Magnetic field dependent cycloidal rotation in pristine and Ge-doped ${\mathrm{CoCr}}_2{\mathrm{O}}_4$

We report a soft x-ray resonant magnetic scattering study of the spin configuration in multiferroic thin films of ${\mathrm{Co}}_{0.975}{\mathrm{Ge}}_{0.025}{\mathrm{Cr}}_2{\mathrm{O}}_4$ (Ge-CCO) and ${\mathrm{CoCr}}_2{\mathrm{O}}_4$ (CCO) under low and high magnetic fields from 0.2 to 6.5 T. A characterization of Ge-CCO at a low magnetic field was performed, and the results were compared with those of pure CCO. The ferrimagnetic phase transition temperature $T_C\approx 95\mathrm{K}$ and the multiferroic transition temperature $T_S\approx 27\mathrm{K}$ in Ge-CCO are comparable with those observed in CCO. In Ge-CCO, the ordering wave vector ($qq0$) observed below $T_S$ is slightly larger compared with that of CCO, and unlike CCO, the diffraction intensity consists of two contributions that show a dissimilar x-ray polarization dependence. In Ge-CCO, the coercive field observed at low temperatures was larger than the one reported for CCO. In both compounds, an unexpected reversal of the spiral helicity, and therefore the electric polarization, was observed on simply magnetic field cooling. In addition, we find a change in the helicity as a function of momentum transfer in the magnetic diffraction peak of Ge-CCO, indicative of the presence of multiple magnetic spirals.

Figure 1

Experimental geometry used in the Resonant Elastic Soft X-ray Scattering end station.

Figure 2

Layout of x-ray exited optical luminescence (XEOL) experiment.

Figure 3

Schematic representation of the experimental geometry. For ($qq0$) reflection, the detector was placed at $2\theta ={140}^{\circ }$ with an incident angle (θ) of 69.75°. The magnetic field during measurements was rotated by an angle $\alpha =32.5^{\circ }$ from incoming x-ray beam.

Figure 4

(a) X-ray reflectivity of Ge-CCO at $T=10\mathrm{K}$ around the $\mathrm{Co}{L}_{2,3}$ edges when field cooled (FC) at 0.2 T, for circular right (${\mathrm{C}}_{+}$) and left (${\mathrm{C}}^{-}$) polarizations. (b) Asymmetry as a function of energy. The dashed line indicates the energy with the largest asymmetry (in absolute values). (c) Magnetic asymmetry as a function of temperature measured at $\mathrm{Co}{L}_3$ edge [energy of the dashed line in (b)], for a sample FC at 0.2 T. The pink dashed line estimates $T_C$. The small asymmetry offset above the Curie temperature is presumably due to an imperfect normalization procedure.

Figure 5

(a) Temperature dependence of the magnetic diffraction peak ($qq0$) of Ge-CCO upon warming, after field cooling in 0.2 T and using ${\mathrm{C}}_{+}$ polarized x rays at 780 eV. The data are presented as a function of both reciprocal lattice units (r.l.u.) (bottom axis) and total momentum transfer ($Q$) (top axis). (b)–(d) represent the temperature dependence of integrated intensity, modulation parameter $q$, and the correlation length $\xi$ extracted from the full width at half maximum (FWHM) of data shown in (a).

Figure 6

Magnetic diffraction ($qq0$) peak for circular and linear polarizations with their respective linear and circular dichroism for (a) and (b) CCO and (c) and (d) Ge-CCO. Data collected at 779 eV.

Figure 7

(a) X-ray absorption spectroscopy (XAS) (black) and integrated XAS (red) of $\mathrm{Co}{L}_{2,3}$ edge on Ge-CCO collected in x-ray exited optical luminescence (XEOL) mode at 10 K, under 6.8 T and field cooled (FC) at −0.2 T. The integrated XAS has been calculated after removal of the two-steplike function (blue). (b) XMCD data obtained from (a).

Figure 8

Magnetic hysteresis loop of Co sublattice in Ge-CCO for various temperatures measured in x-ray exited optical luminescence (XEOL) mode.

Figure 9

Energy dependence of the magnetic diffraction ($qq0$) peak for ${\mathrm{C}}_{+}$ and ${\mathrm{C}}^{-}$ polarizations for (a) pure CCO and (b) Ge-CCO at 5 K, under magnetic field applied of −6 T after field cooled (FC) at −6 T. Energy dependence of the circular dichroism of the ($qq0$) peak for (c) pure CCO and (d) Ge-CCO. Dashed lines indicate the energy corresponding to the extrema of circular dichroism.

Figure 10

Intensity of magnetic diffraction peak ($qq0$) of (a) pure CCO and (b) Ge-CCO for various magnetic fields at 779 eV. At 5 K, data collected with ${\mathrm{C}}_{+}$ polarized light, field cooled at $-1\mathrm{T}$. The origin of the artifact around $q\approx 0.712$ is explained in the text.

Figure 11

Helicity contrast of the ($qq0$) peak for various magnetic fields at 5 K on (a) and (b) pure CCO and (c) and (d) Ge-CCO at 779 eV. (a) and (c) panels are for negative magnetic field cases and (b) and (d) for positive magnetic field cases. Insets in (a) and (b) panels are the sketch of the magnetic modulation vector (orange arrows) and magnetic moments (green arrows). The slight vertical shift between both field cooled (FC) processes for pristine CCO and Ge-CCO is likely to be an experimental artifact, which is in the order of the uncertainty of our experimental data.

Figure 12

Helicity contrast of the ($qq0$) reflection for various magnetic fields after subtracting the zero-field signal. Results of (a) and (b) CCO and (c) and (d) Ge-CCO for negative field cooling (FC) and positive FC, respectively.