2 Size effects in nanomagnets

The finite size effects could yield a modification of the magnetic properties of the system, when one of its dimensions becomes comparable to the exchange correlation length of the system. The most important finite size effects in nanoparticles are the single domain limit and the super-paramagnetic limit.

The macroscopic materials can present a null net magnetization in the absence of applied magnetic field, inclusive if the material is ferromagnetic, it is due to the fact that when the system size is above a certain value, the division of the system into magnetic domains is energetically favorable. If the size of the system is under a certain cutoff, denominated single domain radius ($R_{sd}$), the system prefers a mono-domain state. This phenomenon was initially predicted by Frenkel and Doefman [17]. The single domain radius depends on the magnetic parameters of the system (exchange parameter, saturation magnetization, anisotropy constant) and typically lies in the range of a few tens of nanometers.

If the size of the system continues to decrease then the nanoparticle becomes super-paramagnetic (SP), due to thermal fluctuations and the reduction of the energy barrier of the system. In this state a magnetic particle presents a large magnetic moment and behaves like a giant paramagnetic moment with a fast response to an applied magnetic field and negligible coercivity and remanence.

Thermal measurements have become an important part of the characterization of magnetic nanoparticles systems. Often these measurements include a complex influence of interparticle interactions. However, in other cases, measurements on dilute systems can provide information on individual particles. The results show that even in these cases the extracted information is not always consistent with the approximation picturing the particle as a macroscopic magnetic moment, and this is usually attributed to surface effects.

If the nanoparticle size decreases more, the surface effects start to play a important role and deviations from the collinear spin arrangement appear. When the magnetic properties of magnetic nanoparticles are dominated by the surface effects, the ideal model of a macro-spin formed by all the spins of the particle pointing in the direction of the anisotropy easy axis could be no more valid. The schematic representation of the size effects in nanoparticles is presented in Fig. 1.2.

Figure 1.2: Schematic representation of the dependence of the magnetic behavior of the nanoparticle on its diameter.

Finite size effects also have important consequences in the magnetization behavior of thin films. Indeed, when the film thickness is smaller than the exchange correlation length, the magnetization is homogeneous through the thin film thickness. In these conditions the magnetostatic interactions tend to place the magnetization in-plane competing with the surface anisotropy effects.