Geometrically Frustrated Materials: Difference between revisions
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==What is geometric frustration?== | ==What is geometric frustration?== | ||
Frustration is the inability of a material to find a single ground state and instead has a highly degenerate ground state. The reason for this is because the geometry of the crystal is such that any arrangement of spins on the lattice cannot simultaneously satisfy all interactions. For instance, there is no possible configuration of four Ising spins on the vertices of a tetrahedron where they will all align antiferromagnetically. The size of the frustration parameter ''f'', defined by the ratio of the Curie-Weiss temperature and the expected mean field ordering temperature (Néel temperature) or <math>\frac{theta_{CW}} | Frustration is the inability of a material to find a single ground state and instead has a highly degenerate ground state. The reason for this is because the geometry of the crystal is such that any arrangement of spins on the lattice cannot simultaneously satisfy all interactions. For instance, there is no possible configuration of four Ising spins on the vertices of a tetrahedron where they will all align antiferromagnetically. The size of the frustration parameter ''f'', defined by the ratio of the Curie-Weiss temperature and the expected mean field ordering temperature (Néel temperature) or <math>\frac{\theta_{CW}}{T_N}</math>, is used to determine the extent of the frustration in a material. | ||
Revision as of 08:45, 13 April 2009
The main focus of solid state physics is on macroscopic properties of solid materials that result from interactions between atoms. Solid state physics is extremely interested in how these interaction come to an equilibrium to order in a certain way such as antiferromagnetism. One emergent property is disorder that arises from geometric frustration and this is the subject of much perplexing research because there seems to be no equilibrium between interactions or no unique ordering state.
What is geometric frustration?
Frustration is the inability of a material to find a single ground state and instead has a highly degenerate ground state. The reason for this is because the geometry of the crystal is such that any arrangement of spins on the lattice cannot simultaneously satisfy all interactions. For instance, there is no possible configuration of four Ising spins on the vertices of a tetrahedron where they will all align antiferromagnetically. The size of the frustration parameter f, defined by the ratio of the Curie-Weiss temperature and the expected mean field ordering temperature (Néel temperature) or , is used to determine the extent of the frustration in a material.
