# Magnetic Properties of Nanocomposites
## 2 A Survey of Magnetic Measurements and Typical Magnetic Parameters of Nanocomposite Systems
### Typical Magnetic Parameters and Quantities in Nanoparticle Systems  
_(i) Magnetic anisotropy: crystal._ In real ferromagnetic materials, the experimental evidence typically indicates a directional dependence of the magnetic response on an applied field. This phenomenon, corresponding to a directional preference for the magnetization vector, is known as the _magnetic anisotropy_. Magnetic materials display various types of anisotropies, the most important being _crystal anisotropy_. This anisotropy, determined by crystal structure and having an entirely intrinsic nature, results in a variation of the magnetic properties of the material with respect to a specific crystallographic orientation. The crystallographic axes along which the magnetization is oriented are called _easy axes_ and a state of minimum energy exists when the magnetization vector lies along one of the preferred orientations. If, by application of a magnetic field, the magnetization vector is turned away from this position, work must be done against the anisotropy forces that tend to hold the vector aligned to the easy direction. Crystal anisotropy plays an important role in single crystals and in magnetic NPs, which are typically characterized by a well-defined crystal structure (at least in their core). _(ii) Magnetic anisotropy: shape_. If a ferromagnetic sample is not perfectly spherical, then one or more specific directions become easy magnetization axes solely because of the sample shape. This phenomenon, related to magnetostatic energy, is known as _shape anisotropy_. In an ellipsoidal sample, the demagnetizing field is stronger along a short axis than along a long axis. Therefore, an external field applied along the short axis has to be stronger to produce the same true field inside the specimen than if applied along the long axis. Therefore, shape alone can be a source of magnetic anisotropy. Shape anisotropy plays a central role in magnetic NPs, where it can be comparable in strength to crystal anisotropy. In granular systems, shape anisotropy plays a role both at the level of single NPs (if the particles are not perfectly spherical) or in the presence of strong NP aggregation, when the aggregates take an elongated/ellipsoidal shape in the sample. Often, in NP systems including nanocomposites, a central role is played by the so-called _effective anisotropy Kff_, which encompasses crystal, shape, and surface anisotropy in a single parameter. _Surface anisotropy_ is an additional term, negligible in macroscopic ferromagnetic bodies, which emerges because of the break of lattice periodicity at and around the NP surface. Typically, FC/ZFC curves (see Section 2.1) give information about Kff. _(iii) DC magnetic parameters_. Isothermal magnetization loops are the typical outcome of dc magnetic measurements (see Section 2.1). Here, the important parameters of the hysteresis loop are briefly highlighted. If a previously demagnetized ferromagnetic body is submitted to a very strong magnetic field along one direction, it will eventually reach the positive _magnetic saturation M\({}_{s}\)_ under sufficiently large fields. This corresponds to having all magnetic moments oriented along the field direction. If the field is removed, the material in general will no longer reach the point (0,0) in the \(H\),\(M\) plane. Instead, it will reach a point (0,\(M_{R}\)) on the vertical axis, with \(M_{R}\) being the magnetization that \"remains\" in the material (positive _remanent magnetization_ or _magnetic remanence_). In order to reach the condition \(M=0\), a magnetic field must be applied in the opposite (negative) direction. The point (\(-H_{C}\), 0) on the horizontal axis represents the negative _coercive field_ or _coercivity_ of the material. If the negative \(H\) is further increased in magnitude, the negative magnetic saturation is eventually reached.