Abstract
We determine the low-field ordered magnetic phases of the $S=1$ dimerized antiferromagnet Ba$_3$Mn$_2$O$_8$ using single crystal neutron diffraction. We find that for magnetic fields between $\mu_0 H=8.80$~T and $10.56$~T applied along the $[1\bar{1}0]$ direction the system exhibits spin density wave order with incommensurate wave vectors of type $(\eta,\eta,\epsilon)$. For $\mu_0 H > 10.56$~T, the magnetic order changes to a spiral phase with incommensurate wave vectors only along the $[hh0]$ direction. For both field induced ordered phases, the magnetic moments are lying in the plane perpendicular to the field direction. The nature of these two transitions is fundamentally different: the low-field transition is a second order transition to a spin-density wave ground state, while the one at higher field, toward the spiral phase, is of first order.
