Goldstone modes and low-frequency dynamics of incommensurate chromium alloys

This Letter reports the first solution for the low-energy spin excitations about the incommensurate spin-density-wave (SDW) state of pure Cr and Cr alloys. The Goldstone modes evolving from the magnetic satellites consist of transverse spin-wave modes and longitudinal phason modes, which are associated with the rotational and translational symmetries of the SDW state, respectively. The phason modes bend toward the zone boundary H between the satellites and produce the recently observed 60 meV peak in the longitudinal cross section at H. We also report a new class of collective excitation which is associated with oscillations of the SDW wave vector.