The chromium system, comprising pure Cr and alloys with most transition metals and some nontransition metals, is the archetypical spin-density-wave (SDW) system. This paper supplements, with a brief summary and extension to include recent work, two previous comprehensive reviews on Cr (Fawcett, 1988) and Cr alloys . The magnetic phase diagrams are reviewed. Impurity states in CrFe and CrSi, when suitably doped with V or Mn, produce dramatic effects in the electrical resistivity, including a low-temperature resistance minimum due to impurity-resonance scattering. Curie-Weiss paramagnetism appears just above the Néel temperature in dilute CrV alloys. Recent work on inelastic neutron scattering in pure Cr is reviewed: the apparent absence of dispersion of the spin-wave modes at the wave vectors of the incommensurate SDW where the Bragg satellite peaks occur; the energy-dependent anisotropy of the excitations in the longitudinal-SDW phase; the commensurate magnetic scattering at the centre of the magnetic zone, which at higher energy and temperature dominates the inelastic scattering at the satellites; the Fincher-Burke excitations seen at low-energy in the transverse-SDW phase; and the silent satellites seen in single-Q Cr at off-axis incommensurate points as temperature increases towards the Néel transition. X-ray scattering with synchrotron radiation has illuminated the relation between the SDW in Cr and the incommensurate charge-density wave that accompanies it.

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The initial value problem is considered for the conformally coupled scalar field and higher derivative gravity, by expressing the equations of each theory in harmonic coordinates. For each theory it is shown that the (vacuum) equations can take the form of a diagonal hyperbolic system with constraints on the initial data. Consequently these theories possess well-posed initial value formulations.

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