Spontaneous magnetization

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A simplified phase diagram for isotropic ferromagnets illustrating Bloch's Law: M(T) = M(0) (1-(T/T_C)^3/2)

Spontaneous magnetization is the term used to describe the appearance of an ordered spin state (magnetization) at zero applied magnetic field in a ferromagnetic or ferrimagnetic material below a critical point called the Curie temperature or T_C. At temperatures above T_C, the material is paramagnetic and its magnetic behavior is dominated by spin waves or magnons, which are boson collective excitations with energies in the meV range. The magnetization that occurs below T_C is a famous 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) below T_C.

To first order, the temperature dependence of spontaneous magnetization is given by Bloch's Law. The decrease in spontaneous magnetization at higher temperatures is caused by the increasing excitation of spin waves. In a particle description, the spin waves correspond to magnons, which are the massless Goldstone bosons corresponding to the broken symmetry.