The typical time between two flips is called the Néel relaxation time. In the absence of external applied magnetic field and when the time used to measure the magnetization of the nanoparticles is much longer than the Néel relaxation time, their magnetization appears to be in average zero: they are said to be in the superparamagnetic state. In this state, an external magnetic field is able to magnetize the nanoparticles and saturate the magnetization. Hence, their magnetic susceptibility is much larger than the paramagnets.
Superparamagnetism is characterized by two experimental features: there is no area under the hysteresis loop in the field dependence of the magnetization (M - H is a single-valued curve at a given temperature) and M is a universal function of H/T. Superparamagnetism can be destroyed by cooling, since the characteristic fluctuation time for a particle's moment varies exponentially with temperature as shown below,
where Ku is the magnetocrystalline anisotropy energy, V is the volume of the particle, kB is the Boltzmann constant, T is the temperature, so the magnetization appears to switch sharply to a stable state as the temperature is reduced. The temperature at which this occurs is called the blocking temperature (TB), and it depends linearly on the sample's volume and on the magnitude of the magnetocrystalline anisotropy. The superparamagnetic blocking temperature (TB) is defined as the temperature at which the superparamagnetic relaxation time equals the timescale of the experimental technique used for the study of the magnetic properties. Below TB, superparamagnetic relaxation can be considered negligible, but the magnetization direction may still fluctuate in directions close to the easy axes at θ = 0 ° and θ = 180 °. These fluctuations have been termed 'collective magnetic excitations' [5]. The magnetic excitations in a nanoparticle are illustrated schematically in Figure 1.8.
Figure 1.8: Schematic illustration of magnetic fluctuations in a nanoparticle. At low temperatures the direction of the magnetization vector M fluctuates near one of the easy directions (collective magnetic excitations). At higher temperatures the thermal energy can be comparable to the height, KV, of the energy barrier separating the easy directions, and the magnetization can fluctuate between the easy directions (superparamagnetic relaxation). θ is the angle between easy axis and magnetization direction.
The magnetic dynamics well below the Curie or Neel temperature in both bulk materials and nanoparticles can be described by excitation of spin waves, but the spin wave spectrum of small particles is size-dependent and this can have a substantial influence on the temperature dependence of the magnetization in nanoparticles.
References:
[1]. M.N. Baibich, et al, Phys. Rev. Lett. 61 (1988) 2472.
[2]. G. Binash, P. Grünberg, F. Saurenbach, W. Zinn, Phys. Rev., B 39 (1989) 4828.
[3]. F. Mott, Proc. Roy. Soc. A 153 (1936) 699.
[4]. A. Fert, I.A. Campbell, Phys. Rev. Lett. 21 (1968) 1190; B. Loegel, et al, J. Phys. Chem. Sol. 32 (1971) 2723; A. Fert, et al, J. Physique 32 (1971) C1; A. Fert, I.A. Campbell, J. Phys. F 6 (1976) 849.
[5]. S. Morup, J. Magn. Magn. Mater. 37 (1983) 39
Quiz 1:
(Q1.1). Which is the first device that proved the utilization of spin degree of freedom in spintronics?
(Q1.2). What is the magnetic parameter used to distinguish between diamagnetism and paramagnetism?
(Q1.3). Name few examples for typical diamagnetic material?
(Q1.4). Which law decribes the temperature dependent magnetic susceptbility of a paramagnetic material?
(Q1.5). Are the hysteresis and hystersis parameters intrinsic property of a magnetic material?
(Q1.6). Are the residual magnetism and retentivity of a ferromagnetic material represent the same properties?
(Q1.7). What are the typical experimental features of a material having superparamagentism?