Effect of spin-density waves on the lattice dynamics of lead.

Abstract

The phonon spectrum of Pb, first determined by Brockhouse et al. in 1962, exhibits large depressions in both longitudinal and transverse modes at the zone-boundary points {100}. The origin of this behavior has remained unclear. We show that a possible explanation involves the existence of a cubic family of small-amplitude spin-density waves (SDW's), having wave vectors {Q} at each of the twelve {211}, or alternatively {210}, superlattice points. Each SDW causes a peak in the conduction-electron charge response function \ensuremath{\chi}(q) near the points q=\ifmmode\pm\else\textpm\fi{}Q. SDW's have built-in charge modulations, equal in magnitude but opposite in sign, for both spin states. Only a small shift in the spatial phase \ensuremath{\delta}\ensuremath{\varphi}=\ensuremath{\epsilon}${\ensuremath{\sigma}}_{z}$, depending on the spin ${\ensuremath{\sigma}}_{z}$, creates an additional charge response for q near \ifmmode\pm\else\textpm\fi{}Q. When this spin-split-phase contribution to \ensuremath{\chi}(q) is incorporated into the theory for the phonon spectrum, the anomalous behavior at {100} can be understood.