Néel relaxation theory
Néel relaxation theory is a theory developed by Louis Néel in 1949 to explain time-dependent magnetic phenomena known as magnetic viscosity. It is also called Néel-Arrhenius theory, after the Arrhenius equation, and Néel-Brown theory after a more rigorous derivation by William Fuller Brown, Jr. Néel used his theory to develop a model of thermoremanent magnetization in single-domain ferromagnetic minerals that explained how these minerals could reliably record the geomagnetic field. He also modeled frequency-dependent susceptibility and alternating field demagnetization.
Superparamagnetism occurs in ferromagnetic and ferrimagnetic nanoparticles which are single-domain, i.e. composed of a single magnetic domain. This is possible when their diameter is below 3–50 nm, depending on the materials. In this condition, it is considered that the magnetization of the nanoparticles is a single giant magnetic moment, sum of all the individual magnetic moments carried by the atoms of the nanoparticle. This is what people working in the field of superparamagnetism call the “macro-spin approximation”.
Because of the nanoparticle’s magnetic anisotropy, the magnetic moment has usually only two stable orientations antiparallel to each other, separated by an energy barrier. The stable orientations define the magnetic easy axis of the nanoparticle. At finite temperature, there is a finite probability for the magnetization to flip and reverse its direction. The mean time between two flips is called the Néel relaxation time τN and is given by the Néel-Arrhenius equation:
where KV is the height of the energy barrier, a product of the magnetic anisotropy energy density K and volume V; kB is the Boltzmann constant, T the temperature and their product the thermal energy; and τ0 is a length of time, characteristic of the material, called the attempt time or attempt period (its reciprocal is called the attempt frequency). Typical values for τ0 are between 10−9 and 10−10 seconds.
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