Blocking Temperature
1. Superparamagnetism

For ferromagnetic or ferromagnetic materials, with small enough nanoparticles their magnetization becomes thermally fluctuated. When the time between two magnetization fluctuations (Néel relaxation time) is shorter than the time used to measure the magnetization of the nanoparticles, without external magnetic field the magnetization appears to be average zero for the nanoparticles. This is another form of magnetism, superparamagnetism [1].

Superparmagnetic materials have a high saturation magnetiszation and zero coercivity and remanence, making it to be distinguished from ferromagnetism and paramagnetism, as shown in Fig. 1[2].


Fig. 1 Magnetization hysteresis loops of different magnetic materials.

Superparamagnetism is a size effect of ferromagnetism. Figure 2 shows the influence of magnetic particle size on magnetic properties. The coercivity changes with the particle size, and at small enough size, the coercivity become zero.


Fig. 2 Size effect of particles on magnetic properties.

2. Blocking temperature

In M(T) curves we always obtained two different curves for zero-field-cooling (ZFC) and filed-cooling (FC) program for superparamagnetic materials. In ZFC curve, the moment increased with the temperature and than decreased, while the moment decreased in FC curve. The temperature at the peak point of ZFC curve is the Blocking temperature.

The Néel relaxation time mentioned above is strongly temperature dependent as generally the fluctuation of magnetizations is larger at higher temperature and smaller at lower temperature [3].

As the single domain structure, superparamagnetic materials can fluctuate randomly by thermal fluctuation at high enough temperatures just as an atom spin in paramagnetic materials. At low temperatures, the thermal energy becomes smaller and the magnetic moments become blocked. This temperature is the blocking temperature. Below blocking temperature, superparamagnetic material looses its preferred direction of magnetization in zero magnetic fields [4].

The blocking temperature should be related to:

2.1. The applied field [5]

In theory, the applied field can decrease the crystal-field anisotropy. The higher applied field, the less thermal energy is needed to overcome the barrier between the two easy axis orientation, and achiever the particles’ magnetization. Thus the blocking temperature decreased with the increase of the applied field.

In literatures it was found that the blocking temperature increased with the applied field below 3 kOe, and then decreased for further temperature increasing, as shown in Fig. 3 [6]. To explain the first stage, the blocking temperature increased with the applied field, Zheng [6] claimed that at low magnetic field, the Zeeman energy is much smaller than the thermal energy. The temperature induced net moment increase of newly relaxed larger particles, which can overcome the decrease of the superparamagnetic particles (M−1/T).  At higher magnetic field, however, M(T) decreased much slower than 1/T dependence as the larger Zeeman energy resulting large magnetic moment of the magnetic particles.



Fig. 3 Blocking temperature vs the magnetic field.

2.2. Particle size

The blocking temperature of large particles is higher than small particles, as:
[6]

Where U is the energy barrier, K is the anisotropy constant, V is the volume of the particles, H is the applied magnetic field, and is the anisotropy field. For small particles, they have small volume and thus lower energy barrier and lower blocking temperature.

The size distribution also influence the shape of the M(T) curve. Narrow peaks can be obtained for particles with narrow size distribution, while wide peaks for large size distribution.

4. References

1. http://iramis.cea.fr/Phocea/Vie_des_labos/Ast/ast_visu.php?id_ast=1278

2. http://en.wikipedia.org/wiki/Superparamagnetism

3. Martin H. Dodson and Elizabeth McClelland-Brown. Magnetic blocing temperatures of single-domain grains during slow cooling. Journal of Geophysical Research 1980, 85(5):2625-2637

4. G. F. Goya and M. P. Morales. Field dependence of blocking temperature in magnetite nanoparticles. Journal of Metastable and Nanocrystalline Materials 2004, 20-21:673-678.

 5. http://info.ifpan.edu.pl/firststep/aw-works/fsIV/voskoboynik/voskoboynik.html

6. http://arxiv.org/ftp/cond-mat/papers/0501/0501329.pdf<?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" /?>