TbBaMn2O6 crystallizes in the triclinic P-1 space group. There are two inequivalent Ba sites. In the first Ba site, Ba(1) is bonded to one O(1), one O(11), one O(12), one O(2), one O(6), two equivalent O(3), two equivalent O(9), and three equivalent O(5) atoms to form distorted BaO12 cuboctahedra that share corners with two equivalent Ba(1)O12 cuboctahedra, corners with two equivalent Ba(2)O12 cuboctahedra, faces with two equivalent Ba(1)O12 cuboctahedra, faces with two equivalent Ba(2)O12 cuboctahedra,  a faceface with one Mn(2)O6 octahedra,  a faceface with one Mn(4)O6 octahedra, faces with three equivalent Mn(1)O6 octahedra, and faces with three equivalent Mn(3)O6 octahedra. In the second Ba site, Ba(2) is bonded to one O(1), one O(11), one O(12), one O(2), one O(5), two equivalent O(10), two equivalent O(4), and three equivalent O(6) atoms to form BaO12 cuboctahedra that share corners with two equivalent Ba(1)O12 cuboctahedra, corners with two equivalent Ba(2)O12 cuboctahedra, faces with two equivalent Ba(1)O12 cuboctahedra, faces with two equivalent Ba(2)O12 cuboctahedra,  a faceface with one Mn(1)O6 octahedra,  a faceface with one Mn(3)O6 octahedra, faces with three equivalent Mn(2)O6 octahedra, and faces with three equivalent Mn(4)O6 octahedra. There are two inequivalent Tb sites. In the first Tb site, Tb(1) is bonded in a 9-coordinate geometry to one O(1), one O(11), one O(12), one O(2), one O(7), two equivalent O(3), and two equivalent O(9) atoms. In the second Tb site, Tb(2) is bonded in a 11-coordinate geometry to one O(1), one O(11), one O(12), one O(2), one O(7), two equivalent O(10), two equivalent O(4), and two equivalent O(8) atoms. There are four inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to one O(1), one O(11), one O(3), one O(5), one O(7), and one O(9) atom to form MnO6 octahedra that share corners with two equivalent Mn(4)O6 octahedra, corners with four equivalent Mn(3)O6 octahedra,  a faceface with one Ba(2)O12 cuboctahedra, and faces with three equivalent Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 4-19°. In the second Mn site, Mn(2) is bonded to one O(10), one O(12), one O(2), one O(4), one O(6), and one O(8) atom to form MnO6 octahedra that share corners with two equivalent Mn(3)O6 octahedra, corners with four equivalent Mn(4)O6 octahedra,  a faceface with one Ba(1)O12 cuboctahedra, and faces with three equivalent Ba(2)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 3-16°. In the third Mn site, Mn(3) is bonded to one O(12), one O(2), one O(3), one O(5), one O(7), and one O(9) atom to form MnO6 octahedra that share corners with two equivalent Mn(2)O6 octahedra, corners with four equivalent Mn(1)O6 octahedra,  a faceface with one Ba(2)O12 cuboctahedra, and faces with three equivalent Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 4-19°. In the fourth Mn site, Mn(4) is bonded to one O(1), one O(10), one O(11), one O(4), one O(6), and one O(8) atom to form MnO6 octahedra that share corners with two equivalent Mn(1)O6 octahedra, corners with four equivalent Mn(2)O6 octahedra,  a faceface with one Ba(1)O12 cuboctahedra, and faces with three equivalent Ba(2)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 3-16°. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a 6-coordinate geometry to one Ba(1), one Ba(2), one Tb(1), one Tb(2), one Mn(1), and one Mn(4) atom. In the second O site, O(2) is bonded in a 6-coordinate geometry to one Ba(1), one Ba(2), one Tb(1), one Tb(2), one Mn(2), and one Mn(3) atom. In the third O site, O(3) is bonded to two equivalent Ba(1), two equivalent Tb(1), one Mn(1), and one Mn(3) atom to form distorted OBa2Tb2Mn2 octahedra that share corners with two equivalent O(5)Ba4Mn2 octahedra, corners with two equivalent O(6)Ba4Mn2 octahedra, edges with two