MAGNDATA - Collection of Magnetic Structures

Symmetry operations of the magnetic space group in the setting used:

N	(x,y,z)	Seitz notation
1	x,y,z,+1	{ 1 \| 0 }
2	-z,-x,-y,+1	{ -3⁺₁₁₁ \| 0 }
3	-y,-z,-x,+1	{ -3^-₁₁₁ \| 0 }
4	y+1/2,-z,x,+1	{ -3^-_1-1-1 \| 1/2 0 0 }
5	-z,x,y+1/2,+1	{ -3⁺_-11-1 \| 0 0 1/2 }
6	z,x+1/2,-y,+1	{ -3⁺_1-1-1 \| 0 1/2 0 }
7	y,z+1/2,-x,+1	{ -3^-_-11-1 \| 0 1/2 0 }
8	-y,z,x+1/2,+1	{ -3^-_-1-11 \| 0 0 1/2 }
9	z+1/2,-x,y,+1	{ -3⁺_-1-11 \| 1/2 0 0 }
10	x,y+1/2,-z,+1	{ m₀₀₁ \| 0 1/2 0 }
11	x,-y,-z+1/2,+1	{ 2₁₀₀ \| 0 0 1/2 }
12	-x+1/2,y,-z,+1	{ 2₀₁₀ \| 1/2 0 0 }
13	-z+1/4,-y+1/4,-x+1/4,-1	{ 2'_-101 \| 1/4 1/4 1/4 }
14	-y+1/4,-x+1/4,-z+1/4,-1	{ 2'_1-10 \| 1/4 1/4 1/4 }
15	x+1/4,z+1/4,y+1/4,-1	{ m'_01-1 \| 1/4 1/4 1/4 }
16	y+1/4,-x+1/4,z+3/4,-1	{ 4'^-₀₀₁ \| 1/4 1/4 3/4 }
17	y+3/4,x+1/4,-z+1/4,-1	{ 2'₁₁₀ \| 3/4 1/4 1/4 }
18	-x+1/4,z+1/4,-y+3/4,-1	{ -4'⁺₁₀₀ \| 1/4 1/4 3/4 }
19	-z+1/4,y+3/4,x+1/4,-1	{ 4'^-₀₁₀ \| 1/4 3/4 1/4 }
20	-z+3/4,-y+1/4,x+1/4,-1	{ -4'⁺₀₁₀ \| 3/4 1/4 1/4 }
21	-x+3/4,-z+1/4,y+1/4,-1	{ -4'^-₁₀₀ \| 3/4 1/4 1/4 }
22	-x+1/4,z+3/4,y+1/4,-1	{ 2'₀₁₁ \| 1/4 3/4 1/4 }
23	z+1/4,-y+1/4,x+3/4,-1	{ 2'₁₀₁ \| 1/4 1/4 3/4 }
24	-y+1/4,x+3/4,z+1/4,-1	{ 4'⁺₀₀₁ \| 1/4 3/4 1/4 }
25	-x,-y,-z,+1	{ -1 \| 0 }
26	z,x,y,+1	{ 3⁺₁₁₁ \| 0 }
27	y,z,x,+1	{ 3^-₁₁₁ \| 0 }
28	-y+1/2,z,-x,+1	{ 3^-_1-1-1 \| 1/2 0 0 }
29	z,-x,-y+1/2,+1	{ 3⁺_-11-1 \| 0 0 1/2 }
30	-z,-x+1/2,y,+1	{ 3⁺_1-1-1 \| 0 1/2 0 }
31	-y,-z+1/2,x,+1	{ 3^-_-11-1 \| 0 1/2 0 }
32	y,-z,-x+1/2,+1	{ 3^-_-1-11 \| 0 0 1/2 }
33	-z+1/2,x,-y,+1	{ 3⁺_-1-11 \| 1/2 0 0 }
34	-x,-y+1/2,z,+1	{ 2₀₀₁ \| 0 1/2 0 }
