Characterization of low-energy magnetic excitations in chromium

The low-energy excitations of Cr, i.e., the Fincher-Burke (FB) modes, have been investigated in the transversely polarized spin-density-wave phase by inelastic neutron scattering using a single-${\mathbf{Q}}_{\pm }$ crystal with a propagation vector ${\mathbf{Q}}_{\pm }$ parallel to [001]. The constant-momentum-transfer scans show that the energy spectra consist of two components, namely dispersive FB modes and an almost energy-independent cross section. Most remarkably, we find that the spectrum of the FB modes exhibits one peak at $140\mathrm{K}$ near $\mathbf{Q}=(0,0,0.98)$ and two peaks near $\mathbf{Q}=(0,0,1.02)$, respectively. This is surprising because Cr crystallizes in a centrosymmetric bcc structure. The asymmetry of those energy spectra decreases with increasing temperature. In addition, the observed magnetic peak intensity is independent of $\mathbf{Q}$, suggesting a transfer of spectral weight between the upper and lower FB modes. The energy-independent cross section is localized only between the incommensurate peaks and develops rapidly with increasing temperature.

Figure 1

Dispersion of magnetic excitations based on the previous experimental results in the TSDW phase of Cr. The vertical cones show the dispersion of the high-energy excitations emerging from the incommensurate positions (Refs. 3, 4). The chain lines indicate the FB modes (Refs. 8, 9, 10) and are the subject of the present investigation. The scan trajectories are represented by horizontal and vertical lines. The ellipsoid indicates a typical resolution of the current thermal-neutron experiments.

Figure 2

Energy spectra measured along [001] in the TSDW phase. A single peak and a double peak are observed at the symmetric $\mathbf{Q}$ positions (0,0,0.98) and (0,0,1.02), respectively. The solid lines are drawn as a guide to the eyes. The broken lines show the baseline above which the FB modes appear (see text).

Figure 3

Spectra as measured at symmetric $\mathbf{Q}$ positions above $T_{\mathrm{sf}}$ (a) (0,0,0.98) and (b) (0,0,1.02). The FB modes and the $\mathbf{Q}$-independent scattering (broken line) disappear below $T_{\mathrm{sf}}$ (solid line). The energy resolution is shown by thick horizontal bars.

Figure 4

$\mathbf{Q}$ dependence of (a) the peak position and (b) the observed peak intensity measured at $T=140\mathrm{K}$. The gray region at ${\mathbf{Q}}_{\pm }$ indicates the region where the incommensurate scattering is dominant. (a) The peak width is expressed by vertical thick bars. In (b), the peak intensity corresponds to a sum of $I_{\mathrm{UFB}}+I_{\mathrm{LFB}}+I_{\mathrm{const}}$.

Figure 5

Contour map around (0,0,1) for $E=3\mathrm{meV}$. The intensity around (0,0,1.02) is due to the imbalance of the FB mode shown in Fig. 4a. The inset shows a scan keeping the energy transfer fixed at $E=3\mathrm{meV}$. The triangles point towards the $\mathbf{Q}$ positions, where FB excitations were expected according to Ref. 10.

Figure 6

Thermal evolution of energy spectra at $(0,0,1\pm 0.02)$. $I_{\mathrm{const}}$ is shown by broken lines.

Figure 7

Cold-neutron data of constant-$\mathbf{Q}$ scans at the symmetrical positions (a) (0,0,1.02) and (b) (0,0,0.98). The energy resolution of $\Delta E⩽0.4\mathrm{meV}$ (FWHM) is shown by the horizontal bar in (a). The background level was estimated from data at two points (0,0,0.9) and (0,0,1.1).