Extraordinary Hall effect in (Ni₈₀Fe₂₀) _x(SiO₂)_1-x thin films

The extraordinary Hall effect (EHE) in ferromagnetic samples is generally attributed to scatterings of iterant electrons in the presence of spin-orbit interactions. In this work, our study of the thickness dependence of the EHE in the (Ni₈₀Fe₂₀)_x(SiO₂)_1-x system showed the spontaneous Hall resistivity, ρ_xy^S to be quite independent of the film thickness while the Hall coefficient, R _s (≡ρ_xy^S/M_S, where M _S is the saturated magnetization), increased monotonically owing to a depression in M_S. We point out that the independence of ρ_xy^S with reducing thickness could arise if the morphological structure of the sample becomes two dimensional with decreasing film thickness, which is expected from classical percolation theory. We also find in the (Ni₈₀Fe₂₀)_x(SiO₂) _1-x system (with varying x) that ρ_xy^{S ∝}ρ_xx^γ where γ=0.53, which disagrees with the value of 2 frequently attributed to the side jump effect, but which can be explained in terms of the more general form ρ _xy^S=ρ_xxΔ_ye/ Λ_SO, where Δ_ye is the side jump displacement and Λ_SO is the spin-orbit mean free path.