoresistance with strong temperature dependence were found below about 150 K. The magnetoresistance was found to be as large as 30% at 15 K at a magnetic field of 9 T. From the transport data we found that the transition near 155 K was accomplished in two steps: first one occurs at 155 K which may be associated with the structural transition, the second one takes place at about 140 K which may correspond to the spin-density wave like transition. In the superconducting sample with $T_c$ = 50 $ $K, it is found that the Hall coefficient also reveals a strong temperature dependence with a negative sign. But the magnetoresistance becomes very weak and does not satisfy the Kohlers scaling law. These dilemmatic results (strong Hall effect and very weak magnetoresistance) prevent to understand the normal state electric conduction by a simple multi-band model by taking account the electron and hole pockets. Detailed analysis further indicates that the strong temperature dependence of $R_H$ cannot be easily understood with the simple multi-band model either. A picture concerning a suppression to the density of states at the Fermi energy in lowering temperature is more reasonable. A comparison between the Hall coefficient of the undoped sample and the superconducting sample suggests that the doping may remove the nesting condition for the formation of the SDW order, since both samples have very similar temperature dependence above 175 K.