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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.
While the Mermin–Wagner theorem prevents any spontaneous symmetry breaking on a global scale, ordering transitions of Kosterlitz–Thouless–type may be allowed. This is the case for the XY model where the continuous (internal) O(2) symmetry on a spatial lattice of dimension d ≤ 2, i.e. the (spin-)field's expectation value, remains zero for any finite temperature (quantum phase ...
A magnetic moment which is present even in the absence of the external magnetic field is called spontaneous magnetization. Materials with this property are known as ferromagnets, such as iron, nickel, and magnetite. However, when these materials are heated up, at a certain temperature they lose their spontaneous magnetization, and become ...
The other is ferrimagnetism, where some magnetic moments point in the opposite direction but have a smaller contribution, so spontaneous magnetization is present. [ 4 ] [ 5 ] : 28–29 In the special case where the opposing moments balance completely, the alignment is known as antiferromagnetism ; antiferromagnets do not have a spontaneous ...
In other words, the easy axis is an energetically favorable direction of spontaneous magnetization. Because the two opposite directions along an easy axis are usually equivalently easy to magnetize along, the actual direction of magnetization can just as easily settle into either direction, which is an example of spontaneous symmetry breaking.
Theoretical model of magnetization m against magnetic field h. Starting at the origin, the upward curve is the initial magnetization curve. The downward curve after saturation, along with the lower return curve, form the main loop. The intercepts h c and m rs are the coercivity and saturation remanence.
The magnetization rotates continuously from one direction to the other (it has two choices of rotation direction, though). For a given angle θ, the switching field is the point where the solution switches from an energy minimum (∂ 2 η/∂ φ 2 > 0) to an energy maximum (∂ 2 η/∂ φ 2 < 0).