  Applying a magnetic field in the hexagonal plane of YMn$_6$Sn$_6$ leads to a
complex magnetic phase diagram of commensurate and incommensurate phases, one
of which coexists with the topological Hall effect (THE) generated by a unique
fluctuation-driven mechanism. Using unpolarized neutron diffraction, we report
on the solved magnetic structure for two previously identified, but unknown,
commensurate phases. These include a low-temperature, high-field fan-like phase
and a room-temperature, low-field canted antiferromagnetic phase. An
intermediate incommensurate phase between the fan-like and forced ferromagnetic
phases is also identified as the last known phase of the in-plane
field-temperature diagram. Additional characterization using synchrotron powder
diffraction reveals extremely high-quality, single-phase crystals, which
suggests that the presence of two incommensurate magnetic structures throughout
much of the phase diagram is an intrinsic property of the system.
Interestingly, polarized neutron diffraction shows that the centrosymmetric
system hosts preferential chirality in the zero-field double-flat-spiral phase,
which, along with the THE, is a topologically non-trivial characteristic.