equivalent O(3)Ba2Tb2Mn2 octahedra, and faces with two equivalent O(5)Ba4Mn2 octahedra. The corner-sharing octahedral tilt angles range from 60-62°. In the fourth O site, O(4) is bonded in a 2-coordinate geometry to two equivalent Ba(2), two equivalent Tb(2), one Mn(2), and one Mn(4) atom. In the fifth O site, O(5) is bonded to one Ba(2), three equivalent Ba(1), one Mn(1), and one Mn(3) atom to form distorted OBa4Mn2 octahedra that share corners with two equivalent O(10)Ba2Tb2Mn2 octahedra, corners with two equivalent O(3)Ba2Tb2Mn2 octahedra, corners with two equivalent O(5)Ba4Mn2 octahedra, corners with two equivalent O(6)Ba4Mn2 octahedra, edges with two equivalent O(5)Ba4Mn2 octahedra, edges with two equivalent O(6)Ba4Mn2 octahedra, and faces with two equivalent O(3)Ba2Tb2Mn2 octahedra. The corner-sharing octahedral tilt angles range from 1-62°. In the sixth O site, O(6) is bonded to one Ba(1), three equivalent Ba(2), one Mn(2), and one Mn(4) atom to form distorted OBa4Mn2 octahedra that share corners with two equivalent O(10)Ba2Tb2Mn2 octahedra, corners with two equivalent O(3)Ba2Tb2Mn2 octahedra, corners with two equivalent O(5)Ba4Mn2 octahedra, corners with two equivalent O(6)Ba4Mn2 octahedra, edges with two equivalent O(5)Ba4Mn2 octahedra, edges with two equivalent O(6)Ba4Mn2 octahedra, and faces with two equivalent O(10)Ba2Tb2Mn2 octahedra. The corner-sharing octahedral tilt angles range from 1-61°. In the seventh O site, O(7) is bonded in a 3-coordinate geometry to one Tb(1), one Tb(2), one Mn(1), and one Mn(3) atom. In the eighth O site, O(8) is bonded in a 2-coordinate geometry to two equivalent Tb(2), one Mn(2), and one Mn(4) atom. In the ninth O site, O(9) is bonded in a 2-coordinate geometry to two equivalent Ba(1), two equivalent Tb(1), one Mn(1), and one Mn(3) atom. In the tenth O site, O(10) is bonded to two equivalent Ba(2), two equivalent Tb(2), one Mn(2), and one Mn(4) atom to form distorted OBa2Tb2Mn2 octahedra that share corners with two equivalent O(5)Ba4Mn2 octahedra, corners with two equivalent O(6)Ba4Mn2 octahedra, edges with two equivalent O(10)Ba2Tb2Mn2 octahedra, and faces with two equivalent O(6)Ba4Mn2 octahedra. The corner-sharing octahedral tilt angles range from 59-62°. In the eleventh O site, O(11) is bonded in a 6-coordinate geometry to one Ba(1), one Ba(2), one Tb(1), one Tb(2), one Mn(1), and one Mn(4) atom. In the twelfth O site, O(12) is bonded in a 6-coordinate geometry to one Ba(1), one Ba(2), one Tb(1), one Tb(2), one Mn(2), and one Mn(3) atom.
TbBaMn2O6 crystallizes in the triclinic P-1 space group. There are two inequivalent Ba sites. In the first Ba site, Ba(1) is bonded to one O(1), one O(11), one O(12), one O(2), one O(6), two equivalent O(3), two equivalent O(9), and three equivalent O(5) atoms to form distorted BaO12 cuboctahedra that share corners with two equivalent Ba(1)O12 cuboctahedra, corners with two equivalent Ba(2)O12 cuboctahedra, faces with two equivalent Ba(1)O12 cuboctahedra, faces with two equivalent Ba(2)O12 cuboctahedra,  a faceface with one Mn(2)O6 octahedra,  a faceface with one Mn(4)O6 octahedra, faces with three equivalent Mn(1)O6 octahedra, and faces with three equivalent Mn(3)O6 octahedra. The Ba(1)-O(1) bond length is 2.87 Å. The Ba(1)-O(11) bond length is 3.04 Å. The Ba(1)-O(12) bond length is 3.00 Å. The Ba(1)-O(2) bond length is 2.88 Å. The Ba(1)-O(6) bond length is 2.76 Å. There is one shorter (2.86 Å) and one longer (2.90 Å) Ba(1)-O(3) bond length. There is one shorter (3.05 Å) and one longer (3.10 Å) Ba(1)-O(9) bond length. There are a spread of Ba(1)-O(5) bond distances ranging from 2.73-2.85 Å. In the second Ba site, Ba(2) is bonded to one O(1), one O(11), one O(12), one O(2), one O(5), two equivalent O(10), two equivalent O(4), and three equivalent