Size-dependent electrical transport properties in Co nanocluster-assembled granular films

A series of Co nanocluster-assembled films with cluster sizes ranging from 4.5 nm to 14.7 nm were prepared by the plasma-gas-condensation method. The size-dependent electrical transport properties were systematically investigated. Both of the longitudinal resistivity ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\rho }_{xx}$$\end{document}ρ x x) and saturated anomalous Hall resistivity ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\rho }_{xy}^{A}$$\end{document}ρ x y A) continuously increased with the decrease of the cluster sizes ( d ). The \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\rho }_{xx}$$\end{document}ρ x xfirstly increased and then decreased with increasing the temperature for all samples, which could be well described by involving the thermally fluctuation-induced tunneling (FIT) process and scattering. The tunneling effect was verified to result in the invalidation of classical anomalous Hall effect (AHE) scaling relation. After deducting the contribution from tunneling effect to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\rho }_{xx}$$\end{document}ρ x x, the AHE scaling relation between \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\rho }_{xy}^{A}$$\end{document}ρ x y Aand the scattering resistivity ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\rho }_{S}$$\end{document}ρ S) by varying the temperature was reconstructed. The value of scaling exponent γ increased with increasing Co cluster sizes. The size dependence of γ might be qualitatively interpreted by the interface and surface-induced spin flip scattering. We also determined the scaling relation between \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\rho }_{xy}^{A}$$\end{document}ρ x y Aand \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\rho }_{S}$$\end{document}ρ Sat 5 K by changing the Co cluster sizes, and a large value of γ  = 3.6 was obtained which might be ascribed to the surface and interfacial scattering.