Domain wall
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2008-06-22T07:11:45Z
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/* Depinning of a domain wall */
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]].
==Magnetism==
[[Image:Domain_wall_vectors.svg|thumb|right|300px|Domain wall (B) with gradual re-orientation of the magnetic moments between two 180-degree domains (A) and (C)]]
In [[magnetism]], a domain wall is an interface separating [[magnetic domain]]s. It is a transition between different magnetic [[Moment (physics)|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 (<math>J_{\mathrm{ex}}</math>), 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 defect]]s. 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 exact solutions to classical nonlinear equations of magnets ([[Landau-Lifshitz equation]], [[nonlinear Schrodinger equation]] and so on).
{{expert|date=June 2008}}
==String theory==
In [[string theory]], a domain wall is a theoretical 2-dimensional [[Gravitational singularity|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-brane]]s are domain walls in [[type II string theory]]. In [[M-theory]], the existence of [[Horava-Witten domain wall]]s, "ends of the world" that carry a [[E8 (mathematics)|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 wave]]s if two such walls would collide. As the [[LIGO|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.
==Depinning of a domain wall==
[[Image:Barkhausensprung.gif|thumb|300px|Schematic representation of domain wall unpinning]]
Non-magnetic [[inclusion]]s in the volume of a ferromagnetic material, or [[dislocation]]s 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 noise]] and in effect it is most likely to be the source of [[magnetic hysteresis]].
==General==
Domain walls are [[topological soliton]]s which occur whenever a [[discrete symmetry]] is [[spontaneous symmetry breaking|spontaneously broken]].
==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.
==References==
* [[Kip Thorne]] (1999), ''Spacetime Warps and the Quantum: A Glimpse of the Future'', ITP & [[CalTech]] ([http://online.kitp.ucsb.edu/online/plecture/thorne/ lecture slides and audio])
==See also==
===General===
*[[Soliton (topological)]]
*[[Topological defect]]
===Magnetism===
*[[Bloch wall]]
*[[Ferromagnetism]]
===Gravity===
*[[Cosmic string]]
*[[Gravitational singularity]]
===Fiction===
[[Category:Electric and magnetic fields in matter]]
[[Category:Hypothetical astronomical objects]]
[[Category:Large-scale structure of the cosmos]]
[[Category:Physics in fiction]]
[[Category:String theory]]
[[Category:Magnetism]]
[[fr:Mur de domaine]]
[[vi:Vách đômen]]