Magnetic Ground State of Pure and Doped ${\mathrm{C}\mathrm{e}\mathrm{F}\mathrm{e}}_2$

A combination of neutron elastic and inelastic, resonant x-ray scattering, and ${}^{\mathrm{57}}\mathrm{F}\mathrm{e}$ Mössbauer experiments are used to determine the unusual magnetic ground state of $\mathrm{C}\mathrm{e}\mathrm{F}{\mathrm{e}}_{\mathrm{2}}$. The complementarities between different time-scale techniques may allow one to understand the dynamic features of the ground state in ${\mathrm{C}\mathrm{e}\mathrm{F}\mathrm{e}}_2$ and its pseudobinary compounds, and how the frustration of Fe tetrahedra leads the appearance of antiferromagnetic fluctuations in the presence of ferrimagnetism. The resulting model can be used to rationalize many of the unusual and conflicting experimental results reported for this material in the literature.

Figure 1

Contour plots of the dynamical magnetic susceptibility ${\chi }^{\prime \prime }(\mathbf{Q},\omega )$ determined by inelastic neutron scattering at the Laboratoire Léon Brillouin (Saclay, France) around the Brillouin zone boundary $(\frac{3}{2},\frac{3}{2},\frac{3}{2})$, and along the $[111]$ direction. The data are collected at 100 K in the F phase (upper panel) and at 17 K in the AF phase (lower panel). ${\chi }^{\prime \prime }(\mathbf{Q},\omega )$ is obtained collating both constant-$Q$ and constant-$E$ scans, after subtraction of background and phonon contributions, and renormalization of the signal by the Bose factor. The data points (open circles) used for the fits are obtained by deconvolution of constant-$E$ scans with the instrument resolution [9]. The thick lines are the fit of the parabolic F (continuous lines) and of the linear AF (broken lines) spin wave dispersions. Measurements in different Brillouin zones establish that all the inelastic response is associated with the Fe spins [6]. The response at 100 K (above $T_N$ as in top frame) shown here for doped compound is identical to that found in pure $\mathrm{C}\mathrm{e}\mathrm{F}{\mathrm{e}}_{\mathrm{2}}$ as discussed in Ref. 6.

Figure 2

Azimuthal dependence of resonant magnetic x-ray scattering intensities of the reflections $(\frac{5}{2},\frac{5}{2},\frac{5}{2})$ (black points) and $(\frac{5}{2},\frac{5}{2},\frac{3}{2})$ (open points) at Ce $L_3$ edge (upper panel) and Fe $K$ edge (lower panel), taken at 12 K in the $\sigma \mathrm{\text{−}}\pi$ channel. The lines are the calculations of the angular dependence of the resonant intensities with the Ce and the Fe moment directions aligned as shown in Fig. 3. The insets show the energy dependence of the magnetic Bragg reflection $(\frac{5}{2},\frac{5}{2},\frac{5}{2})$ at the Ce $L_3$ edge (upper) and Fe $K$ edge (lower), and the broken lines show the absorption coefficients determined by fluorescence yield at the Ce $L_3$ edge and the Fe $K$ pre-edge.

Figure 3

Magnetic structure in the AF state determined combining neutron and x-ray scattering results (model B in Table ). The Fe sublattice has two inequivalent sites, with $\frac{3}{4}$ of Fe having the magnetic moment direction parallel to [111] (red arrows) and $\frac{1}{4}$ of Fe parallel to the $[1\overline{1}0]$ direction (blue arrows). The Ce magnetic moments point along the [111] direction (green arrows).