In the present paper, reported literature data on the grain-size dependence of resistivity of Ni and Cu are critically evaluated by two conceptually different methods. One is the phenomenological approach of Andrews (Phys. Lett. 19: 558, 1965) according to which in a polycrystalline metal there is a resistivity contribution inversely proportional to the average grain diameter, the proportionality constant defined as the Andrews parameter A. The other method is the customary Mayadas–Shatzkes (MS) model (Phys Rev B 1: 1382, 1970) yielding a grain-boundary reflection coefficient R. During the analysis, special care was taken to rely only on data for which the surface scattering resistivity contribution was definitely negligibly small and the grain size was determined by direct microscopy imaging. By sorting out with this analysis the most reliable grain-size-dependent resistivity data for polycrystalline Ni and Cu metals with random grain boundaries, we have then derived the current best room-temperature values of the Andrews parameter A, the specific grain-boundary resistivity and the reflection coefficient R. We have also found a fairly good relation between the parameters A and R and compared the experimental values with their theoretical estimates reported in the literature. Then, the conceptual differences between the two approaches are discussed and the deficiencies of the MS model, especially in connection with the validity of Matthiessen’s rule, are highlighted. A major conclusion is that by the Andrews method one can derive a model-independent reliable parameter characterizing the grain-boundary contribution to the resistivity of metals.

An analysis of both magnetic and magnetotransport properties is presented for electrodeposited multilayers prepared intentionally under conditions to make the superparamagnetic (SPM) magnetization contribution comparable to or larger than the ferromagnetic term. Based on a model elaborated for the giant magnetoresistance (GMR) of granular metals [N. Wiser, J. Magn. Magn. Mater. 159, 119 (1996); B. Hickey et al., Phys. Rev. B. 51, 667 (1995)], it is shown that in such multilayers both the magnetization and the GMR can be decomposed into ferromagnetric and superparamagnetic contributions where the latter term is described by a Langevin function. The size of the SPM regions estimated from the experimental data is in the nanoscale regime. It is believed that the method applied here gives a quantitative answer to the problem of the often observed nonsaturating behavior of GMR in multilayers. Electrodeposited multilayers are particularly prone to this feature although the occurrence of SPM regions is quite common in multilayers prepared by any technique. Therefore, this type of analysis should help better understanding of the factors influencing the GMR of multilayer films.

A detailed study of the evolution of the magnetoresistance was performed on electrodeposited Co/Cu multilayers with Cu-layer thicknesses ranging from 0.5 to 4.5 nm. For thin Cu layers (up to 1.5 nm), anisotropic magnetoresistance (AMR) was observed, whereas multilayers with thicker Cu layers exhibited clear giant magnetoresistance (GMR) behavior. The GMR magnitude increased up to about 3.5–4 nm Cu-layer thickness and slightly decreased afterward. According to magnetic measurements, all samples exhibited ferromagnetic (FM) behavior. The relative remanence turned out to be about 0.75 for both AMR- and GMR-type multilayers. This clearly indicates the absence of an antiferromagnetic (AF) coupling between adjacent magnetic layers for Cu layers even above 1.5 nm where the GMR effect occurs. The AMR behavior at low spacer thicknesses indicates the presence of strong FM coupling (due to, e.g., pinholes in the spacer and/or areas of the Cu layer where the layer thickness is very small). With increasing spacer thickness, the pinhole density reduces and/or the layer thickness uniformity improves, which both lead to a weakening of the FM coupling. This improvement in multilayer structure quality results in a better separation of magnetic layers and the weaker coupling (or complete absence of interlayer coupling) enables a more random magnetization orientation of adjacent layers, all this leading to an increase in the GMR. Coercive field and zero-field resistivity measurements as well as the results of a structural study reported earlier on the same multilayers provide independent evidence for the microstructural features established here. A critical analysis of former results on electrodeposited Co/Cu multilayers suggests the absence of an oscillating GMR in these systems. It is pointed out that the large GMR reported previously on such Co/Cu multilayers at Cu-layer thicknesses of around 1 nm can be attributed to the presence of a fairly large superparamagnetic (SPM) fraction rather than being due to a strong AF coupling. In the absence of SPM regions as in the present study, AMR only occurs at low spacer thicknesses due to the dominating FM coupling.

The purpose of the present study was to provide a reliable value for the specific grain-boundary resistivity ρ_SGBR of Ni metal. New results are presented on the room-temperature electrical resistivity of nanocrystalline (nc) Ni metal samples produced by electrodeposition with various grain sizes. These resistivity data were compared with previous reports on nc-Ni and all results were analysed according to the procedure of Andrews [Phys. Lett. 19, 558 (1965)] who found that the resistivity increment due to grain boundaries is proportional to the grain-boundary surface area per unit volume which is, on the other hand, inversely proportional to the grain size. It is pointed out that the grain size directly accessible by transmission electron microscopy imaging is the relevant parameter for the evaluation of ρ_SGBR whereas the crystallite size deduced from X-ray diffraction line broadening leads to an underestimation of ρ_SGBR because coherency-breaking intragrain defects not contributing significantly to the resistivity also cause a line broadening. From the evaluation of the nc-Ni resistivity data at room temperature, we find that 4.45·10⁻¹⁶ Ω·m² < ρ_SGBR(Ni) < 6.2·10⁻¹⁶ Ω·m² and our upper bound agrees exactly with the most recent calculated value in the literature.