Néel relaxation theory is a theory developed by
Louis Néel
Louis Eugène Félix Néel (; 22 November 1904 – 17 November 2000) was a French physicist born in Lyon who received the Nobel Prize for Physics in 1970 for his studies of the magnetic properties of solids.
Biography
Néel studied at the Lyc ...
in 1949
to explain time-dependent magnetic phenomena known as ''magnetic viscosity''. It is also called ''Néel-Arrhenius theory'', after the
Arrhenius equation
In physical chemistry, the Arrhenius equation is a formula for the temperature dependence of reaction rates. The equation was proposed by Svante Arrhenius in 1889, based on the work of Dutch chemist Jacobus Henricus van 't Hoff who had noted in 188 ...
, 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 When an igneous rock cools, it acquires a thermoremanent magnetization (TRM) from the Earth's field. TRM can be much larger than it would be if exposed to the same field at room temperature (see isothermal remanence). This remanence can also be ver ...
in
single-domain ferromagnetic minerals that explained how these minerals could reliably record the
geomagnetic field
Earth's magnetic field, also known as the geomagnetic field, is the magnetic field that extends from Earth's interior out into space, where it interacts with the solar wind, a stream of charged particles emanating from the Sun. The magne ...
. He also modeled frequency-dependent
susceptibility and alternating field demagnetization.
Superparamagnetism
Superparamagnetism
Superparamagnetism is a form of magnetism which appears in small ferromagnetic or ferrimagnetic nanoparticles. In sufficiently small nanoparticles, magnetization can randomly flip direction under the influence of temperature. The typical time betw ...
occurs in ferromagnetic and ferrimagnetic
nanoparticle
A nanoparticle or ultrafine particle is a particle of matter 1 to 100 nanometres (nm) in diameter. The term is sometimes used for larger particles, up to 500 nm, or fibers and tubes that are less than 100 nm in only two directions. At ...
s which are
single-domain, i.e. composed of a single
magnetic domain
A magnetic domain is a region within a magnetic material in which the magnetization is in a uniform direction. This means that the individual magnetic moments of the atoms are aligned with one another and they point in the same direction. When c ...
. 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 are working on in the subfield of superparamagnetism call “macro-spin approximation”.
Mean transition time
Because of the nanoparticle’s
magnetic anisotropy
In condensed matter physics, magnetic anisotropy describes how an object's magnetic properties can be anisotropy, different depending on direction. In the simplest case, there is no preferential direction for an object's magnetic moment. It will ...
, the magnetic moment has usually only two stable orientations antiparallel to each other, separated by an
energy barrier
In the Arrhenius model of reaction rates, activation energy is the minimum amount of energy that must be available to reactants for a chemical reaction to occur. The activation energy (''E''a) of a reaction is measured in kilojoules per mole (k ...
. 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 and is given by the Néel-Arrhenius equation:
[
:,
where is the height of the energy barrier, a product of the magnetic anisotropy energy density and volume ; is the ]Boltzmann constant
The Boltzmann constant ( or ) is the proportionality factor that relates the average relative thermal energy of particles in a ideal gas, gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin (K) and the ...
, the temperature and their product the thermal energy; and 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 are between 10−9 and 10−10 seconds.
The Néel relaxation time can be anywhere from a few nanoseconds to years or much longer. In particular, it is an exponential function of the grain volume, which explains why the flipping probability becomes rapidly negligible for bulk materials or large nanoparticles.
Blocking temperature
Suppose that the magnetization of a single superparamagnetic nanoparticle is measured over a time . If this time is much greater than the relaxation time , the nanoparticle magnetization will flip several times during the measurement. In zero field, the measured magnetization will average to zero. If , the magnetization will not flip during the measurement, so the measured magnetization will be equal to the initial magnetization. In the former case, the nanoparticle will appear to be in the superparamagnetic state whereas in the latter case it will be ''blocked'' in its initial state. The state of the nanoparticle (superparamagnetic or blocked) depends on the measurement time. A transition between superparamagnetism and the blocked state occurs when . In several experiments, the measurement time is kept constant but the temperature is varied, so the transition between superparamagnetism and blocked state is a function of the temperature. The temperature for which is called the ''blocking temperature'':
:
For typical laboratory measurements, the value of the logarithm in the previous equation is in the order of 20–25.
References
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{{DEFAULTSORT:Neel relaxation theory
Magnetism
Non-equilibrium thermodynamics