35	-x,y,z+1/2,+1	{ m₁₀₀ \| 0 0 1/2 }
36	x+1/2,-y,z,+1	{ m₀₁₀ \| 1/2 0 0 }
37	z+3/4,y+3/4,x+3/4,-1	{ m'_-101 \| 3/4 3/4 3/4 }
38	y+3/4,x+3/4,z+3/4,-1	{ m'_1-10 \| 3/4 3/4 3/4 }
39	-x+3/4,-z+3/4,-y+3/4,-1	{ 2'_01-1 \| 3/4 3/4 3/4 }
40	-y+3/4,x+3/4,-z+1/4,-1	{ -4'^-₀₀₁ \| 3/4 3/4 1/4 }
41	-y+1/4,-x+3/4,z+3/4,-1	{ m'₁₁₀ \| 1/4 3/4 3/4 }
42	x+3/4,-z+3/4,y+1/4,-1	{ 4'⁺₁₀₀ \| 3/4 3/4 1/4 }
43	z+3/4,-y+1/4,-x+3/4,-1	{ -4'^-₀₁₀ \| 3/4 1/4 3/4 }
44	z+1/4,y+3/4,-x+3/4,-1	{ 4'⁺₀₁₀ \| 1/4 3/4 3/4 }
45	x+1/4,z+3/4,-y+3/4,-1	{ 4'^-₁₀₀ \| 1/4 3/4 3/4 }
46	x+3/4,-z+1/4,-y+3/4,-1	{ m'₀₁₁ \| 3/4 1/4 3/4 }
47	-z+3/4,y+3/4,-x+1/4,-1	{ m'₁₀₁ \| 3/4 3/4 1/4 }
48	y+3/4,-x+1/4,-z+3/4,-1	{ -4'⁺₀₀₁ \| 3/4 1/4 3/4 }
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49	x+1/2,y+1/2,z+1/2,+1	{ 1 \| 1/2 1/2 1/2 }
50	-z+1/2,-x+1/2,-y+1/2,+1	{ -3⁺₁₁₁ \| 1/2 1/2 1/2 }
51	-y+1/2,-z+1/2,-x+1/2,+1	{ -3^-₁₁₁ \| 1/2 1/2 1/2 }
52	y,-z+1/2,x+1/2,+1	{ -3^-_1-1-1 \| 0 1/2 1/2 }
53	-z+1/2,x+1/2,y,+1	{ -3⁺_-11-1 \| 1/2 1/2 0 }
54	z+1/2,x,-y+1/2,+1	{ -3⁺_1-1-1 \| 1/2 0 1/2 }
55	y+1/2,z,-x+1/2,+1	{ -3^-_-11-1 \| 1/2 0 1/2 }
56	-y+1/2,z+1/2,x,+1	{ -3^-_-1-11 \| 1/2 1/2 0 }
57	z,-x+1/2,y+1/2,+1	{ -3⁺_-1-11 \| 0 1/2 1/2 }
58	x+1/2,y,-z+1/2,+1	{ m₀₀₁ \| 1/2 0 1/2 }
59	x+1/2,-y+1/2,-z,+1	{ 2₁₀₀ \| 1/2 1/2 0 }
60	-x,y+1/2,-z+1/2,+1	{ 2₀₁₀ \| 0 1/2 1/2 }
61	-z+3/4,-y+3/4,-x+3/4,-1	{ 2'_-101 \| 3/4 3/4 3/4 }
62	-y+3/4,-x+3/4,-z+3/4,-1	{ 2'_1-10 \| 3/4 3/4 3/4 }
63	x+3/4,z+3/4,y+3/4,-1	{ m'_01-1 \| 3/4 3/4 3/4 }
64	y+3/4,-x+3/4,z+1/4,-1	{ 4'^-₀₀₁ \| 3/4 3/4 1/4 }
65	y+1/4,x+3/4,-z+3/4,-1	{ 2'₁₁₀ \| 1/4 3/4 3/4 }
