The spin density wave (SDW) is an antiferromagnetic ground state of metals for which the density of the conduction electron spins is spatially modulated. In conventional antiferromagnets like MnF2 the magnetic moments have opposite orientation and are located at two crystallographic sublattices. On the contrary the SDW is a many-particle phenomenon of an itinerant magnetism which is not fixed to the crystal lattice. SDW are observed in metals and alloys; most prominent is chromium and its alloys. The SDW also occurs as ground state in strongly anisotropic systems, for example the one-dimensional organic conductors.

In analogy to the magnetic order of antiferromagnets below Nčel temperature, the electron gas becomes unstable for temperatures below an ordering temperature TSDW and enters a collectively ordered ground state of an itinerant antiferromagnet. The reason of the instability of the electron gas at the transition to the SDW ground state is the so-called nesting of the Fermi surface.
In a metal the density of the conduction electrons with spin ↑ and with spin ↓ is the same everywhere; the spatial variation of the total charge density is given by

and only reflects the periodicity of the crystal lattice. The development of a SDW violates the translational invariance; now the charge density ρ↑(↓) has a sinusoidal modulation
with σ0 the amplitude and Q the wavevector of the SDW. The wavelength λ=2π/Q of SDW is determined by the Fermi surface of the conduction electrons and in general not a multiple of (i.e. commensurate with) the lattice period a. In fact, the ration λ/a can change with temperature, external pressure, doping and other parameters.
For the understanding of a SDW, the nesting of the Fermi surface is essential. This describes the property of the reciprocal (momentum) space to map parts of the Fermi surface with electron or hole character on top of each other by translation with the wavevector Q. The case is most obvious for one dimension, where the Fermi surface consists of two parallel planes at ± kF. In two or three dimensions a complete nesting by just a single Q-vector is not possible any more, but different parts of the Fermi surface can be mapped by different Q vectors in a more or less perfect way.
The spatial modulation of the electron spin density leads to a superstructure, and an energy gap 2Δ(T) opens at the Fermi energy; the gap value increases with decreasing temperature the same way as the magnetization. The electrical resistivity exhibits a semiconducting behavior below TSDW. The pinning of the entire SDW on impurities in the crystal leads to collective transport only above a certain threshold field and in an alternating electric field with frequency ω0.
There is a certain analogy between a SDW and a charge density wave (CDW) which also results in an instability of the electron gas. Like for a SDW we find an energy gap opening at the Fermi edge and the ordered state to be semiconducting. however the CDW leads to a modulation of the entire charge density ρ0(r) of the conduction electrons, which is accompanied by a superstructure of the underlying lattice.
A typical example of a one-dimensional metal which undergoes a SDW transition is the Bechgaard salt (TMTSF)2PF6.

Contact: M. Dressel