# Magnetic Nanowires
## 3 Results
### Spin Caloritronics in Nanowire Networks  
A current trend is pushing the development of the next generation of thermoelectric materials to exploit spin-based transport mechanisms [91]. In this context, the coupling of thermal transport with spintronics is at the heart of the emerging field of spin caloritronics [92; 93]. Previous studies on metallic nanostructures, magnetic tunnel junctions and magnetic insulators have led to the observation of several novel physical phenomena that may differ strongly from conventional thermoelectric effects such as Seebeck spin effects [94; 95], thermally controlled spin injection [96] and thermally assisted spin transfer torque [97; 98]. However, the low conversion efficiency of the observed effects and the low power of spin caloritronic devices greatly limit the spectrum of applications. Another difficulty is the lack of experimental approaches for reliable measurements of spin caloritronic material parameters. It has recently been shown that arrays of interconnected nanowires embedded in porous polymer films provide a simple and cost-effective way to fabricate flexible spin caloritronic devices at the macroscopic scale [64; 65]. The diffusion thermopower arises from a diffusion of charge carriers opposite to the temperature gradient. It is related to the energy dependent conductivity of the material \(\sigma(\epsilon)\) by [PERSON]'s formula:  
\[S=-eL_{0}T\bigg{(}\frac{\text{d}\ln\sigma(\epsilon)}{\text{d}\epsilon}\bigg{)} \Big{|}_{\epsilon=\epsilon_{\text{F}}}, \tag{5}\]  
with \(L_{0}=2.44\times 10^{-8}\) V\({}^{2}\)K\({}^{-2}\) the Lorenz number and \(\epsilon\) the electron charge (positive). According to [PERSON]'s relation for a metal or alloy with isotropic properties, the conductivity is proportional to the density of states \(N(\epsilon)\) and to the scattering time \(\tau(\epsilon)\), where both terms are to be evaluated at the Fermi level \(\epsilon_{\text{F}}\). Because of the pronounced structure of the d-band and the high energy derivative of the density of states at the Fermi level in 3d ferromagnetic metals, large diffusion thermopowers are obtained (e.g., \(S\approx-30\) uV/K in cobalt at RT). In addition, these magnetic metals exhibit significant magnon-drag contribution to the thermoelectric power within a wide temperature range [99; 100]. Importantly, the largest RT thermoelectric power factor (PF = \(S^{2}\sigma\), with \(\sigma\) the electrical conductivity), which is the physical parameter that relates to the output power density of a thermoelectric material, is achieved for Co (PF \(\approx\) 15 mW/K\({}^{2}\)m) [101]. In multilayer stacks made of ferromagnetic (FM) metals and Cu, the Seebeck coefficient in a direction perpendicular to the layers can be calculated from the corresponding transport properties using [PERSON]'s rules [102],  
\[S_{\perp}=\frac{S_{\text{Cu}}\kappa_{\text{FM}}+\lambda S_{\text{FM}}\kappa_{ \text{Cu}}}{\lambda\kappa_{\text{Cu}}+\kappa_{\text{FM}}}, \tag{6}\]  
where \(S_{\text{FM, Cu}}\) and \(\kappa_{\text{FM, Cu}}\) represent the thermopower and the thermal conductivity of the ferromagnetic material and Cu and \(\lambda=t_{\text{FM}}/t_{\text{Cu}}\) the thickness ratio of FM and Cu layers. In metals,heat conductivity is primarily due to free electrons. Therefore, considering FM/Cu multilayers and using Wiedemann-Franz law (\(\kappa\rho=LT\) where L is the Lorenz ratio), Equation (6) simply reduces to  
\[S_{\perp}=\frac{S_{\text{Cu}}\rho_{\text{Cu}}+\lambda S_{\text{FM}}\rho_{\text{ FM}}}{\lambda\rho_{\text{FM}}+\rho_{\text{Cu}}}, \tag{7}\]  
with \(\rho_{\text{FM}}\) and \(\rho_{\text{Cu}}\) the corresponding electrical resistivities. According to Equation (7), \(S_{\perp}\) is mainly determined by the large thermopower of the FM metal in case the thickness ratio \(\lambda\) is not too small since \(S_{\text{FM}}\rho_{\text{FM}}\gg S_{\text{Cu}}\rho_{\text{Cu}}\).