66	-x+3/4,z+3/4,-y+1/4,-1	{ -4'⁺₁₀₀ \| 3/4 3/4 1/4 }
67	-z+3/4,y+1/4,x+3/4,-1	{ 4'^-₀₁₀ \| 3/4 1/4 3/4 }
68	-z+1/4,-y+3/4,x+3/4,-1	{ -4'⁺₀₁₀ \| 1/4 3/4 3/4 }
69	-x+1/4,-z+3/4,y+3/4,-1	{ -4'^-₁₀₀ \| 1/4 3/4 3/4 }
70	-x+3/4,z+1/4,y+3/4,-1	{ 2'₀₁₁ \| 3/4 1/4 3/4 }
71	z+3/4,-y+3/4,x+1/4,-1	{ 2'₁₀₁ \| 3/4 3/4 1/4 }
72	-y+3/4,x+1/4,z+3/4,-1	{ 4'⁺₀₀₁ \| 3/4 1/4 3/4 }
73	-x+1/2,-y+1/2,-z+1/2,+1	{ -1 \| 1/2 1/2 1/2 }
74	z+1/2,x+1/2,y+1/2,+1	{ 3⁺₁₁₁ \| 1/2 1/2 1/2 }
75	y+1/2,z+1/2,x+1/2,+1	{ 3^-₁₁₁ \| 1/2 1/2 1/2 }
76	-y,z+1/2,-x+1/2,+1	{ 3^-_1-1-1 \| 0 1/2 1/2 }
77	z+1/2,-x+1/2,-y,+1	{ 3⁺_-11-1 \| 1/2 1/2 0 }
78	-z+1/2,-x,y+1/2,+1	{ 3⁺_1-1-1 \| 1/2 0 1/2 }
79	-y+1/2,-z,x+1/2,+1	{ 3^-_-11-1 \| 1/2 0 1/2 }
80	y+1/2,-z+1/2,-x,+1	{ 3^-_-1-11 \| 1/2 1/2 0 }
81	-z,x+1/2,-y+1/2,+1	{ 3⁺_-1-11 \| 0 1/2 1/2 }
82	-x+1/2,-y,z+1/2,+1	{ 2₀₀₁ \| 1/2 0 1/2 }
83	-x+1/2,y+1/2,z,+1	{ m₁₀₀ \| 1/2 1/2 0 }
84	x,-y+1/2,z+1/2,+1	{ m₀₁₀ \| 0 1/2 1/2 }
85	z+1/4,y+1/4,x+1/4,-1	{ m'_-101 \| 1/4 1/4 1/4 }
86	y+1/4,x+1/4,z+1/4,-1	{ m'_1-10 \| 1/4 1/4 1/4 }
87	-x+1/4,-z+1/4,-y+1/4,-1	{ 2'_01-1 \| 1/4 1/4 1/4 }
88	-y+1/4,x+1/4,-z+3/4,-1	{ -4'^-₀₀₁ \| 1/4 1/4 3/4 }
89	-y+3/4,-x+1/4,z+1/4,-1	{ m'₁₁₀ \| 3/4 1/4 1/4 }
90	x+1/4,-z+1/4,y+3/4,-1	{ 4'⁺₁₀₀ \| 1/4 1/4 3/4 }
91	z+1/4,-y+3/4,-x+1/4,-1	{ -4'^-₀₁₀ \| 1/4 3/4 1/4 }
92	z+3/4,y+1/4,-x+1/4,-1	{ 4'⁺₀₁₀ \| 3/4 1/4 1/4 }
93	x+3/4,z+1/4,-y+1/4,-1	{ 4'^-₁₀₀ \| 3/4 1/4 1/4 }
94	x+1/4,-z+3/4,-y+1/4,-1	{ m'₀₁₁ \| 1/4 3/4 1/4 }
95	-z+1/4,y+1/4,-x+3/4,-1	{ m'₁₀₁ \| 1/4 1/4 3/4 }
96	y+1/4,-x+3/4,-z+1/4,-1	{ -4'⁺₀₀₁ \| 1/4 3/4 1/4 }

