Second and third harmonics of the spin density wave in chromium metal

Abstract

Neutron-diffraction measurements with a single crystal of chromium in an approximately single-$Q$ state have revealed the existence of a satellite reflection at three times the wave vector $\stackrel{\ensuremath{\rightarrow}}{\mathrm{Q}}$ of the spin density wave (SDW). This $3Q$ harmonic is itself an SDW with a polarization identical to that of the primary SDW and an amplitude ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{M}}}_{3Q}$ which is (1.65 \ifmmode\pm\else\textpm\fi{} 0.05) \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}2}$ times the amplitude ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{M}}}_{1Q}$ of the primary SDW at 200 K. The amplitude $|{\stackrel{\ensuremath{\rightarrow}}{\mathrm{M}}}_{3Q}|$ is found to be proportional to ${|{\stackrel{\ensuremath{\rightarrow}}{\mathrm{M}}}_{1Q}|}^{3}$ for temperatures close to the N\'eel point; for temperatures below about 220 K there is a tendency for $|{\stackrel{\ensuremath{\rightarrow}}{\mathrm{M}}}_{3Q}|$ to approach a saturated value. This behavior is contrasted with that of the recently discovered $2Q$ harmonic whose amplitude ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{A}}}_{2Q}$ is found to be proportional to ${|{\stackrel{\ensuremath{\rightarrow}}{\mathrm{M}}}_{1Q}|}^{2}$ even at low temperatures.