Spin density wave
3201966
199608832
2008-03-20T15:30:09Z
134.105.184.202
'''Spin-density wave''' (SDW) and '''charge-density wave''' (CDW) are names for two similar low-energy ordered states of solids. Both these states occur at low temperature in anisotropic, low-dimensional materials or in metals that have high densities of states at the Fermi level <math>N(E_F)</math>. Other low-temperature [[ground state]]s that occur in such materials are [[superconductivity]], [[ferromagnetism]] and [[antiferromagnetism]]. The transition to the ordered states is driven by the condensation energy which is approximately <math>N(E_F) \Delta</math> where <math>\Delta</math> is the magnitude of the [[energy gap]] opened by the transition. Note that SDWs are distinct from [[spin wave]]s, which are an excitation mode of [[ferromagnet]]s and [[antiferromagnet]]s.
Fundamentally SDWs and CDWs involve the development of a periodic modulation in the density of the electronic [[Spin (physics)|spins]] and charges with a characteristic spatial frequency <math>q</math> that does not transform according to the symmetry group that describes the ionic positions.
The new periodicity associated with CDWs can easily be observed using [[scanning tunneling microscopy]] or [[electron diffraction]] while the more elusive SDWs are typically observed via [[neutron diffraction]] or [[susceptibility]] measurements. If the new periodicity is a rational fraction or multiple of the [[lattice constant]], the density wave is said to be [[commensurate]]; other the density wave is termed [[incommensurate]].
[[Image:Crnest.png|thumb|A sketch in k-space of a (001) section of the Fermi surface of Cr. The band structure of Cr yields an electron pocket (green) centered at Gamma and a hole pocket (blue) centered at H. The surrounding black square indicates the boundary of the first [[Brillouin zone]].]]
Why do some solids with a high <math>N(E_F)</math> form density waves while others choose a superconducting or magnetic ground state at low temperatures? The answer has to do with the existence of [[nesting vectors]] in the materials' [[Fermi surface]]s. The concept of a nesting vector is illustrated in the Figure for the famous case of Cr, which transitions from a paramagnetic to SDW state at a [[Louis Eugene Felix Neel|Néel]] temperature of 311 K. Cr is a [[body-centered cubic]] metal whose Fermi surface features many parallel boundaries between electron pockets centered at <math>\Gamma</math> and at H. These large parallel regions can be spanned by the nesting wavevector <math>q</math> shown in red. The real-space periodicity of the resulting spin-density wave is given by <math>2\pi/q</math>. The formation of a SDW with a corresponding spatial frequency causes the opening of an energy gap that lowers the system's energy. The existence of the SDW in Cr was first posited in 1960 by [[Albert Overhauser]] of [[Purdue]]. [[Clifford Glenwood Shull|Cliff Shull]] of [[MIT]] won the [[Nobel Prize/Physics|Physics Nobel Prize]] in 1994 for his experimental observation of the Cr SDW. The theory of CDWs was first put forth by [[Rudolf Peierls]] of [[Oxford University]], who was trying to explain superconductivity.
Many low-dimensional solids have anisotropic Fermi surfaces that have prominent nesting vectors. Well-known examples include layered materials like <math>NbSe_3</math>, <math>TaSe_3</math> and <math>K_{0.03}MoO_3</math> (a [[Chevrel phase]]) and quasi-1D organic conductors like TMTSF or TTF-TCNQ. CDWs are also common at the surface of solids where they are more commonly called [[surface reconstruction]]s or even dimerization. Surface so often support CDWs because they can be described by two-dimensional Fermi surfaces like those of layered materials.
The most intriguing properties of density waves are their dynamics. Under an appropriate electric field or magnetic field, a density wave will "slide" in the direction indicated by the field due to the electrostatic or magnetostatic force. Typically the sliding will not begin until a "depinning" threshold field is exceeded where the wave can escape from a potential well caused by a defect. The [[hysteresis|hysteretic]] motion of density waves is therefore not unlike that of [[dislocations]] or [[magnetic domain]]s. The current-voltage curve of a CDW solid therefore shows a very high electrical resistance up to the depinning voltage, above which it shows a nearly [[Ohm's Law|ohmic]] behavior.
==References==
#A pedagogical article about the topic: [http://www.sciamdigital.com/browse.cfm?sequencenameCHAR=item2&methodnameCHAR=resource_getitembrowse&interfacenameCHAR=browse.cfm&ISSUEID_CHAR=A9362308-C3A8-4DC4-AC9C-8DE25B1A481&ARTICLEID_CHAR=181A387B-4ECD-4443-8927-9A3926F28B2&sc=I100322 "Charge and Spin Density Waves,"] Stuart Brown and George Gruner, ''Scientific American'' 270, 50 (1994).
#Authoritative work on Cr: [http://dx.doi.org/10.1103/RevModPhys.60.209 "Spin-density-wave antiferromagnetism in chromium,"] E. Fawcett, ''Rev. Mod. Phys.'' 60, 209 (1988).
#About Fermi surfaces and nesting: ''Electronic Structure and the Properties of Solids,'' Walter A. Harrison, ISBN 0-486-66021-4.
#[http://www.techfak.uni-kiel.de/matwis/amat/semi_en/kap_a/advanced/ta_4_1.html Peierls instability.]
[[Category:Condensed matter physics]]
[[Category:Electric and magnetic fields in matter]]
[[de:Spindichtewelle]]