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Magnetic domains at the surface of a ferroelectric monodomain BiFeO3 singlecrystal have been imaged by hard X-ray magnetic scattering. Magnetic domains upto several hundred microns in size have been observed, corresponding tocycloidal modulations of the magnetization along the wave-vectork=2\pi(\delta,\delta,0) and symmetry equivalent directions. The rotationdirection of the magnetization in all magnetic domains, determined bydiffraction of circularly polarized light, was found to be unique and inagreement with predictions of a combined approach based on a spin-modelcomplemented by relativistic density-functional simulations. Imaging of thesurface shows that the largest adjacent domains display a 120 degree vortexstructure.

X-ray imaging and multiferroic coupling of cycloidal magnetic domains in ferroelectric monodomain BiFeO3