  We report a soft x-ray resonant magnetic scattering study of the spin
configuration in multiferroic thin films of Co$_{0.975}$Ge$_{0.025}$Cr$_2$O$_4$
(Ge-CCO) and CoCr$_2$O$_4$ (CCO), under low- and high-magnetic fields, from 0.2
T up to 6.5 T. A characterization of Ge-CCO at a low magnetic field is
performed and the results are compared to those of pure CCO. The ferrimagnetic
phase transition temperature $T_C \approx 95$ K and the multiferroic transition
temperature $T_S \approx 27$ K in Ge-CCO are comparable to those observed in
CCO. In Ge-CCO, the ordering wave vector $\textit{(qq0)}$ observed below $T_S$
is slightly larger compared to 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.
