Domain wall
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A domain wall is a term used in physics which can have one of two distinct but similar meanings in either magnetism or string theory. It is also used as technobabble in science fiction.
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[edit] Magnetism
In magnetism, a domain wall is an interface separating magnetic domains. It is a transition between different magnetic moments and usually undergoes an angular displacement of 90° or 180°. Domain wall is a gradual reorientation of individual moments across a finite distance. The domain wall thickness depends on the anisotropy of the material, but on average spans across around 100-150 atoms.
The energy of a domain wall is simply the difference between the magnetic moments before and after the domain wall was created. This value is usually expressed as energy per unit wall area.
The width of the domain wall varies due to the two opposing energies that create it: the Magnetocrystalline anisotropy energy and the exchange energy (Jex), both of which want to be as low as possible so as to be in a more favorable energetic state. The anisotropy energy is lowest when the individual magnetic moments are aligned with the crystal lattice axes thus reducing the width of the domain wall. Whereas the exchange energy is reduced when the magnetic moments are aligned parallel to each other and thus makes the wall thicker, due to the repulsion between them. (Where anti-parallel alignment would bring them closer - working to reduce the wall thickness.) In the end an equilibrium is reached between the two and the domain wall's width is set as such.
An ideal domain wall would be fully independent of position, however, they are not ideal and so get stuck on inclusion sites within the medium, also known as Crystallographic defects. These include missing or different (foreign) atoms, oxides, insulators and even stresses within the crystal. This prevents the formation of domain walls and also inhibits their propagation through the medium. Thus a greater applied magnetic field is required to overcome these sites.
Note that the magnetic domain walls are an exact solutions classical nonlinear equations of magnets (Landau-Lifshitz equation, Heisenberg ferromagnet equation, Ishimori equation, Mikhailov-Yaremchuk equiation, nonlinear Schrodinger equation and so on).
[edit] String theory
In string theory, a domain wall is a theoretical 2-dimensional singularity. A domain wall is meant to represent an object of codimension one embedded into space (a defect in space localized in one spatial dimension). For example, D8-branes are domain walls in type II string theory. In M-theory, the existence of Horava-Witten domain walls, "ends of the world" that carry a E8 gauge theory, is important for various relations between superstring theory and M-theory.
If domain walls exist, it seems plausible that they will violently emit gravitational waves if two such walls would collide. As the Laser Interferometer Gravitational-Wave Observatory and future observatories of its kind will search for direct evidence of gravitational waves, this phenomenon would be included as well in such searches.
[edit] Depinning of a domain wall
Non-magnetic inclusions in the volume of a ferromagnetic materials, or dislocations in crystalographic structure, can cause "pinning" of the domain walls (see animation). Such pinning sites cause the domain wall to seat in a local energy minimum and external field is required to "unpin" the domain wall from its pinned position. The act of unpinning will cause sudden movement of the domain wall and sudden change of the volume of both neighbouring domains. This causes Barkhausen effect and in effect it is most likely to be the source of magnetic hysteresis.
[edit] General
Domain walls are topological solitons which occur whenever a discrete symmetry is spontaneously broken.
[edit] Science fiction
Domain walls have been in science fiction novels. Stephen Baxter's Xeelee series suggests domain walls being used to power spacecraft, through manipulation of gravity.
[edit] References
- Kip Thorne (1999), Spacetime Warps and the Quantum: A Glimpse of the Future, ITP & CalTech (lecture slides and audio)
