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A useful tool for dealing with high frequency magnetic effects is the complex permeability. While at low frequencies in a linear material the magnetic field and the auxiliary magnetic field are simply proportional to each other through some scalar permeability, at high frequencies these quantities will react to each other with some lag time. [36]
Assuming the external magnetic field is uniform and shares a common axis with the paramagnet, the extensive parameter characterizing the magnetic state is , the magnetic dipole moment of the system. The fundamental thermodynamic relation describing the system will then be of the form U = U ( S , V , I , N ) {\displaystyle U=U(S,V,I,N)} .
The magnetization field or M-field can be defined according to the following equation: =. Where is the elementary magnetic moment and is the volume element; in other words, the M-field is the distribution of magnetic moments in the region or manifold concerned.
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.
The Stoner–Wohlfarth model is a physical model explaining hysteresis in terms of anisotropic response ("easy" / "hard" axes of each crystalline grain). Micromagnetics simulations attempt to capture and explain in detail the space and time aspects of interacting magnetic domains, often based on the Landau-Lifshitz-Gilbert equation.
For terbium which is a rare-earth metal and has a high orbital angular momentum the magnetic moment is strong enough to affect the order above its bulk temperatures. It is said to have a high anisotropy on the surface, that is it is highly directed in one orientation. It remains ferromagnetic on its surface above its Curie temperature (219 K ...
In physics and engineering, permeation (also called imbuing) is the penetration of a permeate (a fluid such as a liquid, gas, or vapor) through a solid.It is directly related to the concentration gradient of the permeate, a material's intrinsic permeability, and the materials' mass diffusivity. [1]
Strip of permalloy. Permalloy is a nickel–iron magnetic alloy, with about 80% nickel and 20% iron content.Invented in 1914 by physicist Gustav Elmen at Bell Telephone Laboratories, [1] it is notable for its very high magnetic permeability, which makes it useful as a magnetic core material in electrical and electronic equipment, and also in magnetic shielding to block magnetic fields.