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Symmetry operations of the magnetic point group in the setting used:

N	(x,y,z)	Seitz notation
1	x,y,z,+1	1
2	-z,-x,-y,+1	-3⁺₁₁₁
3	-y,-z,-x,+1	-3^-₁₁₁
4	y,-z,x,+1	-3^-_1-1-1
5	-z,x,y,+1	-3⁺_-11-1
6	z,x,-y,+1	-3⁺_1-1-1
7	y,z,-x,+1	-3^-_-11-1
8	-y,z,x,+1	-3^-_-1-11
9	z,-x,y,+1	-3⁺_-1-11
10	x,y,-z,+1	m₀₀₁
11	x,-y,-z,+1	2₁₀₀
12	-x,y,-z,+1	2₀₁₀
13	-z,-y,-x,-1	2'_-101
14	-y,-x,-z,-1	2'_1-10
15	x,z,y,-1	m'_01-1
16	y,-x,z,-1	4'^-₀₀₁
17	y,x,-z,-1	2'₁₁₀
18	-x,z,-y,-1	-4'⁺₁₀₀
19	-z,y,x,-1	4'^-₀₁₀
20	-z,-y,x,-1	-4'⁺₀₁₀
21	-x,-z,y,-1	-4'^-₁₀₀
22	-x,z,y,-1	2'₀₁₁
23	z,-y,x,-1	2'₁₀₁
24	-y,x,z,-1	4'⁺₀₀₁
25	-x,-y,-z,+1	-1
26	z,x,y,+1	3⁺₁₁₁
27	y,z,x,+1	3^-₁₁₁
28	-y,z,-x,+1	3^-_1-1-1
29	z,-x,-y,+1	3⁺_-11-1
30	-z,-x,y,+1	3⁺_1-1-1
31	-y,-z,x,+1	3^-_-11-1
32	y,-z,-x,+1	3^-_-1-11
33	-z,x,-y,+1	3⁺_-1-11
34	-x,-y,z,+1	2₀₀₁
35	-x,y,z,+1	m₁₀₀
36	x,-y,z,+1	m₀₁₀
37	z,y,x,-1	m'_-101
38	y,x,z,-1	m'_1-10
39	-x,-z,-y,-1	2'_01-1
40	-y,x,-z,-1	-4'^-₀₀₁
41	-y,-x,z,-1	m'₁₁₀
42	x,-z,y,-1	4'⁺₁₀₀
43	z,-y,-x,-1	-4'^-₀₁₀
44	z,y,-x,-1	4'⁺₀₁₀
45	x,z,-y,-1	4'^-₁₀₀
46	x,-z,-y,-1	m'₀₁₁
47	-z,y,-x,-1	m'₁₀₁
48	y,-x,-z,-1	-4'⁺₀₀₁

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Magnetic atoms:

Label	Atom type	x	y	z	Multiplicity	Symmetry constraints on M	M_x	M_y	M_z	\|M\|
Tb1	Tb	0.12500	0.00000	0.25000	24	m_x,0,0	5.7	0.0	0.0	5.70

Non-magnetic atoms:

Label	Atom type	x	y	z	Multiplicity
Al1	Al	0.00000	0.00000	0.00000	16
Al2	Al	0.37500	0.00000	0.25000	24
O1	O	0.148	-0.0314	0.0502	96

[Show all atoms in unit cell and their moment relations]

Positions and magnetic moments of all atoms in unit cell, with magnetic moment relations explicitly given:

Magnetic atoms:

Set of atoms in the unit cell related by symmetry with the magnetic atom Tb1:

