# Microstructural Changes Influencing the Magnetoresistive Behavior of Bulk Nanocrystalline Materials
## 1 Introduction  
While the change in resistance in magnetic fields of ferromagnetic materials is small but well known for more than 150 years [1], the groups of [PERSON] et al. and [PERSON] et al. showed that changes of resistance with magnetic field, especially at low temperatures, can be gigantic when using thin layers of alternating Fe and Cr [2, 3]. Some years after the discovery of the giant magnetoresistance (GMR) for layered thin film systems, it was also found for thin films and for bulk materials containing finely dispersed small ferromagnetic particles (granules) [4, 5, 6, 7, 8]. Thus, the effect was labelled granular GMR. Materials processed by severe plastic deformation (SPD) using high-pressure torsion (HPT) show such a GMR effect [9, 10, 11] and this group of materials is in the focus of this investigation. As a definition, GMR can be distinguished from ordinary magnetoresistance (OMR) and anisotropic magnetoresistance (AMR) by its negativity in all directions of applied magnetic field with respect to the current flow direction [12] and furthermore by its isotropic behavior [5]. This gives the evident advantage of 3D-bulk materials over 2D-thin film materials in the aspect of shaping when going towards applications. Within this publication, GMR will be calculated according to  
\[GMR=\frac{\Delta R}{R}=\frac{R(H)-R(H=0)}{R(H=0)} \tag{1}\]taking into account the resistance \(R\) within the magnetic field \(H\) and at zero field. Although the present study focusses on the GMR behavior of nanostructured bulk materials, many important observations were found in studies on thin films. [PERSON] and [PERSON] [13] investigated different types of binary systems, including Co-Ag, Fe-Ag, Fe-Cu, Fe-Au, and Fe-Pt. Thin film samples were produced using magnetron co-sputtering and magneto-transport properties in the as-deposited and annealed states were measured. The main findings of this study can be summarized as follows:  
1. The (partial) immiscibility of both phases is a prerequisite for the appearance of granular GMR. The solid solution forming Fe-Pt did not show GMR behavior. Regarding the systems in focus of this publication, the solubility of Cu and Co and vice versa is smaller than 1 at% at 900 K [14]. The same is true for Cu-Fe below \(\sim\)1000 K [15]. 2. A peak in GMR occurs for ferromagnetic volume fractions between 15% and 25%. This was found to be universal for all systems showing granular GMR. Within the Cu-Fe-series, the highest GMR was found for Fe\({}_{20}\)Cu\({}_{80}\) (in vol%). 3. The strength of GMR is affected by subsequent thermal treatments of the magnetron sputtered material. GMR is slightly larger for the Fe-Ag-system and for the Co-Ag-system after thermal treatment between 200 \({}^{\circ}\)C to 330 \({}^{\circ}\)C (depending on the chosen system) for 15 min and decreases again for even higher temperatures. For the Fe-Cu system, the maximum value was already found in the as-deposited state. 4. A reduction of the saturation field for GMR is found for annealed materials. This has to be seen in connection with reduced fields for saturating the magnetization, found in hysteresis measurements, and the dependence of GMR on the magnetized state of the material. The same reductions in magnetization saturation fields were found for annealed HPT-deformed materials [16]. Having a closer look at the Cu-Co-system, [PERSON] et al. [4] found higher GMR for magnetron sputtered Cu\({}_{81}\)Co\({}_{19}\) and Cu\({}_{72}\)Co\({}_{28}\) annealed at 484 \({}^{\circ}\)C, in comparison to the as-sputtered state. Giving an idea on the quantity of GMR in these studies: Measured at room temperature (RT) and in magnetic fields of 20 kOe, the resistance varies between 1% and 7% depending on material's composition and history. Using the same production route, [PERSON] et al.