# Magnetic Nanowires
## 3 Results
### Spin Caloritronics in Nanowire Networks
Measurements of magnetoresistance and thermoelectric power were performed as a function of temperature and chromium content in these diluted alloys. The changes in sign observed in the Seebeck coefficient and in the anisotropic magnetoresistance were related to significant changes in the density of the for the majority spin electrons. The evolution of the MR ratio with respect to the Cr content for NiCr NW networks is shown in Figure 15a at RT and \(T=100\) K. For all samples, positive values are found at RT, showing a rapid decrease in MR with the increasing Cr concentration. In contrast, the negative MR ratio was measured at \(T=100\) K for the NiCr sample with 4 and 7 at.% of Cr. The inset in Figure 15a shows that the MR ratio of the Ni\({}_{66}\)Cr\({}_{4}\) NW sample gradually increases from its negative value at low temperature to positive values for \(T>150\) K. In contrast, CoCr alloy NWs display negative AMR at RT for a Cr concentration \(\geq 3\) at. %. Negative values are also obtained at \(T=100\) K for all CoCr NW samples, and the absolute values for MR at low temperatures are almost independent of the alloy content even for a Cr concentration as small as \(\sim 1\)at.%. The inset of Figure 15b shows the gradual change in the sign of MR(\(T\)) for the sample with the lower Cr concentration (Co\({}_{99}\)Cr\({}_{1}\)). Overall, our experiments performed on both NiCr and CoCr alloy NW networks are in qualitatively good agreement with the model predictions of [PERSON], [PERSON], and [PERSON] [111; 112]. In this simplified model, the sign of the AMR ratio has been tentatively linked to the value of the spin asymmetry coefficient \(\alpha=\rho_{\downarrow}/\rho_{\uparrow}\) in the alloy through a model based on a spin-orbit mechanism. The model predicts that at low temperatures, the AMR is proportional to the quantity \(\alpha-1\), and so a negative AMR ratio is expected when electronic conduction is dominated by minority spin electrons, as expected for dilute NiCr and CoCr alloys. Moreover, the experimental results obtained at low temperature on CoCr NWs follow the prediction of MR being independent of the impurity concentration, as shown in Figure 15b. The influence of the impurity concentration on the thermoelectric power has been also investigated. Figure 15c,d show the variation of the Seebeck coefficient with the Cr content at some selected temperatures in the absence of any external magnetic field. As shown in Figure 15c, the thermopower of NiCr suddenly changes sign from negative to relatively large positive values with the addition of Cr impurities in Ni. The RT Seebeck coefficient goes from \(-20\)\(\mu\)V/K to about \(+17.5\)\(\mu\)V/K for the NiCr alloys with 7 at.% of Cr. Similar changes in thermopower sign have been reported in bulk NiCr alloys where minority spin  
Figure 14: (**a**) the two-current model for the resistivity and the thermopower considering both parallel (P) and antiparallel (AP) magnetic configurations; (**b**) measured Seebeck coefficients at zero applied field \(S_{\rm AP}\) (blue circles) and at saturating magnetic field \(S_{\rm P}\) (red circles) of a CoNi/Cu NW network 80 nm in diameter and 3% packing density, along with the corresponding calculated \(S_{\uparrow}\) (orange circles) and \(S_{\downarrow}\) (violet circles) from Equations (11) and (12) (from [64]). dominates the electrical conduction [107; 108; 113]. The sign inversion of the Seebeck coefficient from negative to positive in dilute NiCr alloys could also be explained on the basis of a virtual bound state passing through the Fermi level in the spin up band [107; 108]. In contrast, the sign of the Seebeck coefficient does not change for any value of Cr concentration for CoCr NW networks (see Figure 15d). The RT thermopower drops rapidly from \(-28\)\(\upmu\)V/K for pure Co to much smaller negative values approaching \(-5\)\(\upmu\)V/K for Co\({}_{95}\)Cr\({}_{5}\) NWs. The CoCr NW samples are found to exhibit the same features at lower temperatures, as also shown in Figure 15d.