The magnetization depends on the temperature and if the material is heated it will eventually go through a phase transition from an ordered phase, where the spins points in well defined directions, to a disordered phase. This is similar to the case of ice and water. At low temperatures the atoms are ordered in a lattice but above 0 °C the ice melts and forms a disordered liquid. The temperature where the phase transition takes place is called the critical temperature (Tc). Tc depends on the material but also on the spatial extension or the spatial dimensionality. The concept of dimensionality is easiest understood by every-day life analogies. A cardboard box is three dimensional while a sheet of paper can represent two dimensions and sewing threads symbolize one dimensional objects. The critical temperature of samples made in the form of thin films can be controlled by the film thickness, the thinner the film; the lower Tc is obtained. Magnetic materials also have a spin dimensionality, which describes the possible directions of the spins. Spin is a property of the electron that constitutes the foundation of magnetization and it is usually visualized as an arrow. All magnetic materials can be divided into nine groups, called universality classes, depending on their dimensionalities.
The temperature dependence of the magnetization can be described by a simple equation close to the phase transition. The important parameter of this equation is an exponent denoted β. The value of β depends only on the spatial and spin dimensionality (the universality class) of the sample irrespectively of the material. Experimental determinations of the exponent can be compared to theory, making it possible to draw conclusions about the magnetization in materials from simple measurements. In reverse, measurements are also used to compare theories and calculations to reality.
Numerous experiments have shown that strikingly diverse materials, with properties far from the idealized conditions in theoretical calculations, show the same magnetic behavior close to the critical temperature. But some materials do not fit in the simple picture of universality classes. It is therefore of great interest to try to answer the question of which microscopic interactions are of importance in a phase transition and which are not.
The internal magnetization of patterned magnetic materials can be made visible through diffraction.
Through the magneto optical Kerr effect (MOKE) the magnetic response of materials can be obtained as a function of an externally applied magnetic field. MOKE measurements are performed by measuring polarization changes of a laser beam reflected from the material. By measuring the changes in the polarization the magnetic characteristics of different magnetic materials can be determined.
For materials with an artificially patterned structure of a periodicity comparable to the wavelength of the light the laser beam is not only reflected of the patterned surface but also diffracted.
As with the reflected beam the diffracted beams contain information on the magnetic state of the patterned samples. While the information in the reflected beam corresponds to an average magnetic moment over the illuminated area the magnetic information in each diffracted beam is proportional to the Fourier component of the magnetization for that diffraction order.
Through magnetization measurements recorded at the diffracted beams the internal magnetization distribution can therefore be reconstructed. Diffracted MOKE measurements therefore provide information on the magnetic domain structure and reversal mechanism within small particles and can even be used to distinguish the magnetic behavior of individual structures or parts of complex patterns.