We examine, both experimentally and theoretically, the behavior of an incommensurate magnetic helicoidal structure in a magnetic field applied in the plane in which spins lie. The experimental study is performed on the multiferroic ${\mathrm{NdFe}}_3{\left({\mathrm{BO}}_3\right)}_4$ using bulk magnetic measurements and single-crystal neutron diffraction. We obtain that the wave vector of the helicoidal magnetic structure remains unchanged upon the field increasing until 0.9 T, when the first-order transition to the commensurate spin-flopped antiferromagnetic structure takes place. We propose a theoretical model describing this field evolution. It is shown that the field-induced distortion of the incommensurate magnetic helix can be deduced from the field evolution of the uniform magnetization and intensities of magnetic satellites measured by the single-crystal neutron diffraction.

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• Magnetic order
• Insulators
• Holstein-Primakoff method
• Neutron diffraction