Resonant soft x-ray magnetic scattering from the $4f$ and $3d$ electrons in $\mathrm{Dy}{\mathrm{Fe}}_4{\mathrm{Al}}_8$: Magnetic interactions in a cycloidal antiferromagnet

Soft x-ray resonant scattering has been used to examine the charge and magnetic interactions in the cycloidal antiferromagnetic compound $\mathrm{Dy}{\mathrm{Fe}}_4{\mathrm{Al}}_8$. By tuning to the Dy $M_4$ and $M_5$ absorption edges and the Fe $L_2$ and $L_3$ absorption edges, we can directly observe the behavior of the Dy $4f$ and Fe $3d$ electron shells. Magnetic satellites surrounding the (110) Bragg peak were observed below $65\mathrm{K}$. The diffraction peaks display complex spectra at the Dy $M_5$ edge, indicative of a split $4f$ electron band. This is in contrast to the simple resonance observed at the Fe $L_3$ absorption edge, which probes the Fe $3d$ electron shell. Temperature-dependent measurements detail the ordering of the magnetic moments on both the iron and the dysprosium antiferromagnetic cycloids. The ratio between the superlattice peak intensities of the Dy $M_4$ and $M_5$ absorption edges remained constant throughout the temperature range, in contrast to a previous study conducted at the Dy $L_{2,3}$ edges. Our results demonstrate the ability of soft x-ray diffraction to separate the individual magnetic components in complicated multielement magnetic structures.

Figure 1

(Color online) Crystal structure of $\mathrm{Dy}{\mathrm{Fe}}_4{\mathrm{Al}}_8$. The dysprosium (large dark blue) atoms are at the origin and the center of the unit cell in a cage formed by the eight iron (red) atoms. The remaining atomic positions are those of aluminum (small light green).

Figure 2

Superlattice peaks measured at the Dy $M_5$ edge in the [110] direction from the origin at $20\mathrm{K}$. Data measured at X1B.

Figure 3

Scattered x-ray intensity as a function of incident photon energy at the constant wave vector of $\vec{Q}=\left(\mathrm{a}\right)$ (110) (b) $(1-\tau ,1-\tau ,0)$, and (c) $(1-2\tau ,1-2\tau ,0)$ through the Dy $M_4$ and $M_5$ edges. Data measured at $20\mathrm{K}$ (ID08).

Figure 4

(Color online) (a) Position and (b) integrated intensity of the $(1-\tau ,1-\tau ,0)$ and $(1-2\tau ,1-2\tau ,0)$ superlattice peaks measured at the Dy $M_5$ edge as a function of temperature. The inset of (b) shows the same plot on a logarithmic scale. This clarifies the existence of a signal up to $65\mathrm{K}$. (c) Temperature dependence of the integrated intensity $(1-\tau ,1-\tau ,0)$ and $(1-2\tau ,1-2\tau ,0)$ superlattice peaks as measured at the Dy $M_4$ edge. (d) shows the ratio of the integrated intensity of the superlattice peaks at the $M_5$ and $M_4$ edges. Note that the integrated intensities in (b) and (c) are normalized. Data measured at X1B.

Figure 5

(Color online) Intensity of the scattered x-ray beam at the Fe $L_3$ edge along [110]. The small peak at (0.5, 0.5, 0) is $\lambda ∕2$ leakthrough from the (110) Bragg peak, while the $(1-3\tau ,1-3\tau ,0)$ satellite can be seen as the weak peak near (0.6, 0.6, 0). The inset plot shows the widths of the $(1-3\tau ,1-3\tau ,0)$ satellite peaks at both the Fe $L_3$ edge and Dy $M_5$ edge. In addition the (001) Bragg peak at the Dy $M_5$ edge is shown.

Figure 6

Scattered x-ray intensity as a function of incident photon energy at the constant wave vector $\vec{Q}=(1-3\tau ,1-3\tau ,0)$, measured through the Fe $L_{2,3}$ edges. No signal was observed at the Fe $L_1$ edge. The scan was conducted at $17\mathrm{K}$ at X1B.

Figure 7

(Color online) Temperature dependence of the (a) wave vector and (b) intensity of the $(1-3\tau ,1-3\tau ,0)$ peak at the Fe $L_3$ edge. The integrated intensity of the $(1-3\tau ,1-3\tau ,0)$ peak as measured at the Dy $M_5$ edge as a function of temperature. (c) is shown for comparison. Data measured at X1B.