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Magnetic structure of CeRhIn$_{5}$ under magnetic field

The magnetically ordered ground state of CeRhIn$_{5}$ at ambient pressure and zero magnetic field is an incomensurate helicoidal phase with the propagation vector $\bf{k}$=(1/2, 1/2, 0.298) and the magnetic moment in the basal plane of the tetragonal structure. We determined by neutron diffraction the two different magnetically ordered phases of CeRhIn$_{5}$ evidenced by bulk measurements under applied magnetic field in its basal plane. The low temperature high magnetic phase corresponds to a sine-wave structure of the magnetization being commensurate with $\bf{k}$=(1/2, 1/2, 1/4). At high temperature, the phase is incommensurate with $\bf{k}$=(1/2, 1/2, 0.298) and a possible small ellipticity. The propagation vector of this phase is the same as the one of the zero-field structure.