Atom	x	y	z	Symmetry constraints on M	M_x	M_y	M_z
1	0.12500	0.00000	0.25000	m_x,0,0	5.70000	0.00000	0.00000
2	0.75000	0.87500	0.00000	0,m_x,0	0.00000	5.70000	0.00000
3	0.00000	0.75000	0.87500	0,0,m_x	0.00000	0.00000	5.70000
4	0.50000	0.75000	0.12500	0,0,-m_x	0.00000	0.00000	-5.70000
5	0.75000	0.12500	0.50000	0,-m_x,0	0.00000	-5.70000	0.00000
6	0.12500	0.50000	0.75000	-m_x,0,0	-5.70000	0.00000	0.00000
7	0.37500	0.00000	0.75000	-m_x,0,0	-5.70000	0.00000	0.00000
8	0.00000	0.25000	0.12500	0,0,m_x	0.00000	0.00000	5.70000
9	0.25000	0.12500	0.00000	0,m_x,0	0.00000	5.70000	0.00000
10	0.37500	0.50000	0.25000	m_x,0,0	5.70000	0.00000	0.00000
11	0.75000	0.37500	0.00000	0,-m_x,0	0.00000	-5.70000	0.00000
12	0.00000	0.75000	0.37500	0,0,-m_x	0.00000	0.00000	-5.70000
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13	0.62500	0.50000	0.75000	m_x,0,0	5.70000	0.00000	0.00000
14	0.25000	0.37500	0.50000	0,m_x,0	0.00000	5.70000	0.00000
15	0.50000	0.25000	0.37500	0,0,m_x	0.00000	0.00000	5.70000
16	0.00000	0.25000	0.62500	0,0,-m_x	0.00000	0.00000	-5.70000
17	0.25000	0.62500	0.00000	0,-m_x,0	0.00000	-5.70000	0.00000
18	0.62500	0.00000	0.25000	-m_x,0,0	-5.70000	0.00000	0.00000
19	0.87500	0.50000	0.25000	-m_x,0,0	-5.70000	0.00000	0.00000
20	0.50000	0.75000	0.62500	0,0,m_x	0.00000	0.00000	5.70000
21	0.75000	0.62500	0.50000	0,m_x,0	0.00000	5.70000	0.00000
22	0.87500	0.00000	0.75000	m_x,0,0	5.70000	0.00000	0.00000
23	0.25000	0.87500	0.50000	0,-m_x,0	0.00000	-5.70000	0.00000
24	0.50000	0.25000	0.87500	0,0,-m_x	0.00000	0.00000	-5.70000

Non-magnetic atoms:

Set of atoms in the unit cell related by symmetry with the atom Al1:

Atom	x	y	z
1	0.00000	0.00000	0.00000
2	0.50000	0.00000	0.00000
3	0.00000	0.00000	0.50000
4	0.00000	0.50000	0.00000
5	0.25000	0.25000	0.25000
6	0.25000	0.25000	0.75000
7	0.75000	0.25000	0.25000
8	0.25000	0.75000	0.25000
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9	0.50000	0.50000	0.50000
10	0.00000	0.50000	0.50000
11	0.50000	0.50000	0.00000
12	0.50000	0.00000	0.50000
13	0.75000	0.75000	0.75000
14	0.75000	0.75000	0.25000
15	0.25000	0.75000	0.75000
16	0.75000	0.25000	0.75000

Set of atoms in the unit cell related by symmetry with the atom Al2:

Atom	x	y	z
1	0.37500	0.00000	0.25000
2	0.75000	0.62500	0.00000
3	0.00000	0.75000	0.62500
4	0.50000	0.75000	0.37500
5	0.75000	0.37500	0.50000
6	0.37500	0.50000	0.75000
7	0.12500	0.00000	0.75000
8	0.50000	0.25000	0.62500
9	0.62500	0.00000	0.75000
10	0.25000	0.37500	0.00000
11	0.00000	0.25000	0.37500
12	0.25000	0.62500	0.50000
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13	0.87500	0.50000	0.75000
14	0.25000	0.12500	0.50000
15	0.50000	0.25000	0.12500
16	0.00000	0.25000	0.87500
17	0.25000	0.87500	0.00000
18	0.87500	0.00000	0.25000
19	0.62500	0.50000	0.25000
20	0.00000	0.75000	0.12500
21	0.12500	0.50000	0.25000
22	0.75000	0.87500	0.50000
23	0.50000	0.75000	0.87500
24	0.75000	0.12500	0.00000

Set of atoms in the unit cell related by symmetry with the atom O1:

