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The magnetization that occurs below T C is an example of the "spontaneous" breaking of a global symmetry, a phenomenon that is described by Goldstone's theorem. The term "symmetry breaking" refers to the choice of a magnetization direction by the spins, which have spherical symmetry above T C, but a preferred axis (the magnetization direction ...
A bogus argument analogous to the argument in the last section now establishes that the magnetization in the Ising model is always zero. Every configuration of spins has equal energy to the configuration with all spins flipped. So for every configuration with magnetization M there is a configuration with magnetization −M with equal probability.
Ferromagnets is a term that most people are familiar with, and, as with ferroelastics, the spontaneous magnetization of a ferromagnet can be attributed to a breaking of point symmetry in switching from the paramagnetic to the ferromagnetic phase. In this case, is normally known as the Curie temperature.
At this temperature (called the Curie temperature) there is a second-order phase transition, [7] and the system can no longer maintain a spontaneous magnetization. This is because at higher temperatures the thermal motion is strong enough that it exceeds the tendency of the dipoles to align.
Here μ 0 is the permeability of free space; M the magnetization (magnetic moment per unit volume), B = μ 0 H is the magnetic field, and C the material-specific Curie constant: = (+), where k B is the Boltzmann constant, N the number of magnetic atoms (or molecules) per unit volume, g the Landé g-factor, μ B the Bohr magneton, J the angular ...
Gadolinium has a spontaneous magnetization just below room temperature (293 K) and is sometimes counted as the fourth ferromagnetic element. There has been some suggestion that Gadolinium has helimagnetic ordering, [ 5 ] but others defend the longstanding view that Gadolinium is a conventional ferromagnet.
When the temperature rises beyond a certain point, called the Curie temperature, there is a second-order phase transition and the system can no longer maintain a spontaneous magnetization, so its ability to be magnetized or attracted to a magnet disappears, although it still responds paramagnetically to an external field.
If the magnetic moment is and the volume of the particle is , the magnetization is = / = (,,), where is the saturation magnetization and ,, are direction cosines (components of a unit vector) so + + =. The energy associated with magnetic anisotropy can depend on the direction cosines in various ways, the most common of which are discussed below.