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 $M\left(H\right)\mathrm{}]$ 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 $M\left(H\right)\mathrm{}$ 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.

Room-temperature measurements of magnetization and giant magnetoresistance were performed on rapidly solidified granular ${\mathrm{Cu}}_{100-x}{\mathrm{Co}}_x$ systems ($x=5, 10, 15$). The magnetoresistance of melt-spun ${\mathrm{Cu}}_{100-x}{\mathrm{Co}}_x$ ribbons was enhanced either by suitable furnace annealings or by exploiting the dc Joule-heating technique in the attempt of precipitating smaller magnetic particles. The particle-size distribution, the particle density, and mean distance are obtained for all compositions and heat treatments through a suitable analysis of the magnetic behavior of samples. The magnetoresistance is plotted as a function of the reduced magnetization, and a significant deviation from the quadratic behavior predicted by the independent-moment approach is observed at low fields. A simple theory taking explicitly into account the correlation existing among the magnetic particles is proposed. A general expression for the magnetoresistance in granular magnetic systems is obtained, and shown to accurately fit all the experimental curves, indicating that this effect is basically determined by the ratios between two distinct correlation ranges for the magnetic-moment fluctuations and the electronic mean free path.

The magnetic hysteresis of granular magnetic systems is investigated in the high-temperature limit $(T\gg$ blocking temperature of magnetic nanoparticles). Measurements of magnetization curves have been performed at room temperature on various samples of granular bimetallic alloys of the family ${\mathrm{Cu}}_{100-x}{\mathrm{Co}}_x\hspace{0.5em}(x=5\mathrm{}–20\hspace{0.5em}\mathrm{at}.\mathrm{}\%)$ obtained in ribbon form by planar flow casting in a controlled atmosphere, and submitted to different thermal treatments. The loop amplitude and shape, which are functions of sample composition and thermal history, are studied taking advantage of a novel method of graphical representation, particularly apt to emphasize the features of thin, elongated loops. The hysteresis is explained in terms of the effect of magnetic interactions of the dipolar type among magnetic-metal particles, acting to hinder the response of the system of moments to isothermal changes of the applied field. Such a property is accounted for in a mean-field scheme, by introducing a memory term in the argument of the Langevin function which describes the anhysteretic behavior of an assembly of noninteracting superparamagnetic particles. The rms field arising from the cumulative effect of dipolar interactions is linked by the theory to a measurable quantity, the reduced remanence of a major symmetric hysteresis loop. The theory’s self-consistence and adequacy have been properly tested at room temperature on all examined systems. The agreement with experimental results is always striking, indicating that at high temperatures the magnetic hysteresis of granular systems is dominated by interparticle, rather than single-particle, effects. Dipolar interactions seem to fully determine the magnetic hysteresis in the high-temperature limit for low Co content $(x<~10).$ For higher concentrations of magnetic metal, the experimental results indicate that additional hysteretic mechanisms have to be introduced.