**1. Introduction**

The giant magneto-resistance (GMR), independently discovered by the two groups of Fert and Grünberg [1,2] at the end of the 1980s, was first observed for stacks of very thin multilayers of alternating ferromagnetic/antiferromagnetic Fe and Cr. These layers couple magnetically, resulting in a giant decrease of resistivity with an increasingly applied magnetic field. Some years after the discovery of GMR, it was found that this phenomenon is not only restricted to layered systems but can also be found for materials containing dispersed ferromagnetic particles (granules) [3,4]; thus it was labeled as granular GMR.

If grains are not subjected to an external magnetic field, a random orientation of magnetic moments or domains prevails. With an increasing magnetic field, the magnetic domains gradually align by rotating the magnetization, and become aligned parallel to the magnetic field. This results in an overall decrease of resistance. It was shown that the increase in resistance for randomly oriented magnetic particles originates from spin-dependent scattering of conduction electrons at the magnetic-nonmagnetic interfaces [5,6]. Rabedeau et al. [5] found this fact by using small angle X-ray scattering measurements on thin films, making the particle sizes accessible. If the GMR originates

from scattering within the ferromagnetic particles, the GMR would weakly depend on the particle size (providing that all the ferromagnetic atoms can be found in the particles). However, as GMR scaled with the inverse of the cluster size (interfaces per volume, r2/r3) instead, an interfacial spin-dependent scattering was proposed.

Upon applying a magnetic field, the gradual change in the magnetization direction of single domain particles leads to a gradual change of the resistivity and this property can be directly linked to the hysteresis loop of the material. One method to characterize the relationship between the specimens' resistance and the magnetic field is the squared global relative magnetization μ (*H*) = (*M* (*H*)/MS) <sup>2</sup> [4], which is the ratio of the magnetization *M* (*H*) at a certain applied field *H* and the saturation magnetization MS. The GMR-effect is described in the following way:

$$\text{GMR} = \frac{\Delta \mathcal{R}}{\mathcal{R}} = \frac{\mathcal{R}(H) - \mathcal{R}(H = 0)}{\mathcal{R}(H = 0)} = \text{ A } \mu(H)^2 \text{ } \tag{1}$$

where A determines the effect amplitude and is different for each experimental setup. In some cases, the GMR of Equation (1) is expressed by *R* (*H*) in the denominator instead of *R* (*H* = 0), or *R* (*H* = 0) is replaced by *R* (*H* = *H*C). It is stated [4] that the change in resistance, which is a measure for the GMR-effect, is proportional to A\* (M (*H*)/Ms) 2; thus, the strength of the GMR-effect can be quantified by the proportionality factor A. For a magnetron sputtered thin film specimen consisting of 84 at% Cu and 16 at% of Co (Cu84Co16) and a temperature of 5 K, this proportionality factor A was found to be −0.065 [4]. To allow comparison, all compositions in this work will be given in at%, except stated otherwise.

Research on granular GMR first started with thin films. They were produced using a variety of different techniques, such as magnetron sputtering [3,4,7–11], molecular beam epitaxy [5], ion beam co-sputtering [12], cluster beam deposition [13], thermal evaporation [14], or by electrochemical deposition [15–17]. Later, research was extended to bulk materials and mixed granular materials were produced using different techniques such as mechanical alloying/ball milling [18–22] or melt spinning [9,23–25]. Research focused on a small number of binary, sometimes ternary systems such as CuCo [3–5,9,14,16,17,19,21,23,25,26], AgCo [4,6,7,9,11,12,18], CuFe [13,19], CoFe-Cu [10,20,22], CrFe [8], and AuCo [9,24]. A common feature of these systems is the small mutual solubility of ferromagnetic and non-magnetic elements, as well as the nonmagnetic phase representing the major phase. Reduced solubility promotes the production of small, finely dispersed ferromagnetic particles within a nonmagnetic metal matrix; either directly during production or after adequate annealing treatments. With increasing ferromagnetic content, a transition towards anisotropic magneto-resistance (AMR) is found [10]. Thomson discovered this anisotropy of ferromagnetic materials in magnetic fields [27], where the resistance for currents parallel and perpendicular to the magnetic field is different. For parallel alignment, the magneto-resistance increases with an increasing field and for the perpendicular alignment, the magneto-resistance decreases. The effect of AMR is typically in the size of the GMR or about one magnitude smaller and with a change of the sign of A (A > 0), depending on the investigated material.

The restricted mutual solubility is known for Cu and Co. and the granular GMR was discovered on magnetron sputtered CuCo [3,4]. They found a strong dependence of the resistance with the applied magnetic field, and the resistivity being highest in the initial non-magnetized state decreases with increasing applied field. The resistivity increases again upon decreasing the field and reaches a local maximum at the coercive field. However, resistivity is slightly lower than in the initial, non-magnetized state. To give a first idea on the amount of GMR present, some results of original works [3,4] are presented: Berkowitz et al. [3] investigated Cu containing 12, 19, and 28 at% Co and found for Cu81Co19 (as an example) a GMR of 10% at 10 K at the highest applied magnetic fields of 20 kOe. Negligible GMR was found at room temperature. Xiao et al. [4] found a GMR of 16.5% at 5 K for magnetron sputtered Cu80Co20, annealed for 10 min at 500 ◦C. A review on GMR, including granular GMR, is provided in reference [28].

The goal of this work was to produce bulk materials of different amounts of ferromagnetic and diamagnetic components. This enables the investigation of the influence of composition and processing parameters on the evolving microstructure, on the development of small, ferromagnetic particles and thus on the GMR. The chosen method is high pressure torsion (HPT) [29], a special method of severe plastic deformation (SPD), as it provides the opportunity to easily produce bulk samples from elemental powder mixtures [30]. The principle idea of HPT is based on the work of Bridgman [31], where material is confined under high hydrostatic pressure between two anvils. One anvil is rotated against the other and the material is severely deformed by shear deformation and the microstructure gets refined. This refinement saturates at a certain grain size—mostly depending on the amount of alloying elements, impurities, and deformation temperature [32].

Regarding the investigation of different magnetic properties of materials deformed by HPT, numerous studies focusing on the magnetic properties of HPT-processed materials are available [33–42]. Other techniques to apply severe deformation onto materials include ball milling, mechanical alloying, and equal channel angular pressing (ECAP), with some studies focusing on the magnetic properties of these alternative processing routes [18–21,26,43,44]. However, to the best knowledge of the authors, there are only two studies on HPT-deformed materials, which also contain information on magneto-resistive properties [34,37]. In references [34,37], the authors used arc-melted Cu-10 wt % Co for HPT deformation. The magneto-resistive drop was ~0.25% at room temperature and ~ 2.5% at 77 K, with both measured in fields of 6 kOe.

In summary, a detailed GMR—Study of the influences of HPT process parameters including deformation temperature and composition on GMR is lacking, which is the motivation for and aim of the presented work. Within this study, the Cu-Co-system was thoroughly investigated to understand the dependency of composition on the GMR, and to demonstrate the applicability of HPT throughout the whole compositional range.
