Ba2MgMnO4 crystallizes in the monoclinic Cm space group. There are two inequivalent Ba sites. In the first Ba site, Ba(1) is bonded to one O(2) and four equivalent O(3) atoms to form BaO5 square pyramids that share corners with four equivalent Ba(1)O5 square pyramids,  a cornercorner with one Mg(1)O5 trigonal bipyramid, and edges with four equivalent Ba(1)O5 square pyramids. In the second Ba site, Ba(2) is bonded in a 5-coordinate geometry to one O(3) and four equivalent O(2) atoms. Mg(1) is bonded to one O(2) and four equivalent O(1) atoms to form distorted MgO5 trigonal bipyramids that share  a cornercorner with one Ba(1)O5 square pyramid and corners with four equivalent Mg(1)O5 trigonal bipyramids. Mn(1) is bonded in a 5-coordinate geometry to one O(3) and four equivalent O(1) atoms. There are three inequivalent O sites. In the first O site, O(1) is bonded in a 4-coordinate geometry to two equivalent Mg(1) and two equivalent Mn(1) atoms. In the second O site, O(2) is bonded to one Ba(1), four equivalent Ba(2), and one Mg(1) atom to form distorted OBa5Mg octahedra that share corners with four equivalent O(2)Ba5Mg octahedra, edges with four equivalent O(2)Ba5Mg octahedra, and edges with four equivalent O(3)Ba5Mn octahedra. The corner-sharing octahedral tilt angles are 9°. In the third O site, O(3) is bonded to one Ba(2), four equivalent Ba(1), and one Mn(1) atom to form OBa5Mn octahedra that share corners with four equivalent O(3)Ba5Mn octahedra, edges with four equivalent O(2)Ba5Mg octahedra, and edges with four equivalent O(3)Ba5Mn octahedra. The corner-sharing octahedral tilt angles are 4°.
Ba2MgMnO4 crystallizes in the monoclinic Cm space group. There are two inequivalent Ba sites. In the first Ba site, Ba(1) is bonded to one O(2) and four equivalent O(3) atoms to form BaO5 square pyramids that share corners with four equivalent Ba(1)O5 square pyramids,  a cornercorner with one Mg(1)O5 trigonal bipyramid, and edges with four equivalent Ba(1)O5 square pyramids. The Ba(1)-O(2) bond length is 2.58 Å. There are a spread of Ba(1)-O(3) bond distances ranging from 2.83-2.87 Å. In the second Ba site, Ba(2) is bonded in a 5-coordinate geometry to one O(3) and four equivalent O(2) atoms. The Ba(2)-O(3) bond length is 2.71 Å. There are a spread of Ba(2)-O(2) bond distances ranging from 2.83-2.88 Å. Mg(1) is bonded to one O(2) and four equivalent O(1) atoms to form distorted MgO5 trigonal bipyramids that share  a cornercorner with one Ba(1)O5 square pyramid and corners with four equivalent Mg(1)O5 trigonal bipyramids. The Mg(1)-O(2) bond length is 2.06 Å. All Mg(1)-O(1) bond lengths are 2.09 Å. Mn(1) is bonded in a 5-coordinate geometry to one O(3) and four equivalent O(1) atoms. The Mn(1)-O(3) bond length is 2.11 Å. All Mn(1)-O(1) bond lengths are 2.17 Å. There are three inequivalent O sites. In the first O site, O(1) is bonded in a 4-coordinate geometry to two equivalent Mg(1) and two equivalent Mn(1) atoms. In the second O site, O(2) is bonded to one Ba(1), four equivalent Ba(2), and one Mg(1) atom to form distorted OBa5Mg octahedra that share corners with four equivalent O(2)Ba5Mg octahedra, edges with four equivalent O(2)Ba5Mg octahedra, and edges with four equivalent O(3)Ba5Mn octahedra. The corner-sharing octahedral tilt angles are 9°. In the third O site, O(3) is bonded to one Ba(2), four equivalent Ba(1), and one Mn(1) atom to form OBa5Mn octahedra that share corners with four equivalent O(3)Ba5Mn octahedra, edges with four equivalent O(2)Ba5Mg octahedra, and edges with four equivalent O(3)Ba5Mn octahedra. The corner-sharing octahedral tilt angles are 4°.