Observability of Charge-Density Waves by Neutron Diffraction

Abstract

It is shown that atomic displacements $\stackrel{\ensuremath{\rightarrow}}{\mathrm{A}}sin\stackrel{\ensuremath{\rightarrow}}{\mathrm{Q}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{L}}$ associated with a charge-density wave (CDW) modulation of a metal crystal cause several changes in the anticipated diffraction properties. Very weak satellite reflections should occur at locations $\ifmmode\pm\else\textpm\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{Q}}$ from the ordinary (cubic) reflections. However it is found that vibrational excitations, corresponding to phase modulation of the CDW, may weaken the satellite intensities below the level of observation. The structure factors of the cubic reflections are reduced from unity to (the Bessel function) ${J}_{0}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{K}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{A}})$, where $\stackrel{\ensuremath{\rightarrow}}{\mathrm{K}}$ is the scattering vector. Measurements of structure factors are difficult to interpret in the alkali metals because of severe primary extinction (mosaic block size \ensuremath{\sim}0.5 mm) and unknown anharmonic contributions to the Debye-Waller factor. Nevertheless, an unambiguous test for CDW structure is possible since $\stackrel{\ensuremath{\rightarrow}}{\mathrm{Q}}$ (and $\stackrel{\ensuremath{\rightarrow}}{\mathrm{A}}$) must be orientable by a large magnetic field at 4\ifmmode^\circ\else\textdegree\fi{}K. Consequently high-index Bragg reflections should be turned off or on by a magnetic field rotated parallel or perpendicular to $\stackrel{\ensuremath{\rightarrow}}{\mathrm{K}}$. Motivation for such an experiment is suggested by a survey of electronic anomalies which have been reported in the alkali metals and which can be explained with the CDW model.