However, the Pauli Exclusion Principle still holds, and the electrons each must possess a unique wavefunction. Similarly to the atomic case, neighboring electrons minimize their coulombic repulsion by aligning their spin angular momenta. As the equation suggests, the exchange energy is dependent on the dot product of the spin angular momenta of the two electrons.
Since the magnetic moment of an atom is proportional to the spin angular momentum of an atom and lies in the same direction, the exchange interaction directly affects the magnetic moments within a material. This is consistent with the above conclusion that the energy is minimized when magnetic moments are parallel.
This also suggests that there is an energy maximum when the magnetic moments are anti-parallel, and the smaller the angle between them the lower the energy.
Due to the low-symmetry nature of crystalline solids, many materials exhibit anisotropy. Anisotropy is the property of being directionally dependent. Magnetocrystalline anisotropy refers to a crystal's property to be more easily magnetized in some directions in comparison to others.
For a crystal, the axis easiest to magnetize is known as the easy axis, and the axis hardest to magnetize is known as the hard axis. These easy and hard axes are often fundamental, easy to define, crystallographic direction. This propensity to get magnetized in some directions, represents an energetic minimum for magnetic moments to lie in that direction.
Thus, forces due to magnetocrystalline anisotropy prefer all magnetic moments pointing in the direction of the easy direction. So far, the three main interacting forces causing domain wall formation and domain separation have been discussed: the exchange interaction, magnetocrystalline anisotropy, and minimization of the external magnetic field.
Multiple magnetic domains form within one material because it is energetically unfavorable to have one uniform domain, so the magnetic moments split into multiple domains to minimize the internal energy of the system. In figure 1, the entire material is one uniform domain with the magnetic moment in the direction of the materials easy axis.
The exchange energy and the magnetocrystalline anisotropy energy are both at absolute minima, however this state also has the highest possible external field energy. Therefore, this state is not at a total energy minimum.
In figure 2, the material is split into two domains, one up and one down. The material now has a much smaller, but still present, external magnetic field. However, the two magnetic domains are anti-parallel with one another, so the exchange interaction between the two domains are at an energy maximum. The two domains are both lying in the direction of the easy axis, so the energy for the anisotropy term is at a minimum.
Their atomic makeup is such that smaller groups of atoms band together into areas called domains , in which all the electrons have the same magnetic orientation. Below is an interactive animation that shows you how these domains respond to an outside magnetic field. In the Ferromagnetic Material pictured above, the domains are randomly aligned the illustration shows how this phenomenon works, not the actual size or shape of domains.
Normally invisible Magnetic Field Lines , depicted in red, are seen emanating from the poles of the Bar Magnet. Use the Magnet Position slider to move the magnet closer to the ferromagnetic material so that it interacts with the field lines. A permanent magnet is nothing more than a ferromagnetic object in which all the domains are aligned in the same direction.
There are only four elements in the world that are ferromagnetic at room temperature and can become permanently magnetized: iron, nickel, cobalt and gadolinium. Add a comment.
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