Logarithmic temperature dependence of electrical resistivity of (Co$_{41}$Fe$_{39}$B$_{20}$)$_{x}$(Al–O)$_{100-x}$ nanocomposites

The temperature dependence of the electrical conductivity $\sigma(T)$ of (Co$_{41}$Fe$_{39}$B$_{20}$)$_{x}$(Al–O)$_{100-x}$ of nanocomposite films for different concentrations x of amorphous ferromagnetic metal (56 $>x>$ 30) has been studied in the temperature range of 4.2–300 K. It has been shown that, for concentrations in the interval 5 $>x>$ 49, the conductivity obeys the logarithmic law $\sigma(T) = =A(1+\alpha\ln T)$, where $A$ and $\alpha$ depend on the concentration. According to the theory developed by Efetov et al., this logarithmic dependence is connected with specificities of the Coulomb interaction in nanogranulated alloys on the intergranule tunneling in the transient region of concentrations from metallic conduction to the dielectric regime. The comparison of the theory with the experiment has revealed only qualitative agreement. The reasons of the quantitative disagreement have been discussed. The resistivity of samples with the concentrations lying in the range 49 $>x>$ 30 obeys the 1/2 power law.