Magnetoresistance of insulating amorphous Ni_xSi_1-x films exhibiting Mott variable-range hopping laws

Magnetoresistance (MR) ratios R(B, T)/R(0, T) have been measured in an insulating three-dimensional amorphous nickel-silicon film that exhibits the Mott variable-range hopping (VRH) law in its zero-field resistance behavior. Surprisingly, the resistance displayed a decrease in small fields; only in moderately strong magnetic fields did the resistance exhibit a large increase over its zero-field value. These results are described by a phenomenological empirical model of two hopping processes acting simultaneously-the orbital magnetoconductance (forward-interference) model yielding negative magnetoresistances and the wave-function shrinkage model contributing positive magnetoresistances. The fits use numerical values for estimating the R(B, T)/R(0, T) ratios, based upon the wave-function shrinkage model. The model includes three fitting parameters, whose magnitudes are extracted from the MR ratio data at T = 10.5K. Agreement between the predicted and measured data is acceptable at high temperatures. A crossover of the conductivity to an Efros-Shklovskii (ES) variable-range hopping law is observed around T = 6K. At lower temperatures for this ES case, predicted values for the R(B, T)/R(0, T) ratios are fitted to the data. For a second weakly insulating film, which also exhibits a Mott VRH law in its resistance, the negative magnetoresistance contribution is greatly depressed.