# Magnetic Self-Healing Composites: Synthesis and Applications
## 2 Magnetic (Nano)Particles
### Magnetic Properties  
The magnetic properties of materials find their origin in the orbital and spin motion of electrons, and how they interact with each other. The best manner to introduce the different types of magnetism is to describe how materials respond to an external magnetic field [27]. Typically, they are classified into diamagnetic, paramagnetic, ferromagnetism, ferrimagnetic, and antiferromagnetic materials. Hysteresis loops are the most common characterization routines for studying the magnetic features of materials under the influence of an external magnetic field [27]. As shown in Figure 2, the saturation magnetization (\(M_{\mathrm{s}}\)), remanence magnetization (\(M_{\mathrm{r}}\)) and coercive field (\(H_{\mathrm{c}}\)) can be obtained from hysteresis loops. The first value corresponds to the magnetization when all the particle moments are aligned along the external applied magnetic field and is obtained by a linear fit of the high field zone of the hysteresis loop curve. The second corresponds to the residual magnetization when the applied magnetic field is removed. Finally, \(H_{\mathrm{c}}\) corresponds to the magnetic field that must be applied to cancel the sample magnetization. Magnetic (nano)particles are composed of magnetic domains, which are regions with uniform magnetization separated by domain walls and which help in reducing the magnetostatic energy. Among magnetic materials, ferromagnetic and ferrimagnetic are the most chosen systems for preparing magnetic self-healing composites since they exhibit spontaneous magnetization in the absence of a magnetic field due to the full or partial parallel alignment of their magnetic moments. If the volume of the particle is small enough, it can be composed of a single magnetic domain (see Figure 2a). Due to their small volume, single-domain particles usually present a superparamagnetic behaviour, which means that thermal energy is sufficient to spontaneously change the magnetization of the particles, leading to an absence of remanent magnetization in the absence of a magnetic field [28]. However, in the presence of a magnetic field, there will be a net statistical alignment of the magnetic moments analogous to a paramagnet but with a higher magnetic moment, which can be up to \(10^{4}\) times larger than that of an atomic paramagnet. To name some examples, superparamagnetic iron oxide nanoparticles (SPIONs) composed of Fe\({}_{3}\)O\({}_{4}\) or \(\gamma\)-Fe\({}_{2}\)O\({}_{3}\) have been widely investigated for applications in health, e.g., as magnetic resonance imaging (MRI) contrast agents, drug delivery systems or antennas for magnetic hyperthermia, due to their low toxicity and good magnetic performance [1; 2; 3; 4]. Figure 2: **(a)** A scheme showing the effects of the particle size with variations in \(H_{\mathrm{c}}\) and \(M_{\mathrm{s}}\), from small superparamagnetic nanoparticles to multidomain domain magnetic (nano)particles. (i) Nanoparticles smaller than 3 nm show superparamagnetic behaviour with \(H\mathrm{c}=0\), and moderate values of \(M_{\mathrm{s}}\) due to the large contribution of paramagnetic atoms on the particle surface. (ii, iii) As the particle size increases, longer relaxation times are observed, stabilizing the blocked state and increasing the \(H_{\mathrm{c}}\). (iv) Lastly, above the critical size for a single-domain formation, the particle is multidomain, which leads to a decrease in \(H_{\mathrm{c}}\). (b) Hysteresis loops of hard (left) and soft (right) self-healing magnetic composites at the same temperature. The saturation magnetization (\(M_{\mathrm{s}}\)), the remanence magnetization (\(M_{\mathrm{r}}\)) and the coercive field (\(H_{\mathrm{c}}\)) are indicated in grey solid spheres. The figure is reprinted under an open access Creative Commons CC BY 4.0 license [29]. Magnetic (nano)particles can also be classified as soft or hard depending on their responses to an external magnetic field [4]. Soft-magnetic (nano)particles are generally composed of iron-nickel alloys, iron-silicon alloys, soft-ferrites, etc.