Field induced spin density and spiral phases in a layered antiferromagnet

We will present neutron scattering measurements examining the low-field ordered magnetic phases of the $S=1$ dimerized antiferromagnet Ba$_3$Mn$_2$O$_8$. We have found that for magnetic both spin density wave order with incommensurate wave vectors and a higher field 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. More recent SANS measurements of the magnetic phases with H $||$ c will be presented if available at the time of the meeting.