Phonon spectra of both hcp Y and Zr have been calculated using shell-model pseudopotentials. Whereas Y displays no significant anomaly in its spectrum, the phonon frequency of the [001] LO branch of Zr exhibits a pronounced softening near the zone center. We have found that the anomalous behavior of the LO phonons in Zr can be well understood with the conjecture that Zr has a longitudinally polarized spin-density wave with wave vector Q=(2π/c)(0,0,1). This conjecture is consistent with several other experimental results for Zr, including its large magnetic anisotropy, its lack of anisotropic magnetic scattering, and the topology of its Fermi surface.

• Received 27 July 1990

DOI:https://doi.org/10.1103/PhysRevB.42.10873