Anisotropy of the Incommensurate Fluctuations in ${\mathrm{S}\mathrm{r}}_2{\mathrm{R}\mathrm{u}\mathrm{O}}_4$: A Study with Polarized Neutrons

The anisotropy of the magnetic incommensurate fluctuations in ${\mathrm{S}\mathrm{r}}_2{\mathrm{R}\mathrm{u}\mathrm{O}}_4$ has been studied by inelastic neutron scattering with polarized neutrons. We find a sizable enhancement of the out-of-plane component by a factor of 2 for intermediate energy transfer, which appears to decrease for higher energies. Our results qualitatively confirm calculations of the spin-orbit coupling, but the experimental anisotropy and its energy dependence are weaker than predicted.

Figure 1

Results of the scans across the incommensurate position at $\mathbf{Q}=(0.7,0.3,0)$ for an energy transfer of 8 meV and at $T=1.5\mathrm{K}$ [(a)–(d)] and at $T=300\mathrm{K}$ [(e) and (f)]. (a) Non-spin-flip intensity that does not exhibit a peak. (b) Total sum of the spin-flip scattering and the corresponding spin-flip background. (c) Spin-flip scattering for the different orientations of the neutron polarization including the spin-flip background. (d) The out-of-plane and in-plane susceptibilities obtained from (c) and Eqs. (3, 4, 5). (e),(f) The corresponding results obtained at 300 K.

Figure 2

Results of the scans across the incommensurate position at $\mathbf{Q}=(1.3,0.3,0)$ for different energies at $T=1.5\mathrm{K}$. Closed symbols designate the spin-flip scattering in the $I_{\parallel }$ channel and open symbols the spin-flip background. Lines are guides to the eye.

Figure 3

Energy dependence of the anisotropy ratio ${\chi }_{zz}^{\prime \prime }/{\chi }_{a,b}^{\prime \prime }$ of the incommensurate fluctuations measured at $(1.3,0.3,0)$ (points); the NMR result by Ishida et al. [14] and the two values obtained at $\mathbf{Q}=(0.7,0.3,0)$ corresponding to the peak height and integrated intensity, respectively, are denoted by stars, and the line represents the energy dependence obtained for the parameters discussed in the text.

Figure 4

Results of the scans across the incommensurate position at $(0.7,0.3,0)$ for 8 meV and 1.5 K in diagonal direction. For $k=1$, $\mathbf{Q}$ is $(1,0,0)$ corresponding to the two-dimensional ferromagnetic zone center, all polarization configurations are shown. The inset presents the spin-flip scattering and its background close to the ferromagnetic zone center.