# Superparamagnetism

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Superparamagnetism

Superparamagnetism is a form of magnetism. A superparamagnetic material is composed of small ferromagnetic clusters (e.g. crystallites), but where the clusters are so small that they can randomly flip direction under thermal fluctuations. As a result, the material as a whole is not magnetized except in an externally applied magnetic field (in that respect, it is like paramagnetism).

Description

Specifically, superparamagnetism is a phenomenon in which magnetic materials may exhibit a behavior similar to paramagnetism at temperatures below the Curie or the Néel temperature. This is a small length-scale phenomenon, where the energy required to change the direction of the magnetic moment of a particle is comparable to the ambient thermal energy. At this point, the rate at which the particles will randomly reverse direction becomes significant.

Normally, coupling forces in ferromagnetic materials cause the magnetic moments of neighboring atoms to align, resulting in very large internal magnetic fields. This is what distinguishes ferromagnetic materials from paramagnetic materials. At temperatures above the Curie temperature (or the Neel temperature for antiferromagnetic materials), the thermal energy is sufficient to overcome the coupling forces, causing the atomic magnetic moments to fluctuate randomly. Because there is no longer any magnetic order, the internal magnetic field no longer exists and the material exhibits paramagnetic behavior. If the material is non-homogeneous, one can observe a mixture of ferromagnetic and paramagnetic clusters of atoms at the same temperature, the superparamagnetic stage. The idea of superparamagnetism is used in [http://ctwc.weizmann.ac.il/spc.html SuperParamagnetic Clustering] algorithm (SPC) as well as in its extension [http://vcclab.org/lab/spc global SPC] .

Superparamagnetism occurs when the material is composed of very small crystallites (1–10 nm). In this case even when the temperature is below the Curie or Neel temperature (and hence the thermal energy is not sufficient to overcome the coupling forces between neighboring atoms), the thermal energy is sufficient to change the direction of magnetization of the entire crystallite. The resulting fluctuations in the direction of magnetization cause the magnetic field to average to zero. Thus the material behaves in a manner similar to paramagnetism, except that instead of each individual atom being independently influenced by an external magnetic field, the magnetic moment of the entire crystallite tends to align with the magnetic field.

The energy required to change the direction of magnetization of a crystallite is called the crystalline anisotropy energy and depends both on the material properties and the crystallite size. As the crystallite size decreases, so does the "crystalline anisotropy energy", resulting in a decrease in the temperature at which the material becomes superparamagnetic.

The rate at which particles will lose their direction is governed by the Néel-Arrhenius equation. In particular, it is a function of the exponential of the grain volume.

Néel-Arrhenius equation

The Néel-Arrhenius equation (closely related to the standard Arrhenius equation) states:

:$au = au_0 exp\left(E/\left(k_BT\right)\right)$where
*τ is the average length of time that it takes for a ferromagnetic cluster (often, a crystallite) to randomly flip directions as a result of thermal fluctuations,
0 is a length of time, characteristic of the material, called the "attempt time" or "attempt period" (its reciprocal is called the "attempt frequency"),
*"E" is the magnetic anisotropy energy, which can be thought of as the energy barrier associated with the magnetization moving from its initial "easy axis" direction, through a "hard axis", ending at another easy axis,
*kB is the Boltzmann constant,
*"T" is the temperature.

In other words, when an external magnetic field is applied for a long time and then removed, the clusters will not randomize their direction immediately, but rather it will take some length of time to do so. This length of time can be anywhere from fractions of a second to years or much longer. Larger clusters tend to have larger anisotropy energy (the energy is approximately proportional to volume), and consistent with the Néel-Arrhenius equation, they tend to hold their magnetization for much longer.

A superparamagnetic system can be measured with AC susceptibility measurements, where an applied magnetic field varies in time, and the magnetic response of the system is measured. A superparamagnetic system will show a characteristic frequency dependence: When the frequency is much higher than 1/τ, there will be a different magnetic response than when the frequency is much lower than 1/τ, since in the latter case, but not the former, the ferromagnetic clusters will have time to respond to the field by flipping their magnetization. [http://www.qdusa.com/resources/pdf/1078-201.pdf] The precise dependence can be calculated from the Néel-Arrhenius equation, assuming that the neighboring clusters behave independently of one another (if clusters interact, their behavior becomes more complicated).

Effect on hard drives

Superparamagnetism sets a limit on the storage density of hard disk drives due to the minimum size of particles that can be used. This limit is known as the superparamagnetic limit. Current hard disk technology with longitudinal recording has an estimated limit of 100 to 200 Gbit/in², though this estimate is constantly changing. [Kryder, M.H. (April 2005) "Magnetic recording beyond the superparamagnetic limit". "Magnetics Conference, 2000. INTERMAG 2000 Digest of Technical Papers. 2000 IEEE International" pp. 575-575]

One suggested technique to further extend recording densities on hard disks is to use perpendicular recording rather than the conventional longitudinal recording. This changes the geometry of the disk and alters the strength of the superparamagnetic effect. [http://www.hitachigst.com/hdd/hddpdf/tech/chart13.pdf] [http://www.hitachigst.com/hdd/research/recording_head/pr/PerpendicularAnimation.html] .Perpendicular recording is predicted to allow information densities of up to around 1 Tbit/in² (1024 Gbit/in²). --reference is on the perpendicular recording page

Another technique in development is the use of HAMR drives, which use materials that are stable at much smaller sizes. But, they require heating before the magnetic orientation of a bit can be changed.

Applications of superparamagnetism

General Applications

*Ferrofluid: tunable viscosity
*Sensors: more sensitivity (GMR,BARCIII)
*Self-assembly

Biomedical applications

*Detection: Magnetic Resonance Imaging (MRI)
*Separation: cell-, DNA-, protein- separation, RNA fishing
*Treatment: drug-delivery, hyperthermia, magnetofection

ee also

*Single-molecule magnet

References