# Magnetic Properties of Nanocomposites
## 3 Polymer Nanocomposites
### Anisotropic Magnetic Structures in Polymer Nanocomposites
As a result, each chain is characterized by a net global magnetization: the magnetic dipoles tend to align along the major axis of the ellipsoid when no field is applied and a demagnetizing field appears when the external field is applied along the ellipsoid's short axis. The anisotropic morphology of this NC is reflected in the anisotropy of its magnetic properties. For instance, the coercive field measured along directions parallel/perpendicular to the chains is shown  
Figure 5: Morphology of a magnetic chain in the Fe\({}_{3}\)O\({}_{4}\)@TiO\({}_{2}\) NC (not to scale). Within the chain, the crystal axes of magnetite NPs are randomly directed. Reprinted in modified form from the work of [41] with permission from Elsevier. in Figure 6 (top left) as a function of measurement temperature. Generally speaking, the coercive field of hysteresis loops increases with decreasing temperature, as usual; however, it also depends on the direction of the applied field. The uncertainty on the \(Hc\) values being typically less than 1 Oe, the measured differences arise from a real effect. This anisotropy is simply explained by considering the effect of the demagnetizing field. As shown in Figure 6 (top right), when the loops measured (in this case, at T = 50 K) in the parallel and perpendicular field configuration are plotted (red and blue dotted curves, respectively), they are different, with the loop taken in the parallel configuration being steeper. However, when the data taken in the perpendicular configuration are plotted against the true field \(\mathrm{H_{true}}\) = H \(-\)\(\mathrm{H_{dem}}\) = H \(-\)\(2\pi\)M(H) [41], the curve (blue full symbols) becomes almost perfectly superimposed to the one obtained in the parallel configuration, and the difference between coercive fields vanishes. In the parallel configuration, the applied field is coincident with the true field, with \(\mathrm{H_{dem}}\) being negligible in this case. Anisotropic effects are also observed in FC/ZFC curves, as shown in Figure 6 (bottom left). Here, a magnetic field of 100 Oe was applied parallel and perpendicular to the chains; the resulting FC/ZFC curves are not only different in magnitude, but also in shape, as shown by the bottom right panel of Figure 6.  
Both ZFC curves display a broad maximum before merging with the FC curves. In both measuring configurations, the ZFC curve maxima are at \(T_{max}\) = 160 K and the ZFC/FC curves merge at T\({}_{\mathrm{MERG}}\) = 250 K. In the considered sample, the curves taken in the parallel configuration (i.e., along  
Figure 6: (**Top left**): anisotropic coercive field as a function of temperature; (**top right**): hysteresis loops measured at T = 50 K. The loops are different when plotted vs. the applied field; they become coincident when plotted vs. the true field; (**bottom left**): anisotropic FC/ZFC curves (applied field: 100 Oe); (**bottom right**): reduced FC-ZFC curve differences in parallel and perpendicular field configurations. the short axis of the sample) are higher than the ones observed in the perpendicular configuration. The general features of FC/ZFC curves can only partially be explained by the spread in the NP size determined through TEM image analysis, and probably also arise from dipolar interparticle interactions. Note that the ZFC curve is closer to the corresponding FC when the field is applied perpendicular to the chains. This anisotropic behavior has been explained by a model that takes into account the role of chain shape anisotropy (a mesoscopic effect) in determining the choice of the easy axis of local crystal anisotropy (a nanoscale effect), along which the magnetization of each NP blocks on cooling in the absence of a magnetic field. Shape anisotropy, favoring dipole alignment along the major axis of the chains, is responsible for the directional dependence of the ZFC curve, which becomes closer to the corresponding FC curve when the measurement configuration is perpendicular.