# Magnetic Nanowires
## 3 Results  
### Magnetization Reversal Processes in Magnetic Nanowires  
Anisotropic magnetoresistance (AMR) arising from the relativistic spin-orbit coupling is a powerful tool for studying the magnetization reversal in magnetic nanowires. AMR is related to the dependence of the resistance on the angle between the magnetization of the ferromagnet and the electrical current direction. The change in resistance between current parallel and perpendicular to magnetization is often less than a few percent. However, as a high accuracy in the electrical resistance measurement can be obtained, AMR was used to investigate the reversal of magnetization of magnetic nanowires at different temperatures [17; 73] and quantitative analysis of the results was conducted using classical models describing magnetization reversal. The magnetoresistive curve \(R(H)\) is related to the magnetization \(M(H)\) by  
\[R(H)=R_{0}+(\Delta R)_{\text{max}}\frac{M(H)}{M_{\text{s}}}, \tag{1}\]  
where \(M(H)=M_{\text{s}}\cos[\varphi(H)]\) is uniform and measured along the wire axis, \(M_{\text{s}}\) is the saturation magnetization and \(\varphi\) is the angle between the applied field and the current (which is along the wire axis). In Equation (1), the quantity \((\Delta R)_{\text{max}}/R_{0}\) defines the AMR ratio. Figure 5a shows the magnetoresistive hysteresis loops obtained at room temperature on a single 75 nm Ni nanowire for the angles \(\varphi=10^{\circ}\) and \(\varphi=75^{\circ}\). Low density Ni nanowire arrays constitute an attractive model system in which the magnetization easy axis is simply determined by shape anisotropy. As shown in Figure 5a, the AMR curves are composed of continuous variations of the resistance corresponding to a reversible rotation of the magnetization and of discontinuous jumps of resistivity at  
Figure 5: (**a**) AMR characteristics at 300 K of a single 75 nm Ni nanowire for 2 angles between the wire axis and magnetic field direction. Inset: zoom of R(T) at low fields (from [17]); (**b**) nucleation field \(H_{\text{n}}\) at 300 K vs. the angle between wire axis and field direction for a single 75 nm Ni wire (from [17]). Dashed line: expected nucleation field for an infinite cylinder 75 nm in diameter (curling reversal mode). Solid line: expected nucleation field for a volume of aspect ratio 4.3:1 (curling reversal mode). Figure adapted from ref. [17] with permission of the author. fields corresponding to magnetization reversal. It involves processes such as nucleation of small reversed domains at the end of the wire, before their possible expansion through domain-wall motion [14]. The jumps in AMR curves refer to successive pinning and depinning of the domain wall. The inset of Figure 5a shows a zoom in the region where the discontinuity occurs. Two resistance jumps appear for two field values that are close to each other. The first one refers to the nucleation of the magnetization reversal and propagation of a domain wall until it is trapped at a pinning center due to the presence of structural defects. The domain wall is evacuated when the external magnetic field reaches a higher field (giving rise to a second jump) where the magnetization of the wire is completely reversed. The nucleation field was measured on individual nanowires as a function of the angle between the applied field and the wire axis. The results were then compared with predictions of the micromagnetic theories. Figure 5b shows the dependence of the nucleation field Hn with the angle \(\varphi\) for the 75 nm-Ni nanowire. The angular dependence of the nucleation field is consistent with a process controlled by a curling rotational mode [14]. The results show that the magnetization switching is initiated by reversal inside some nucleation volume much smaller than the total volume of the nanowire [17; 73]. For Ni nanowires, the measurements of the nucleation field as a function of temperature evidence an extra uniaxial anisotropy adding to shape anisotropy at low temperatures.