Superparamagnetism

(or collective paramagnetism), the quasi-paramagnetic behavior of substances consisting of very small ferromagnetic or ferrimagnetic particles that weakly interact with each other.

Below the Curie or Néel points, particles with linear dimensions of ~100–10 angstroms (Å) or less undergo a transition to a single-domain ferromagnetic or ferrimagnetic state, that is, a state in which the magnetization is uniform throughout the particle. The direction of the magnetization of such particles, however, varies in a random manner as a result of thermal fluctuations, just as the direction of the magnetic moments of atoms or ions in a paramagnet varies under the action of thermal motion. Consequently, the system of small particles behaves, in magnetic fields and under temperature changes, like a paramagnetic gas of N atoms (N is the number of single-domain particles, each with the magnetic moment M). For such a system, Curie’s law holds in weak magnetic fields, and the Langevin formula for magnetization holds in the region of magnetic saturation.

The magnetization of superparamagnetic substances can be many times greater than that of ordinary paramagnets. For the spatial orientation of the directions of the magnetization of the particles to vary randomly, the energy of thermal motion kT (where k is the Boltzmann constant and T is the temperature) must be of the order of or exceed the magnetic anisotropy energy KV of a particle (where K is the anisotropy constant and V is the volume of the particle). For example, at temperatures of ~100°K, the particle size should be less than 100 Å.

Examples of superparamagnetic systems are the small particles of Co that separate out from a solid solution Cu-Co (2 percent Co); fine precipitates of Fe, Cu, and Ni in β-brass (0.1 percent Fe), Mn, and Au, respectively; and some antiferromagnetic oxides.