Superparamagnetism

Doing some reading I stumbled onto an interesting magnetic behaviour. Beyond our discussions of ferromagnetism, paramagnetism etc there exist more complex states of magnetic order/disorder. In particular there is a state known as superparamagnetism. This occurs in small ferro- or ferrimagnets, and is defined by flips in the overall spin state of the system due to temperature. The ordering of the system is not lost, only the orientation of the ordering (i.e. all spins may flip from up to down but retain <|S|> = 1).

This flipping is characterized by the Neel relaxation time:

tau_N = tau_0*exp ((K*V)/(k_B*T))

Where K is the particles magnetic anisotropic energy. The relaxation time may range from nanoseconds to years for particles. However over a time scale much greater than tau_N the net magnetization will be measured to be zero.

The above was assumed to be in zero magnetic field. However if we now apply a field to the superparamagnetic particle it will order accordingly, much like a paramagnet. Due to this ordering, the particle can be said to have a magnetic susceptibility. This magnetic susceptibility will be far larger than a normal paramagnet hence the term superparamagnet.

This state of magnetism is of great importance to technology, as it is a limiting factor for storage efficiency on magnet-based hard drives. Superparamagnetism sets a lower limit on the particle size which may be used to store information, as the relaxation time is proportional to exp(V).