# Magnetic Nanowires
## 3 Results
### Tunable Magnetic Anisotropy of Magnetic Nanowire Arrays  
The effective magnetic anisotropy in ensembles of parallel nanowires is determined by different contributions, namely shape anisotropy, dipolar interwire coupling, magnetocrystalline (MC) anisotropy and magnetoelastic terms. Magnetoelastic effects were found to be important only at low temperature in low porosity polymer membranes filled with Ni [16; 40] and will be neglected hereafter. Consequently, the effective anisotropy field (\(H_{\text{EF}}\)) with a uniaxial symmetry parallel to the wire axis is given by:  
\[H_{\text{EF}}=H_{\text{S}}-H_{\text{DIP}}\pm H_{\text{MC}}, \tag{2}\]  
which includes the shape anisotropy \(H_{\text{S}}=2\pi M_{\text{S}}\) for an infinite long cylinder, the dipolar coupling between the wires which lowers the magnetostatic energy and, in a mean field approximation, can be written as \(H_{\text{DIP}}=6\pi M_{\text{S}}P\)[19] (with \(P\) the packing factor of the nanowire array), as well as the possible contribution of a magneto-crystalline anisotropy \(H_{\text{MC}}\) that adds or competes with the shape anisotropy. Among the different approaches that have been used to investigate the static and dynamic properties of arrays of magnetic nanowires, ferromagnetic resonance (FMR) has proved to be a very powerful technique [19; 23; 24; 29; 32; 34; 35]. Indeed, at a given constant frequency \(f\), the ferromagnetic resonance condition when the magnetic field is applied parallel to the wires is [19]:  
\[H_{\text{R}}=\frac{f}{\gamma}-H_{\text{EF}}, \tag{3}\]  
where \(H_{\text{R}}\) is the resonance field and \(\gamma\) the gyromagnetic ratio provides a direct and precise quantification of the effective field \(H_{\text{EF}}\). Figure 6a shows typical microwave absorption curves measured on an array of 100 nm Ni nanowires (\(P\approx 27\%\)) as a function of the intensity of the static field applied parallel to the wires [19]. From these results, it can be seen that the absorption curves present an intense absorption peak which varies in position and intensity as the amplitude of the magnetic field is varied. Using porous membranes, the inter-wire spacing can be controlled over a wide range. This allows to explore the properties and dipolar interactions between the wires from the limit of isolated towards the limit of almost touching wires [19]. In Figure 6b-d, we present the dispersion relation and the corresponding hysteresis loops, measured with the magnetic field applied parallel (closed symbols) and perpendicular to the wires (open symbols) for three different Ni samples having a diameter and packing density of (b) 180 nm and 4%, (c) 100 nm and 27% and (d) 115 nm and \(>\)35%. The data were compared to the calculated ones for isolated wires, shown as solid lines. For low packing densities, the measured resonance frequencies in the saturated states agree well with the values expected for an array of isolated wires, see Figure 6b. At higher wire density for both field directions, the measured frequencies are almost identical, as shown in Figure 6c. In addition, above a critical value of the packing (estimated around 33% for an ordered nanowire array), there is a tilt of the easy axis of magnetization between directions parallel to perpendicular to the wire axis, as shown in Figure 6d. Therefore, by increasing the density of the NW array, it is possible to modulate the effective magnetic anisotropy, from the case of isolated wires with the easy axis parallel to the wires to dense NW arrays in which the easy axis is perpendicular to the wires, passing through the particular case of quasi-isotropic magnetic systems. The observed deviations from the frequency-field dispersion curves calculated in weak field conditions are due to the fact that the system is no longer single-domain. A control of the effective magnetic anisotropy can be achieved not only by changing the packing factor nanowire arrays but also by tailoring the magnetocrystalline anisotropy, as demonstrated for Co [24; 29] and CoPt [28] nanowire systems.