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.

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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°. Although they actually look like a very sharp change in magnetic moment orientation, when looked at in more detail there is actually a very gradual reorientation of individual moments across a finite distance.

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 (J_ex), 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.

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.

Depinning of a domain wall

"Depinning of a domain wall" refers to the unfixing of the domain wall by either removing the external field or, more often, reversing its polarity (since the opposite polarity may not have as strong of an influence).

In magnetic materials, a region of homogenous magnetic orientation is called a "domain" and the interface between two such regions is called a "domain wall". A domain wall is said to be "pinned" if it is fixed by an external magnetic field (often created by nearby, strongly magnetized domain).

General

Domain walls are topological solitons which occur whenever a discrete symmetry is 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 (lecture slides and audio)

See also

General

• Soliton (topological)
• Topological defect

Magnetism

• Bloch wall
• Ferromagnetism

Gravity

• Cosmic string
• Gravitational singularity

Fiction