Similar 53-54 The superparamagnetism appears when the

Similar to ferroelectric materials, the spatial regions in bulk magnetic materials in which the spins are aligned parallel to each other are known as magnetic domains. MNPs can be categorized into two general groups: single and multi-domain particles. The domain walls form due to the energy competition between magnetostatic energy, depending on the size of nanoparticles, and the domain wall energy depending on the inter-domain areas. This means that a new domain wall forms when the cost of the magnetostatic energy is larger than the domain wall formation. Therefore, the bigger the particle size, the higher the chance to form further domain walls. On the other hand, when the particle size drops below a certain limit, the energy of the formation of a new domain walls will be higher than the magnetostatic energy of a single domain-particle and thus being single-domain is energetically more favorable.
The dependence of the coercivity HC on the particle size is depicted in Figure 2.11 a. When the particle size is below so-called superparamagnetic size (rSPM) there is no HC. By further increasing the size of particles, HC starts to appear and increases by increasing particle size and at specific particle size (rS) it reduces. Different magnetization responses (HC) originate from the fact that a much higher energy is required to homogeneously rotate the spins in single domains than in multi-domains due to the presence of domain walls (as depicted in Figure 2.11 b).43, 53-54
The superparamagnetism appears when the anisotropy energy barrier EB can be overtaken by thermal fluctuations and consequently its condition is given by: