# Magnetic Nanowires
## 3 Results
### Spin Transport in Multilayered Nanowires  
Multilayered nanowires are ideal structures to investigate the giant magnetoresistance (GMR) and its temperature dependence in the Current Perpendicular to the layer Plane (CPP) geometry. The first measurements were performed in 1994 on Co/Cu nanowires by [PERSON] et al. [10], [PERSON] et al. [77] and [PERSON] et al. [78]. Nanowire systems have key advantages over conventional magnetic multilayers made by vacuum deposition. Firstly, the electrodeposition method into porous templates is much more convenient than vacuum deposition techniques for making multilayers with layer thicknesses close to the micron without degrading the quality of the interfaces. As a result, measurements on nanowires have been very useful to study the regime with layer thicknesses above the spin diffusion length (SDL), to test the theoretical predictions in this regime and to determine the SDL of various materials. Secondly, most of the measurements in CPP geometry on planar multilayers were performed with superconducting niobium contacts. Such measurements are therefore limited to the helium temperature range. On the other hand, measurements on nanowire systems can be carried out up to the ambient temperature, which has made it possible to study the temperature dependence of CPP-GMR [79]. Third, a high aspect ratio of the multilayered nanowires leads to large signals and precise measurements. Up to now, most measurements have been performed on Co/Cu, CoNi/Cu, Py/Cu systems and FeCoNi/Cu [10; 11; 77; 78; 79; 80; 81; 82; 83]. In Figure 9a, we show an example of CPP-GMR curves obtained for a Py/Cu multilayered nanowires sample. The MR ratio reaches 67% at 77 K and 71% at 4.2 K. Another example of experimental results for Co/Cu nanowires is also shown in Figure 9a. In both cases, the thickness of each FM/Cu bilayers is about 15 nm. Most measurements on multilayered nanowires have been analyzed using the Valet-Fert model [84; 85]. This model takes into account the important effects due to the spin accumulation occurring at the interfaces when the conduction in the ferromagnetic layers is spin dependent. In addition to the usual relaxation term for the momentum, the Boltzmann equation of the Valet-Fert model also includes a spin-lattice relaxation term describing the relaxation of spin accumulation by spin-flip scattering. In the case of multilayers with thick ferromagnetic layers, the GMR contribution  
Figure 8: Hysteresis loops measured at 300 K in arrays of Co\({}_{047}\)Pt\({}_{53}\) nanowires with the field applied parallel (solid line) and perpendicular (dashed line) to the wires. (**a**) As-deposited sample and (**b**) annealed sample at 700 \({}^{\circ}\)C. Note the different magnetic field scales in (**a**) and (**b**) (from [28]). Figure adapted from ref. [28] with permission of the author. from bulk scattering dominates that from interface scattering. For FM/Cu multilayers, if FM layers are thicker than the spin diffusion length in FM, and Cu layer much thinner than the one in Cu, the CPP-GMR ratio can be expressed as [5]:  
\[\frac{\Delta R}{R_{\text{P}}}=\frac{2p\beta^{2}\ell_{\text{sf}}^{\text{FM}}}{(1- \beta^{2})t_{\text{FM}}} \tag{4}\]  
with \(\Delta R=R_{\text{AP}}-R_{\text{P}}\) (\(R_{\text{AP}}\) and \(R_{\text{P}}\) are the corresponding resistances for antiparallel and parallel arrangements, respectively), \(\beta\) the bulk scattering spin asymmetry coefficient (\(\beta=(\rho_{\downarrow}-\rho_{\uparrow})/(\rho_{\downarrow}+\rho_{\uparrow})\)), \(\ell_{\text{sf}}^{\text{FM}}\) the spin diffusion length in the FM material, \(t_{\text{FM}}\) the thickness of the FM layers and \(p\) the proportion of antiparallel orientations of the magnetization in consecutive magnetic layers. The spin asymmetry coefficients are usually determined from analysis of the experimental results in the long SDL limit (\(t_{\text{FM}}<<\ell_{\text{sf}}^{\text{FM}}\), \(t_{\text{Cu}}<<\ell_{\text{sf}}^{\text{Cu}}\)). Typical values are \(\beta=0.35\)-\(0.5\) for Co and \(\beta=0.7\)-\(0.8\) for Py.