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.

Normally, any ferromagnetic or ferrimagnetic material undergoes a transition to a paramagnetic state above its Curie temperature.

Superparamagnetism is different from this standard transition since it occurs below the Curie temperature of the material.

Superparamagnetism occurs in nanoparticles which are single-domain, i.e. composed of a single magnetic domain.

The stable orientations define the nanoparticle’s so called “easy axis”.

and is given by the following Néel–Arrhenius equation:[1] where: This length of time can be anywhere from a few nanoseconds to years or much longer.

In particular, it can be seen that the Néel relaxation time is an exponential function of the grain volume, which explains why the flipping probability becomes rapidly negligible for bulk materials or large nanoparticles.

Let us imagine that the magnetization of a single superparamagnetic nanoparticle is measured and let us define

The state of the nanoparticle (superparamagnetic or blocked) depends on the measurement time.

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.

This function is quite complicated but for some simple cases: In the above equations: The initial slope of the

For a randomly oriented sample, the complex susceptibility[3] is: where From this frequency-dependent susceptibility, the time-dependence of the magnetization for low-fields can be derived: 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/τN, there will be a different magnetic response than when the frequency is much lower than 1/τN, since in the latter case, but not the former, the ferromagnetic clusters will have time to respond to the field by flipping their magnetization.

[4] 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).

It is also possible to perform magneto-optical AC susceptibility measurements with magneto-optically active superparamagnetic materials such as iron oxide nanoparticles in the visible wavelength range.

[5] Superparamagnetism sets a limit on the storage density of hard disk drives due to the minimum size of particles that can be used.