Unique magnetic structure of ${\mathrm{YbCo}}_2{\mathrm{Si}}_2$

We report on the results of powder and single-crystal neutron diffraction to investigate the magnetic order in ${\mathrm{YbCo}}_2{\mathrm{Si}}_2$ below the Néel temperature $T_{\mathrm{N}}=1.7$ K in detail. Two different magnetically ordered phases can clearly be distinguished. At lowest temperatures a commensurate magnetic structure with a propagation vector ${\mathbf{k}}_1=\left(0.250.251\right)$ is found, while the intermediate phase ($T>0.9$ K) is characterized by an incommensurate magnetic structure with ${\mathbf{k}}_2=\left(0.250.0861\right)$. The magnetic structure in ${\mathrm{YbCo}}_2{\mathrm{Si}}_2$ is in marked contrast to all other known $R{\mathrm{Co}}_2{\mathrm{Si}}_2$ compounds ($R$ = rare earth element) likely due to some itineracy of the Yb $4f$ states being responsible for the magnetism.

Figure 1

Powder neutron-diffraction patterns of ${\mathrm{YbCo}}_2{\mathrm{Si}}_2$ recorded at $T=0.43, 1.1$, and 2 K on E2 with a neutron wavelength $\lambda =2.39$ Å. The nuclear peaks are labeled and the ticks at the bottom denote their position. The arrows indicate magnetic superstructure peaks. The fit to the 2-K data is shown by a solid red line and the deviation of the fit from the data is displayed by the blue line. Data for different temperatures are shifted vertically with respect to each other.

Figure 2

Color-coded intensity map of the reciprocal $\left(hk0\right)$ plane of ${\mathrm{YbCo}}_2{\mathrm{Si}}_2$ (a) at $T=0.45$ K in the ground state, (b) for $T=1.1$ K in the intermediate phase, and (c) in the paramagnetic regime at $T=2$ K. Additional magnetic peaks are visible in (a) and (b) and are highlighted by yellow circles. Likely due to domain population the intensities at the magnetic $(-1.08\pm 0.250)$ positions in (b) are quite low. The intensity maps have been extracted from the raw single-crystal neutron-diffraction data recorded on SXD.

Figure 3

Scans along $\left[100\right]$ and $\left[010\right]$ across (a,b) the magnetic peak at $\mathbf{Q}\approx \left(0.250.750\right)$ at $T=0.27$ K and (c,d) the magnetic reflection at $\mathbf{Q}\approx \left(0.0860.750\right)$ in the intermediate phase at $T=1.1$ K. Solid lines indicate fits of the magnetic peaks with Gaussian line shape. Data are taken on TAS-2.

Figure 4

Difference neutron-diffraction patterns of ${\mathrm{YbCo}}_2{\mathrm{Si}}_2$ (a) in the ground state at $T=0.45$ K and (b) in the intermediate phase at $T=1.1$ K obtained by subtracting the powder pattern measured at $T=2.0$ K (data of Fig. 1). Red solid lines indicate fits of the magnetic structure to the data (see main text) while blue lines show the deviations of the fits from the experimental data. The row of ticks at the bottom of each panel denote the magnetic peaks corresponding to the appropriate propagation vectors ${\mathbf{k}}_1=\left(0.250.251\right)$ in (a) and ${\mathbf{k}}_2=\left(0.250.0861\right)$ in (b).

Figure 5

(a) Integrated intensity of several magnetic superstructure peaks vs temperature in ${\mathrm{YbCo}}_2{\mathrm{Si}}_2$ as deduced from the powder-diffraction data. (b) Temperature dependence of the ordered magnetic moment as extracted from fits to the whole powder-diffraction patterns. Dashed lines are guides to the eyes, while the red solid lines are power-law fits to the data as described in the main text. Inset: Low-angle part of the difference neutron-diffraction pattern at $T=0.9$ K together with fit (solid line) showing coexisting superstructure peaks of both magnetic phases.

Figure 6

(a) Magnetic structure of the Yb sublattice in ${\mathrm{YbCo}}_2{\mathrm{Si}}_2$ in the ground state at $T<T_L\approx 0.9$ K. (b) The proposed amplitude-modulated magnetic structure (only the tetragonal basal plane is displayed) in the intermediate, incommensurate phase at $T_L<T<T_{\mathrm{N}}\approx 1.7$ K with moments in the basal plane.

Figure 7

Difference neutron-diffraction patterns of ${\mathrm{YbCo}}_2{\mathrm{Si}}_2$ (a) in the ground state at $T=0.45$ K and (b) in the intermediate phase at $T=1.1$ K obtained by subtracting the powder pattern measured at $T=2.0$ K (data of Fig. 1). Solid lines indicate fits of different magnetic structure models to the data. Arrows indicate some pronounced deviations of the fits from the data. The row of ticks at the bottom of each panel denote the magnetic peaks corresponding to the appropriate propagation vectors ${\mathbf{k}}_1=\left(0.250.251\right)$ in (a) and ${\mathbf{k}}_2=\left(0.250.0861\right)$ in (b). In addition, strong magnetic peaks are indexed. Different model fits (together with the corresponding data) are shifted vertically with respect to each other.