Scaling of anomalous Hall effect as a method to determine percolation threshold and metal–insulator transition in magnetic nanocomposites with intergranular interaction

Using the example of nanocomposite (NC) films (CoFeB)$_x$(LiNbO$_3$)$_{100-x}$, in which at relatively high temperatures of $T \gtrsim$ 10 K a ‘weakly insulating’ regime is observed in the logarithmic temperature dependence of the conductivity $\sigma \propto \rm {ln} \it T$, characteristic of a strong tunnel coupling between granules, the scaling in the behavior of the anomalous Hall effect (AHE) resistance as a function of the longitudinal resistance $\rho $ was studied in detail. The studies were carried out in fields up to 14 T at temperatures $T$ = 0.4–200 K in the range of metallic phase content $x \approx$ 35-60 at.%, covering the percolation transition. It was found that the power $n$ in the scaling dependence $\rho _{\rm AHE} \propto$ [$\rho(T)$]$^n$ behaves nonmonotonically. In the ranges $x\approx 35-44$ at.% and $x \approx$ 50–60 at.%, an increase in the power is clearly observed, whereas in the interval $x\approx 44-50$ at.%, the value of $n$ remains practically unchanged. We believe that the kink regions in the dependence $n(x)$ indicate a change in the NC conductivity mechanism and determine the percolation threshold (at $x_{\rm p}\approx 50$ at.%) and the metal–insulator transition ($x_{\rm c}\approx 44$ at.%), which do not coincide in these systems. The results of an analysis of the behavior of $\sigma (T)$ at subhelium temperatures $T = 0.4-3$ K confirm this conclusion. Studies of the magnetic properties of NCs vs the metallic phase content $x$ using ferromagnetic resonance and magneto-optical spectroscopy methods also indicate the pres„ence of specific features in the vicinity of concentrations $x\approx 44$ and 50 at.%.