X-ray-scattering study of charge- and spin-density waves in chromium

We report an x-ray-scattering study of the incommensurate modulations in pure chromium. X-ray magnetic scattering from the spin-density wave (SDW) is observed. No resonant enhancement of the signal is obtained near the Cr K edge. On cooling through the spin-flip transition, the magnetic signal falls to zero, consistent with the polarization dependence of nonresonant magnetic scattering and the known polarization of the SDW. Charge scattering is observed at the second harmonic due to the associated charge-density wave (CDW). The intensity of the second harmonic is unchanged on cooling through the spin-flip transition. A survey of possible second-harmonic satellites reveals that a single Q state exists in the near-surface region. The amplitude of the lattice distortion is estimated to be (${\mathrm{\Delta }}_2$/a)=1.5±0.2×${10}^{\mathrm{-}3}$, consistent with published reports. A fourth harmonic is also observed, suggesting that the CDW is not perfectly sinusoidal. The intensity of the fourth harmonic is 0.05% of the second and we find (${\mathrm{\Delta }}_4$/a)=2.8±0.2×${10}^{\mathrm{-}5}$. The temperature dependence of the charge harmonics is found to obey mean-field scaling.