Spin dynamics of chromium. II. Incommensurate alloys

Abstract

Since the magnetic moments of transition-metal antiferromagnets are created by electron-hole pairs, the spin dynamics of Cr alloys are associated with quasiparticle transitions. In this paper, we use the random-phase approximation to investigate the spin dynamics about the two different spin-density-wave (SDW) states of incommensurate (I) alloys with wave vectors ${\mathit{Q}}_{\ifmmode\pm\else\textpm\fi{}}^{\ensuremath{'}}$=(2\ensuremath{\pi}/a)(0,0,1\ifmmode\pm\else\textpm\fi{}\ensuremath{\partial}\ensuremath{'}). Because of their more complex quasiparticle energies, I alloys have a richer spectrum of collective excitations than the commensurate (C) alloys studied in the previous paper. Associated with the free energy's rotational invariance are transverse spin-wave (SW) modes which evolve from each satellite wave vector ${\mathit{Q}}_{\ifmmode\pm\else\textpm\fi{}}^{\ensuremath{'}}$ with the same temperature-independent mode velocity c=${\mathit{v}}_{\mathit{F}}$/$\sqrt{3}$ as in the C regime. The translational invariance of the ISDW state is responsible for longitudinal phason modes which evolve from the satellite wave vectors and are damped for any nonzero frequency. As T\ensuremath{\rightarrow}${\mathit{T}}_{\mathit{N}}$, the phason mode velocity approaches c. Together with a related longitudinal damped excitation, the phason modes tilt the SW cones towards G/2=(2\ensuremath{\pi}/a) (0,0,1) and produce a peak in the G/2 cross section at 60 meV, as observed experimentally. High-frequency amplitude modes, both transverse and longitudinal, lie near the pair-breaking edge for each satellite, which is about 40% lower than in the C case. Undamped collective modes called wavons are associated with fluctuations of the SDW wave vectors ${\mathit{Q}}_{\ifmmode\pm\else\textpm\fi{}}^{\ensuremath{'}}$ about their equilibrium values. Wavon modes were recently observed as peaks in the satellite cross sections between 15 and 20 meV. Our model predicts the temperature and doping dependences of the phason and wavon peaks. \textcopyright{} 1996 The American Physical Society.