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

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 $\overrightarrow{\mathrm{Q}}$ 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 ${\overrightarrow{\mathrm{M}}}_{3Q}$ which is (1.65 ± 0.05) × ${10}^{-2\mathrm{}}$ times the amplitude ${\overrightarrow{\mathrm{M}}}_{1Q}$ of the primary SDW at 200 K. The amplitude $\left|{\overrightarrow{\mathrm{M}}}_{3Q}\right|$ is found to be proportional to ${\left|{\overrightarrow{\mathrm{M}}}_{1Q}\right|}^3$ for temperatures close to the Néel point; for temperatures below about 220 K there is a tendency for $\left|{\overrightarrow{\mathrm{M}}}_{3Q}\right|$ to approach a saturated value. This behavior is contrasted with that of the recently discovered $2Q$ harmonic whose amplitude ${\overrightarrow{\mathrm{A}}}_{2Q}$ is found to be proportional to ${\left|{\overrightarrow{\mathrm{M}}}_{1Q}\right|}^2$ even at low temperatures.