Features of the Scaling of the Anomalous Hall Effect in (CoFeB)x(LiNbO3)100 − x Nanocomposite Films Below the Percolation Threshold: Manifestation of the Cotunneling Hall Conductance?

A scaling behavior of the anomalous Hall effect resistivity ρ_AHE versus the longitudinal resistivity ρ in (CoFeB)_x(LiNbO₃)_{100 − x} nanocomposites with a low content of dispersed Co and Fe atoms (N_d ~ 4 × 10²⁰ cm⁻³) in an amorphous LiNbO₃ matrix is studied in the range x ≈ 40–48 at % below the percolation threshold x_p ≈ 49 at %. A logarithmic temperature dependence of the conductivity σ ~ lnT  has been observed in the range x ≈ 44–48 at %, which is transformed in the range x ≈ 40–42 at % to a square root law lnσ ∝ ‒(T₀/T)^1/2, which is characteristic of cotunneling transport processes in nanocomposites. It has been found that the exponent n ≈ 0.24 in the scaling law ρ_AHE/x ∝ [ρ(x)]ⁿ coincides within an accuracy of 5% with the exponent n in a similar dependence for nanocomposites based on the (CoFeB)_x(Al₂O₃)_{100 − x} matrix with a high content N_d ~10²¹–10²² cm^–3 and with the exponent n in a parametric dependence ρ_AHE ∝ [ρ(T)]ⁿ for the samples with the minimum content x ≈ 40 at %. The found features are attributed to the correlated change in the probability of cotunneling transitions in a set of more than three centers under the effect of spin–orbit coupling. The manifestation of the barrier tunneling anomalous Hall effect at granule interfaces is also p-ossible.