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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 ...
The concept of a magnon was introduced in 1930 by Felix Bloch [1] in order to explain the reduction of the spontaneous magnetization in a ferromagnet.At absolute zero temperature (0 K), a Heisenberg ferromagnet reaches the state of lowest energy (so-called ground state), in which all of the atomic spins (and hence magnetic moments) point in the same direction.
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.
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 ...
The underlying reason for the difference in dispersion relation is that the order parameter (magnetization) for the ground-state in ferromagnets violates time-reversal symmetry. Two adjacent spins in a solid with lattice constant a that participate in a mode with wavevector k have an angle between them equal to ka .
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.
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.
Since the magnetization in the direction of the field is M s cos φ, these curves are usually plotted in the normalized form m h vs. h, where m h = cos φ is the component of magnetization in the direction of the field. An example is shown in Figure 2. The solid red and blue curves connect stable magnetization directions.