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MnSb$_{2}$O$_{6}$ is based on the structural chiral $P$321 space group #150where the magnetic Mn$^{2+}$ moments ($S=5/2$, $L\approx 0$) orderantiferromagnetically at $T_\mathrm{N}=12$ K. Unlike the related iron basedlangasite (Ba$_3$NbFe$_3$Si$_2$O$_{14}$) where the low temperature magnetism isbased on a proper helix characterized by a time-even pseudoscalar `magnetic'chirality, the Mn$^{2+}$ ions in MnSb$_{2}$O$_{6}$ order with a cycloidalstructure at low temperatures, described instead by a time-even vector`magnetic' polarity. A tilted cycloidal structure has been found [M. Kinoshitaet al. Phys. Rev. Lett. 117, 047201 (2016)] to facilitate ferroelectricswitching under an applied magnetic field. In this work, we apply polarized andunpolarized neutron diffraction analyzing the magnetic and nuclear structuresin MnSb$_{2}$O$_{6}$ with the aim of understanding this magnetoelectriccoupling. We find no evidence for a helicoidal magnetic structure with one ofthe spin envelope axes tilted away from the cycloidal $c$-axis. However, onapplication of a magnetic field $\parallel$ $\vec{c}$ the spin rotation planecan be tilted, giving rise to a cycloid-helix admixture that evolves towards adistorted helix (zero cycloidal component) for fields great than $\approx$ 2 T.We propose a mechanism for the previously reported ferroelectric switchingbased on coupled structural and magnetic chiralities requiring only animbalance of structural chiral domains.

Neutron diffraction in MnSb2O6: Magnetic and structural domains in a helicoidal polar magnet with coupled chiralities