*4.2. Dependence of Magneto-Resistive Properties on Processing and Composition*

The result of coercive field measurement from SQUID magnetometry shows a slightly increased coercivity for CuCo of about equiatomic composition, when compared to reference [40]. Therein, the powder compacted and room temperature HPT-deformed samples were measured with SQUID at 300 K and for the variety of compositions between Cu-28 wt % Co and Cu-67 wt % Co, coercive fields of ~70 Oe ranging down to ~0 Oe, below the resolution limit of SQUID magnetometry, were determined.

As described earlier, there is a variety of methods to produce thin film or bulk materials, showing a GMR. Depending on the production route, yielding different microstructures and particle size distribution—GMR is thus not only depending on the material's composition. In case the material is fully supersatured (e.g., a minor ferromagnetic element is fully dissolved in the matrix) and no ferromagnetic particles can be found, GMR is inexistent. For precipitating ferromagnetic particles, GMR will start to rise up to a maximum value. For further growing ferromagnetic particles, GMR will decrease as the particle size are too large to form single magnetic domain particles and the particle number becomes too small to be efficient scattering sites. The dependence of the strength of GMR on the size distribution is described in reference [54].

Depending on the production route, the material might not be in the state yielding the highest GMR-effect right after processing. Very often, proper thermal treatments lead to an increase of the effect. After the production of bulk materials showing granular GMR, Ikeda et al. [20] found the maximum GMR ratio (6.4%, room temperature) for ball milled Cu80Co20 annealed at 450 ◦C for 1 h in vacuum. Nagamine et al. [22] report 4% (room temperature) for ball milled (Co0.7Fe0.3)20Cu80, which was annealed for 15 min at 500 ◦C. For the as-milled powder they found a negligible effect (<0.2%), due to the almost perfect supersaturation of Fe and Co in Cu. Champion et al. [21] found a value of ~4% at 4.2 K for Cu60Co40 and Cu50Co50 (both in vol%) for ball milled materials. For an as-deposited, magnetron sputtered CuCo thin film, a negligible GMR at room temperature, most likely as a result of an almost perfect supersaturated state was found [3]. Comparing with our results, it is evident that the incomplete supersaturation of Cu with Co improves the GMR effect at room temperature – considering

as-prepared samples. With a short annealing of the Cu81Co19 thin film [3] (10 min at 484 ◦C) the GMR substantially increased. Upon annealing, an increase in GMR from negligibility at room temperature to ~22% at 10 K was found.

For a granular system, the GMR might also get as large as ~50% as reported for multilayer FeCr systems at 4.2 K [1]: For another type of binary alloys, Ag80Co20 thin films, Xiong et al. [7] report on values as large as 84% (They normalize the change in resistivity to the resistance at high fields, which is different to Equation (1).) at 4.2 K for sputtered and subsequently annealed (330 ◦C for 10 min) specimens. Values for GMR of granular systems presented in studies on CuCo-systems are in close agreement with the values reported here. Improved thermo-mechanical treatment during HPT-processing or subsequent annealing of the as-deformed sample should lead to a closure of this small gap. Here, only HPT-processed states have been investigated and will be discussed.

In the following, the different behaviors of magneto-resistive curves shall be discussed with respect to the Co-content of the samples. Coming back to Figure 9: Starting with low ferromagnetic contents (Cu81Co19, Cu64Co36, Cu85Fe15) the dependence of the resistance with applied magnetic field is almost linear and isotropic. The effect is high for Cu81Co19 with an GMR of close to 2% for the highest applied field. No saturation in resistance drop could have been achieved even for the highest magnetic fields of 22.5 kOe. Replacing Co by Fe leads to a decrease in GMR. Through the use of SQUID magnetometry, it was shown in reference [40] that low-Fe containing CuFe composites, processed the same way as described in this work, do not saturate in magnetization even in very high fields of 70 kOe. The CuFe samples with a low Fe-content show a very pronounced paramagnetic behavior. This is explainable by a better dilution of Fe in Cu. Using GMR data from Figures 9 and 10 and comparing the GMR curves for Cu85Fe15 and Cu81Co19, which are almost identical in ferromagnetic composition, the same conclusion of an increased dilution of Fe in Cu compared to Co in Cu can be drawn.