Atom	x	y	z
1	0.14800	0.96860	0.05020
2	0.94980	0.85200	0.03140
3	0.03140	0.94980	0.85200
4	0.46860	0.94980	0.14800
5	0.94980	0.14800	0.46860
6	0.05020	0.64800	0.03140
7	0.96860	0.55020	0.85200
8	0.03140	0.05020	0.64800
9	0.55020	0.85200	0.96860
10	0.14800	0.46860	0.94980
11	0.14800	0.03140	0.44980
12	0.35200	0.96860	0.94980
13	0.19980	0.28140	0.10200
14	0.28140	0.10200	0.19980
15	0.39800	0.30020	0.21860
16	0.21860	0.10200	0.80020
17	0.71860	0.39800	0.19980
18	0.10200	0.30020	0.78140
19	0.19980	0.71860	0.39800
20	0.69980	0.28140	0.39800
21	0.60200	0.19980	0.21860
22	0.10200	0.80020	0.21860
23	0.30020	0.28140	0.89800
24	0.28140	0.89800	0.30020
25	0.85200	0.03140	0.94980
26	0.05020	0.14800	0.96860
27	0.96860	0.05020	0.14800
28	0.53140	0.05020	0.85200
29	0.05020	0.85200	0.53140
30	0.94980	0.35200	0.96860
31	0.03140	0.44980	0.14800
32	0.96860	0.94980	0.35200
33	0.44980	0.14800	0.03140
34	0.85200	0.53140	0.05020
35	0.85200	0.96860	0.55020
36	0.64800	0.03140	0.05020
37	0.80020	0.71860	0.89800
38	0.71860	0.89800	0.80020
39	0.60200	0.69980	0.78140
40	0.78140	0.89800	0.19980
41	0.28140	0.60200	0.80020
42	0.89800	0.69980	0.21860
43	0.80020	0.28140	0.60200
44	0.30020	0.71860	0.60200
45	0.39800	0.80020	0.78140
46	0.89800	0.19980	0.78140
47	0.69980	0.71860	0.10200
48	0.71860	0.10200	0.69980
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49	0.64800	0.46860	0.55020
50	0.44980	0.35200	0.53140
51	0.53140	0.44980	0.35200
52	0.96860	0.44980	0.64800
53	0.44980	0.64800	0.96860
54	0.55020	0.14800	0.53140
55	0.46860	0.05020	0.35200
56	0.53140	0.55020	0.14800
57	0.05020	0.35200	0.46860
58	0.64800	0.96860	0.44980
59	0.64800	0.53140	0.94980
60	0.85200	0.46860	0.44980
61	0.69980	0.78140	0.60200
62	0.78140	0.60200	0.69980
63	0.89800	0.80020	0.71860
64	0.71860	0.60200	0.30020
65	0.21860	0.89800	0.69980
66	0.60200	0.80020	0.28140
67	0.69980	0.21860	0.89800
68	0.19980	0.78140	0.89800
69	0.10200	0.69980	0.71860
70	0.60200	0.30020	0.71860
71	0.80020	0.78140	0.39800
72	0.78140	0.39800	0.80020
73	0.35200	0.53140	0.44980
74	0.55020	0.64800	0.46860
75	0.46860	0.55020	0.64800
76	0.03140	0.55020	0.35200
77	0.55020	0.35200	0.03140
78	0.44980	0.85200	0.46860
79	0.53140	0.94980	0.64800
80	0.46860	0.44980	0.85200
81	0.94980	0.64800	0.53140
82	0.35200	0.03140	0.55020
83	0.35200	0.46860	0.05020
84	0.14800	0.53140	0.55020
85	0.30020	0.21860	0.39800
86	0.21860	0.39800	0.30020
87	0.10200	0.19980	0.28140
88	0.28140	0.39800	0.69980
89	0.78140	0.10200	0.30020
90	0.39800	0.19980	0.71860
91	0.30020	0.78140	0.10200
92	0.80020	0.21860	0.10200
93	0.89800	0.30020	0.28140
94	0.39800	0.69980	0.28140
95	0.19980	0.21860	0.60200
96	0.21860	0.60200	0.19980

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Label	Atom type	x	y	z	Multiplicity	Symmetry constraints on M	M_x	M_y	M_z	\|M\|
Tb1	Tb	0.12500	0.00000	0.25000	24	m_x,0,0	5.7	0.0	0.0	5.70

[Show all magnetic atoms in unit cell and their moment relations]

label	dim. small irrep	dim. full irrep	action	number of modes
mGM2+	1	1	primary	1

MAGNDATA: A Collection of magnetic structures with portable cif-type files

Tb₃Al₅O₁₂ (#0.744)

MAGNDATA: A Collection of magnetic structures with portable cif-type files

Tb3Al5O12 (#0.744)

Tb₃Al₅O₁₂ (#0.744)