Granular Cu-Co alloys as interacting superparamagnets

Abstract

The anhysteretic magnetization of the granular metallic alloy ${\mathrm{Cu}}_{90}{\mathrm{Co}}_{10}$ is experimentally studied over a wide temperature range (2--700 K). The measurements definitely exclude that this alloy is a simple superparamagnet, even in the high-temperature limit, although some features of granular systems [such as the typical Langevin-like form of the anhysteretic magnetization curves $M(H)]$ are often taken as evidence of superparamagnetism. A phenomenological theory is proposed, explicitly considering that particle moments interact through long-ranged dipolar random forces, whose effect is pictured in terms of a temperature ${T}^{*},$ adding to the actual temperature T in the denominator of the Langevin function argument. This simple formula explains all features of the experimental $M(H)$ curves. The theory indicates that the actual magnetic moments on interacting Co particles are systematically larger than those obtained fitting the magnetic data to a conventional Langevin function. The ${\mathrm{Cu}}_{90}{\mathrm{Co}}_{10}$ granular alloy is therefore identified as an ``interacting superparamagnet'' ISP. The ISP regime appears as separating the high-temperature, conventional superparamagnetic phase from the low-temperature, blocked-particle regime. In this way, a magnetic-regime diagram can be drawn for each granular system. The competition between single-particle and collective blocking mechanisms is briefly analyzed. The proposed interpretation is thought to be applicable to other fine particle systems; its main features and intrinsic limits are discussed.