For increasing Co content, approaching about equiatomic composition, the GMR curves for perpendicular and parallel current alignment start to differ from each other, with the curve for parallel alignment being higher. One reason could be a non-perfect globular shape of the particles. Scattering occurs at the nonmagnetic—Ferromagnetic interfaces; thus, a change in the cross-sectional area for different current flow directions could lead to a change in scattering behavior for cigar- or pancake-shaped particles. However, the specimen for probing the GMR for the large Cu55Co45 sample was not taken out the same way as for the smaller HPT-samples. At the same time, the current flow was in the tangential-radial plane (along a secant) for all small specimens, the current flow was in axial direction for the Cu55Co45 specimen. The same qualitative behavior of GMR in differently orientated specimens seems to rule out the particle shape anisotropy as an explanation for the non-perfect isotropic GMR. Another explanation for this might be the existence of large Co-particle or large percolating domains of a Co-rich phase, as these are likely to contain multiple domains. As stated in reference [10], multi-domain particles do not contribute to the GMR and as a result, a superposition of GMR and AMR occurs.

For the equiatomic composition, it was shown that deforming the sample at 200 ◦C leads to increased GMR compared to room temperature processing. The drop in resistivity is even higher for slightly increased process temperature and strongly reduced strain rate. Using the large HPT-tool provides temperature and time and a lower strain rate, for small Co particles to develop. According to Equation (1), an increase in GMR may as well originate from a decreased overall resistivity of the specimen—as can be expected from subsequent annealing processes but also from higher processing temperatures. The measured resistances of the specimen bear a large source for errors as the geometry is of high importance and the production of perfectly prismatic specimens is difficult. Thus, just rough values but more importantly the sequence of measured resistivities shall be given: The room temperature deformed Cu52Co48 has the highest specific resistivity (~0.52 Ω mm2 m<sup>−</sup>1), followed by Cu55Co45 (~0.18 Ω mm2 m<sup>−</sup>1) and finally Cu49Co51 (~0.13 Ω mm<sup>2</sup> m<sup>−</sup>1). The specific resistivities were calculated, taking into account the individual specimen sizes of ~ 5 mm × 1 mm × 0.2 mm. It can be stated that the higher GMR effect for Cu55Co45 is not due to the same amount of GMR sitting atop

of a smaller quantity (residual resistivity) but is truly due to a change in GMR (i.e., Co-segregation behavior), which is a consequence of changing process parameters.

SQUID measurements (Figure 11) show that the magnetization is almost fully saturated in fields of about 20 kOe and thus the approach of drawing the change in resistivity versus relative magnetization according to reference [4] can be followed. A quadratic fit of relative resistivity drop as a function of M/Ms (Figure 13) yields a proportional constant A of −0.031. This value is lower than the one stated in reference [4], who used magnetron sputtered Cu84Co16, resulting in a value of −0.065 at a temperature of 5 K. The shape of the two MR-curves for this composition (Figure 9c) can be explained by a parallel connection of varistor-like components as shown in Figure 13b). On the one hand, there is conduction in the Cu phase, where small Co particles can be found. On the other hand, there is conduction in the partially percolating Co-phase, which gives rise to an anisotropic behavior. Both pathways have individual dependencies on the direction of applied magnetic field. The strength of both resistive branches determines the sign and magnitude of the proportional constant A.

With further increasing Co content, the fraction of AMR becomes more pronounced but still a markedly high drop in parallel alignment can be seen. For pure Co, the difference between both types of about 1% matches the value given by McGuire and Potter [55] of 1.9%. The difference might be explained by the overall higher resistivity of HPT-deformed, nanocrystalline Co, reducing the relative fraction of the AMR regarding total resistivity.

For pure Cu, no change in resistivity with applied magnetic field has been found within the accuracy of the used measurement setup.