O(6) atoms to form BaO12 cuboctahedra that share corners with two equivalent Ba(1)O12 cuboctahedra, corners with two equivalent Ba(2)O12 cuboctahedra, faces with two equivalent Ba(1)O12 cuboctahedra, faces with two equivalent Ba(2)O12 cuboctahedra,  a faceface with one Mn(1)O6 octahedra,  a faceface with one Mn(3)O6 octahedra, faces with three equivalent Mn(2)O6 octahedra, and faces with three equivalent Mn(4)O6 octahedra. The Ba(2)-O(1) bond length is 2.93 Å. The Ba(2)-O(11) bond length is 2.97 Å. The Ba(2)-O(12) bond length is 3.00 Å. The Ba(2)-O(2) bond length is 2.94 Å. The Ba(2)-O(5) bond length is 2.79 Å. There is one shorter (2.82 Å) and one longer (2.88 Å) Ba(2)-O(10) bond length. There is one shorter (2.91 Å) and one longer (2.98 Å) Ba(2)-O(4) bond length. There are a spread of Ba(2)-O(6) bond distances ranging from 2.78-2.82 Å. There are two inequivalent Tb sites. In the first Tb site, Tb(1) is bonded in a 9-coordinate geometry to one O(1), one O(11), one O(12), one O(2), one O(7), two equivalent O(3), and two equivalent O(9) atoms. The Tb(1)-O(1) bond length is 2.49 Å. The Tb(1)-O(11) bond length is 2.61 Å. The Tb(1)-O(12) bond length is 2.64 Å. The Tb(1)-O(2) bond length is 2.54 Å. The Tb(1)-O(7) bond length is 2.38 Å. There is one shorter (2.58 Å) and one longer (2.69 Å) Tb(1)-O(3) bond length. There is one shorter (2.59 Å) and one longer (2.60 Å) Tb(1)-O(9) bond length. In the second Tb site, Tb(2) is bonded in a 11-coordinate geometry to one O(1), one O(11), one O(12), one O(2), one O(7), two equivalent O(10), two equivalent O(4), and two equivalent O(8) atoms. The Tb(2)-O(1) bond length is 2.82 Å. The Tb(2)-O(11) bond length is 2.51 Å. The Tb(2)-O(12) bond length is 2.47 Å. The Tb(2)-O(2) bond length is 2.75 Å. The Tb(2)-O(7) bond length is 2.77 Å. There is one shorter (2.53 Å) and one longer (2.67 Å) Tb(2)-O(10) bond length. There is one shorter (2.66 Å) and one longer (2.68 Å) Tb(2)-O(4) bond length. There is one shorter (2.41 Å) and one longer (2.57 Å) Tb(2)-O(8) bond length. There are four inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to one O(1), one O(11), one O(3), one O(5), one O(7), and one O(9) atom to form MnO6 octahedra that share corners with two equivalent Mn(4)O6 octahedra, corners with four equivalent Mn(3)O6 octahedra,  a faceface with one Ba(2)O12 cuboctahedra, and faces with three equivalent Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 4-19°. The Mn(1)-O(1) bond length is 2.05 Å. The Mn(1)-O(11) bond length is 1.95 Å. The Mn(1)-O(3) bond length is 1.98 Å. The Mn(1)-O(5) bond length is 2.02 Å. The Mn(1)-O(7) bond length is 1.90 Å. The Mn(1)-O(9) bond length is 1.97 Å. In the second Mn site, Mn(2) is bonded to one O(10), one O(12), one O(2), one O(4), one O(6), and one O(8) atom to form MnO6 octahedra that share corners with two equivalent Mn(3)O6 octahedra, corners with four equivalent Mn(4)O6 octahedra,  a faceface with one Ba(1)O12 cuboctahedra, and faces with three equivalent Ba(2)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 3-16°. The Mn(2)-O(10) bond length is 1.97 Å. The Mn(2)-O(12) bond length is 2.03 Å. The Mn(2)-O(2) bond length is 1.91 Å. The Mn(2)-O(4) bond length is 1.96 Å. The Mn(2)-O(6) bond length is 1.99 Å. The Mn(2)-O(8) bond length is 1.93 Å. In the third Mn site, Mn(3) is bonded to one O(12), one O(2), one O(3), one O(5), one O(7), and one O(9) atom to form MnO6 octahedra that share corners with two equivalent Mn(2)O6 octahedra, corners with four equivalent Mn(1)O6 octahedra,  a faceface with one Ba(2)O12 cuboctahedra, and faces with three equivalent Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 4-19°. The Mn(3)-O(12) bond length is 1.95 Å. The Mn(3)-O(2) bond length is 2.07 Å. The Mn(3)-O(3) bond length is 1.96 Å. The Mn(3)-O(5) bond length is 