Commensurate phase of multiferroic ${\text{HoMn}}_2{\text{O}}_5$ studied by x-ray magnetic scattering

The commensurate phase of multiferroic ${\text{HoMn}}_2{\text{O}}_5$ was studied by x-ray magnetic scattering, both off-resonance and in resonant conditions at the $\text{Ho}{L}_3$ edge. Below 40 K, magnetic ordering at the Ho sites is induced by the main Mn magnetic order parameter, and its temperature dependence is well accounted for by a simple Curie–Weiss susceptibility model. A lattice distortion of periodicity twice that of the magnetic order is also evidenced. The azimuthal scans confirm the model of the magnetic structure recently refined from neutron diffraction data for both Mn and Ho sites, indicating that the two sublattices interact via magnetic superexchange.

Figure 1

(Color online) Energy dependence of the magnetic reflection (2.5 3 0.25) and of the fluorescence background around the $\text{Ho}{L}_3$ resonance energy. The quadrupole and dipole contribution at the resonance occurs at 8.068 and 8.076 keV, respectively. At higher energy, the oscillations of the signal, not studied here, are probably related to magnetic EXAFS.

Figure 2

(Color online) Left: Integrated intensities of various Bragg peaks as a function of temperature. The intensity of the magnetic reflection (2.5 3 0.25), collected on warming, is shown off resonance at 6.4 keV (circles) and at the $\text{Ho}{L}_3$ edge at 8.076 keV (squares). The superstructure charge reflection (4 4 0.5) was measured off resonance at 7.96 keV (triangles). Right: Intensity of the (4 4 0.5) superstructure peak against the intensity of the (2.5 3 0.25) peak, for the temperature range of 25–40 K. The line corresponds to a fit with a quadratic law.

Figure 3

Intensity of the resonant magnetic Bragg peak (2.5 3 0.25) as a function of temperature (open symbols). The line corresponds to a fit with a modified low-field Brillouin (Curie–Weiss) function depending on the Mn molecular field (see text for details). The inset shows the dependence for other Bragg peaks at the $\text{Ho}{L}_3$ edge and illustrates that the same overall behavior, with some deviations, is observed irrespective of the scattering vector or azimuth angle.

Figure 4

(Color online) Azimuthal dependence of the magnetic Bragg peak intensities at 25 K. The azimuth $\psi$ value is given with respect to a reference in the (0 0 1) direction. Upper panel: (2.5 3 0.25) reflection, in nonresonant condition at 6.4 keV, in the $\sigma \to \sigma$ (squares) and $\sigma \to \pi$ (crosses) channels, respectively. Lower panel: (2.5 3 0.25) (circles) and (3.5 4 0.25) (dots) reflections at 8.076 keV ($\text{Ho}{L}_3$ edge). The symbols with associated error bars show the experimental data points. The straight lines are calculations performed with the model of the magnetic structure from Ref. 7.