The number of parameters influencing the microstructure and – as a consequence – the magneto-resistive properties is very large. Although this study is very detailed, it is not complete and leaves plenty of ideas for further investigations. In future, further interesting tasks shall be tackled: (i) Larger GMR effects will be investigated by measuring the most promising samples at cryogenic temperatures. (ii) The influence of subsequent thermal treatments of the as-HPT-deformed materials on the microstructure as well as on magneto-resistivity will be investigated.

**Figure 13.** (**a**) Quadratic fit of room temperature GMR data for Cu55Co45 in accordance with reference [4]. (**b**) Schematic representation of electron conduction channels in case of Cu55Co45, consisting of Cu, containing Co-particles on the one side and Co enriched, percolating areas on the other side.

### **5. Conclusions**

The influence of the SPD conditions such as deformation temperature and strain rate on the microstructural evolution and the magneto-resistive response of different combinations of ferromagnetic and diamagnetic elements has been investigated and the following conclusions can be drawn:

It has been shown that not only the processing temperature but also the strain rate is a very important parameter regarding the deformation behavior and microstructural evolution of composite materials. The strain rate influences, in combination with the applied (or naturally evolving) temperature, the diffusion, segregation, and dissolution mechanisms taking place during severe

plastic deformation. As a result, SPD by HPT is a versatile tool for achieving different microstructural states and particle sizes, respectively, when the process parameters are chosen wisely.

Depending on the ferromagnetic content of the HPT-deformed materials, different behaviors regarding magneto-resistivity at room temperature develop. When there is a small ferromagnetic content, isotropic magneto-resistive behavior (GMR) can be found. The highest drop in resistivity that could be measured within the available magnetic field was found for an approximately equiatomic composition of Cu and Co. This sample was deformed at elevated temperatures and—in respect to typical HPT-deformation processes—at a small strain rate. For medium and high Co-content, the characteristics of magneto-resistance show the occurrence of both GMR and AMR.

The investigations of GMR in connection with HPT-deformed materials are interlinked: On the one side, it is possible to first adjust the occurrence of particles and then adjust the particle size distribution. This can be done by first changing all of the material's composition and then by changing the HPT-process parameters such as deformation temperature and strain rate. On the other side, GMR-measurements are a versatile tool to study the as-deformed (and annealed) microstructures regarding the distribution of ferromagnetic particles, thereby gaining deeper insights on the deformation and segregation mechanisms acting during high pressure torsion.

**Author Contributions:** Conceptualization, S.W., R.P. and A.B.; methodology, S.W. and A.B.; software, S.W.; validation, S.W.; formal analysis, S.W.; investigation, S.W., M.S., L.W., P.K., H.K.; resources, P.K., H.K., R.P., A.B.; data curation, S.W.; writing—original draft preparation, S.W.; writing—review and editing, S.W., L.W., M.S., H.K., P.K, R.P., A.B.; visualization, S.W., M.S.; supervision, A.B.; project administration, A.B.; funding acquisition, A.B.

**Funding:** This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (Grant No. 757333).

**Acknowledgments:** The authors are in deep gratitude to Roland Grössinger, who passed away in 2018. He always was a source of fruitful and supportive discussion and he arranged the transfer of parts of the used equipment from the Technical University of Vienna to the Erich Schmid Insitute of Materials Science. Without him, these investigations of severely deformed materials would not have been possible. The measurements leading to some of the results presented here, have been performed at PETRA III P07 at DESY Hamburg (Germany), a member of the Helmholtz Association. The authors thank of the assistance of Norbert Schell and Karoline Kormout, Stefan Zeiler, Florian Spieckermann, Pradipta Gosh and Niraj Chawake for helping with synchrotron measurements and analysis. S.W. deeply appreciates the help of Christoph Gammer for performing the TEM analysis, Mirjam Spuller and Alexander Paulischin for performing the GMR specimen preparation and assistance in resistance measurements.

**Conflicts of Interest:** The authors declare no conflict of interest.