2.02 Å. The Mn(3)-O(7) bond length is 1.91 Å. The Mn(3)-O(9) bond length is 2.03 Å. In the fourth Mn site, Mn(4) is bonded to one O(1), one O(10), one O(11), one O(4), one O(6), and one O(8) atom to form MnO6 octahedra that share corners with two equivalent Mn(1)O6 octahedra, corners with four equivalent Mn(2)O6 octahedra,  a faceface with one Ba(1)O12 cuboctahedra, and faces with three equivalent Ba(2)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 3-16°. The Mn(4)-O(1) bond length is 1.91 Å. The Mn(4)-O(10) bond length is 1.96 Å. The Mn(4)-O(11) bond length is 2.04 Å. The Mn(4)-O(4) bond length is 1.99 Å. The Mn(4)-O(6) bond length is 1.98 Å. The Mn(4)-O(8) bond length is 1.93 Å. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a 6-coordinate geometry to one Ba(1), one Ba(2), one Tb(1), one Tb(2), one Mn(1), and one Mn(4) atom. In the second O site, O(2) is bonded in a 6-coordinate geometry to one Ba(1), one Ba(2), one Tb(1), one Tb(2), one Mn(2), and one Mn(3) atom. In the third O site, O(3) is bonded to two equivalent Ba(1), two equivalent Tb(1), one Mn(1), and one Mn(3) atom to form distorted OBa2Tb2Mn2 octahedra that share corners with two equivalent O(5)Ba4Mn2 octahedra, corners with two equivalent O(6)Ba4Mn2 octahedra, edges with two equivalent O(3)Ba2Tb2Mn2 octahedra, and faces with two equivalent O(5)Ba4Mn2 octahedra. The corner-sharing octahedral tilt angles range from 60-62°. In the fourth O site, O(4) is bonded in a 2-coordinate geometry to two equivalent Ba(2), two equivalent Tb(2), one Mn(2), and one Mn(4) atom. In the fifth O site, O(5) is bonded to one Ba(2), three equivalent Ba(1), one Mn(1), and one Mn(3) atom to form distorted OBa4Mn2 octahedra that share corners with two equivalent O(10)Ba2Tb2Mn2 octahedra, corners with two equivalent O(3)Ba2Tb2Mn2 octahedra, corners with two equivalent O(5)Ba4Mn2 octahedra, corners with two equivalent O(6)Ba4Mn2 octahedra, edges with two equivalent O(5)Ba4Mn2 octahedra, edges with two equivalent O(6)Ba4Mn2 octahedra, and faces with two equivalent O(3)Ba2Tb2Mn2 octahedra. The corner-sharing octahedral tilt angles range from 1-62°. In the sixth O site, O(6) is bonded to one Ba(1), three equivalent Ba(2), one Mn(2), and one Mn(4) atom to form distorted OBa4Mn2 octahedra that share corners with two equivalent O(10)Ba2Tb2Mn2 octahedra, corners with two equivalent O(3)Ba2Tb2Mn2 octahedra, corners with two equivalent O(5)Ba4Mn2 octahedra, corners with two equivalent O(6)Ba4Mn2 octahedra, edges with two equivalent O(5)Ba4Mn2 octahedra, edges with two equivalent O(6)Ba4Mn2 octahedra, and faces with two equivalent O(10)Ba2Tb2Mn2 octahedra. The corner-sharing octahedral tilt angles range from 1-61°. In the seventh O site, O(7) is bonded in a 3-coordinate geometry to one Tb(1), one Tb(2), one Mn(1), and one Mn(3) atom. In the eighth O site, O(8) is bonded in a 2-coordinate geometry to two equivalent Tb(2), one Mn(2), and one Mn(4) atom. In the ninth O site, O(9) is bonded in a 2-coordinate geometry to two equivalent Ba(1), two equivalent Tb(1), one Mn(1), and one Mn(3) atom. In the tenth O site, O(10) is bonded to two equivalent Ba(2), two equivalent Tb(2), one Mn(2), and one Mn(4) atom to form distorted OBa2Tb2Mn2 octahedra that share corners with two equivalent O(5)Ba4Mn2 octahedra, corners with two equivalent O(6)Ba4Mn2 octahedra, edges with two equivalent O(10)Ba2Tb2Mn2 octahedra, and faces with two equivalent O(6)Ba4Mn2 octahedra. The corner-sharing octahedral tilt angles range from 59-62°. In the eleventh O site, O(11) is bonded in a 6-coordinate geometry to one Ba(1), one Ba(2), one Tb(1), one Tb(2), one Mn(1), and one Mn(4) atom. In the twelfth O site, O(12) is bonded in a 6-coordinate geometry to one Ba(1), one Ba(2), one Tb(1), one Tb(2), one Mn(2), and one Mn(3) atom.