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

${\mathrm{MnSb}}_{2}{\mathrm{O}}_{6}$ is based on the structural chiral $P321$ space group No. 150 where the magnetic ${\mathrm{Mn}}^{2+}$ moments $(S=5/2,$ $L\ensuremath{\approx}0)$ order antiferromagnetically at ${T}_{\mathrm{N}}=12\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. Unlike the related iron based langasite $({\mathrm{Ba}}_{3}{\mathrm{NbFe}}_{3}{\mathrm{Si}}_{2}{\mathrm{O}}_{14})$ where the low-temperature magnetism is based on a proper helix characterized by a time-even pseudoscalar ``magnetic'' chirality, the ${\mathrm{Mn}}^{2+}$ ions in ${\mathrm{MnSb}}_{2}{\mathrm{O}}_{6}$ order with a cycloidal structure at low temperatures, described instead by a time-even vector ``magnetic'' polarity. A tilted cycloidal structure has been found [M. Kinoshita et al., Phys. Rev. Lett. 117, 047201 (2016)] to facilitate ferroelectric switching under an applied magnetic field. In this work, we apply polarized and unpolarized neutron diffraction analyzing the magnetic and nuclear structures in ${\mathrm{MnSb}}_{2}{\mathrm{O}}_{6}$ with the aim of understanding this magnetoelectric coupling. We find no evidence for a helicoidal magnetic structure with one of the spin envelope axes tilted away from the cycloidal $c$ axis. However, on the application of a magnetic field $\ensuremath{\parallel}\phantom{\rule{4pt}{0ex}}\mathbit{c}$ the spin rotation plane can be tilted, giving rise to a cycloid---helix admixture that evolves towards a distorted helix (zero cycloidal component) for fields great than $\ensuremath{\approx}2$ T. We propose a mechanism for the previously reported ferroelectric switching based on coupled structural and magnetic chiralities requiring only an imbalance of structural chiral domains.