Resonant magnetic x-ray scattering in the antiferromagnet $\mathrm{Ce}{\left({\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x\right)}_2$

Magnetic resonant x-ray scattering experiments have been performed in Co-doped $\mathrm{Ce}{\mathrm{Fe}}_2$ at Ce $L_{2,3}$ and Fe $K$ edges in the antiferromagnetic state. We could confirm a previous result that Ce moments lie parallel to the distortion rhombohedral axis ⟨111⟩ and Fe magnetic moments are arranged in a noncollinear structure by combining experimental data and numerical ab initio calculations at the Fe $K$ edge. Interestingly, we were also able to qualitatively reproduce the main three peaks in the energy scan at Ce $L$ edges by means of single-particle relativistic multiple-scattering calculations, provided that we extend the cluster radius up to the third shell of Ce nearest neighbors. We not only proved the main dipolar character of these resonances but also identified a non-negligible quadrupolar contribution. These results have suggested analyzing the orbital character of each peak through an azimuth scan. Experimentally, only the lower-energy peak showed the azimuth modulation expected for a quadrupolar transition. These findings, pointing to a single energy-position of $4f$ states, have a natural theoretical framework in a “monovalence” model, instead of the usually adopted “mixed-valence” model. Further analysis in the future would be desirable to clarify this fundamental issue. Finally, the magnetic phase diagram under applied magnetic field is also reported and compared to previous neutron scattering data.

Figure 1

XANES spectra at $L_3$ (upper panel) and $L_2$ (lower panel) edges of Ce taken at $T=13\mathrm{K}$. The data are collected in fluorescence mode and are normalized in terms of absorption coefficient. The solid lines correspond to the fit described in the text according to Eq. (1).

Figure 2

(Color online) (a) Crystallographic and (b) magnetic domain formations in the 7% Co doped $\mathrm{Ce}{\mathrm{Fe}}_2$: (a) (222) Bragg reflection measured at $75\mathrm{K}$ (open circles) above the rhombohedral distortion and at $50\mathrm{K}$ (closed circles) in the antiferromagnetic phase. The inset shows the rhombohedral distortion of the cubic unit cell and the relative directions of the Ce magnetic moments (thick arrows). (b) $(\frac{5}{2},\frac{5}{2},\frac{5}{2})$ magnetic domains measured at the nonresonant energy $E=5.600\mathrm{keV}$ in the $\sigma -{\pi }^{\prime }$ channel. The inset shows the temperature dependence of the integrated intensities of the AF reflection $(\frac{5}{2},\frac{5}{2},\frac{5}{2})$ measured by neutron scattering (open circles) and x-ray scattering (closed circles).

Figure 3

Energy dependence of RXMS intensities collected at $T=12\mathrm{K}$ in $\sigma -{\pi }^{\prime }$ polarization channel across the $L_3$ edge of Ce for specular magnetic reflections. The magnetic intensities are corrected for the absorption coefficient $2\mu$ (top panel) following the fitting procedure described in the text (continuous lines). The broken lines are the results of the fit without the nonresonant contribution.

Figure 4

Energy dependence of resonant magnetic scattering intensities collected at $T=12\mathrm{K}$ in $\sigma -{\pi }^{\prime }$ channel at the $L_2$ edge for two specular magnetic Bragg reflections. The data are corrected for absorption, as in Fig. 3.

Figure 5

Energy dependence of RXMS intensities (dots) collected across the Fe $K$ edge in the rotated $\sigma -{\pi }^{\prime }$ polarization channel (from Ref. 8). The continuous line is the ab initio calculation with the FDMNES program (Ref. 14) and the broken line represents the photoabsorption coefficient collected in the fluorescence yield mode.

Figure 6

(Color online) Primitive cubic cell $\left(Fd\overline{3}m\right)$ and low temperature magnetic structure of $\mathrm{Ce}{\left({\mathrm{Co}}_{0.07}{\mathrm{Fe}}_{0.93}\right)}_2$ determined by combined neutron and x-ray scattering experiments. The open arrows indicate the ⟨111⟩ direction of the Ce magnetic moments, whereas the closed arrows show the two noncollinear Fe magnetic moment directions along the ⟨111⟩ direction for the $\mathrm{Fe}3e$ site and along $⟨1\overline{1}0⟩$ for the $\mathrm{Fe}1b$ site (from Ref. 8).

Figure 7

Experimental data (open circles) and calculated (lines) absorption and RXMS spectra of the AF reflections at the Ce $L_3$ edge. The experimental RMXS intensities are obtained by subtraction of the nonresonant magnetic x-ray signal using the fitting procedure, as described in Sec. 2 [Eq. (4)].

Figure 8

Dependence of the $d_{\uparrow }$ density of states on the radius $R$ of the cluster (expressed in angstrom units).

Figure 9

Energy scans of the reflection $(\frac{5}{2},\frac{5}{2},\frac{5}{2})$ collected at different azimuth angles $\psi$ and normalized at $E_3=5.733\mathrm{keV}$ (rough data without absorption corrections). The inset shows the azimuthal dependence of the resonant amplitudes $A_i^{\mathit{res}}$ determined by the fitting procedure described in Eq. (4), and normalized at $E_3$.

Figure 10

Field dependence of the $(\frac{5}{2},\frac{5}{2},\frac{5}{2})$ magnetic reflection at Ce $L_3$ edge $(E=5.721\mathrm{keV})$ at 2.5 and $4\mathrm{K}$ for the 10% Co (circles) and 7% Co (square) doped samples, respectively. The arrows indicate the field hysteresis loop across the phase transition.

Figure 11

Magnetic phase diagram determined for the 10% (closed circles) and 7% (open circles) Co doped samples. The neutron data for the 7% doped sample (diamonds) are taken from Ref. 13. The inset shows the zero field cooling RMXS intensities as a function of the magnetic field at different temperatures for the 10% Co doped sample.