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	4.	0.0	0.0	4.00

Non-magnetic atoms:

Label	Atom type	x	y	z	Multiplicity
Ga1	Ga	0.00000	0.00000	0.00000	16
Ga2	Ga	0.37500	0.00000	0.25000	24
O1	O	0.0271	0.0553	0.6508	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	4.00000	0.00000	0.00000
2	0.75000	0.87500	0.00000	0,m_x,0	0.00000	4.00000	0.00000
3	0.00000	0.75000	0.87500	0,0,m_x	0.00000	0.00000	4.00000
4	0.50000	0.75000	0.12500	0,0,-m_x	0.00000	0.00000	-4.00000
5	0.75000	0.12500	0.50000	0,-m_x,0	0.00000	-4.00000	0.00000
6	0.12500	0.50000	0.75000	-m_x,0,0	-4.00000	0.00000	0.00000
7	0.37500	0.00000	0.75000	-m_x,0,0	-4.00000	0.00000	0.00000
8	0.00000	0.25000	0.12500	0,0,m_x	0.00000	0.00000	4.00000
9	0.25000	0.12500	0.00000	0,m_x,0	0.00000	4.00000	0.00000
10	0.37500	0.50000	0.25000	m_x,0,0	4.00000	0.00000	0.00000
11	0.75000	0.37500	0.00000	0,-m_x,0	0.00000	-4.00000	0.00000
12	0.00000	0.75000	0.37500	0,0,-m_x	0.00000	0.00000	-4.00000
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13	0.62500	0.50000	0.75000	m_x,0,0	4.00000	0.00000	0.00000
14	0.25000	0.37500	0.50000	0,m_x,0	0.00000	4.00000	0.00000
15	0.50000	0.25000	0.37500	0,0,m_x	0.00000	0.00000	4.00000
16	0.00000	0.25000	0.62500	0,0,-m_x	0.00000	0.00000	-4.00000
17	0.25000	0.62500	0.00000	0,-m_x,0	0.00000	-4.00000	0.00000
18	0.62500	0.00000	0.25000	-m_x,0,0	-4.00000	0.00000	0.00000
19	0.87500	0.50000	0.25000	-m_x,0,0	-4.00000	0.00000	0.00000
20	0.50000	0.75000	0.62500	0,0,m_x	0.00000	0.00000	4.00000
21	0.75000	0.62500	0.50000	0,m_x,0	0.00000	4.00000	0.00000
22	0.87500	0.00000	0.75000	m_x,0,0	4.00000	0.00000	0.00000
23	0.25000	0.87500	0.50000	0,-m_x,0	0.00000	-4.00000	0.00000
24	0.50000	0.25000	0.87500	0,0,-m_x	0.00000	0.00000	-4.00000

Non-magnetic atoms:

Set of atoms in the unit cell related by symmetry with the atom Ga1:

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 Ga2:

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	0.02710	0.05530	0.65080
2	0.34920	0.97290	0.94470
3	0.94470	0.34920	0.97290
4	0.55530	0.34920	0.02710
5	0.34920	0.02710	0.55530
6	0.65080	0.52710	0.94470
7	0.05530	0.15080	0.97290
8	0.94470	0.65080	0.52710
9	0.15080	0.97290	0.05530
10	0.02710	0.55530	0.34920
11	0.02710	0.94470	0.84920
12	0.47290	0.05530	0.34920
13	0.59920	0.19470	0.22290
14	0.19470	0.22290	0.59920
15	0.27710	0.90080	0.30530
16	0.30530	0.22290	0.40080
17	0.80530	0.27710	0.59920
18	0.22290	0.90080	0.69470
19	0.59920	0.80530	0.27710
20	0.09920	0.19470	0.27710
21	0.72290	0.59920	0.30530
22	0.22290	0.40080	0.30530
23	0.90080	0.19470	0.77710
24	0.19470	0.77710	0.90080
25	0.97290	0.94470	0.34920
26	0.65080	0.02710	0.05530
27	0.05530	0.65080	0.02710
28	0.44470	0.65080	0.97290
29	0.65080	0.97290	0.44470
30	0.34920	0.47290	0.05530
31	0.94470	0.84920	0.02710
32	0.05530	0.34920	0.47290
33	0.84920	0.02710	0.94470
34	0.97290	0.44470	0.65080
35	0.97290	0.05530	0.15080
36	0.52710	0.94470	0.65080
37	0.40080	0.80530	0.77710
38	0.80530	0.77710	0.40080
39	0.72290	0.09920	0.69470
40	0.69470	0.77710	0.59920
41	0.19470	0.72290	0.40080
42	0.77710	0.09920	0.30530
43	0.40080	0.19470	0.72290
44	0.90080	0.80530	0.72290
45	0.27710	0.40080	0.69470
46	0.77710	0.59920	0.69470
47	0.09920	0.80530	0.22290
48	0.80530	0.22290	0.09920
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49	0.52710	0.55530	0.15080
50	0.84920	0.47290	0.44470
51	0.44470	0.84920	0.47290
52	0.05530	0.84920	0.52710
53	0.84920	0.52710	0.05530
54	0.15080	0.02710	0.44470
55	0.55530	0.65080	0.47290
56	0.44470	0.15080	0.02710
57	0.65080	0.47290	0.55530
58	0.52710	0.05530	0.84920
59	0.52710	0.44470	0.34920
60	0.97290	0.55530	0.84920
61	0.09920	0.69470	0.72290
62	0.69470	0.72290	0.09920
63	0.77710	0.40080	0.80530
64	0.80530	0.72290	0.90080
65	0.30530	0.77710	0.09920
66	0.72290	0.40080	0.19470
67	0.09920	0.30530	0.77710
68	0.59920	0.69470	0.77710
69	0.22290	0.09920	0.80530
70	0.72290	0.90080	0.80530
71	0.40080	0.69470	0.27710
72	0.69470	0.27710	0.40080
73	0.47290	0.44470	0.84920
74	0.15080	0.52710	0.55530
75	0.55530	0.15080	0.52710
76	0.94470	0.15080	0.47290
77	0.15080	0.47290	0.94470
78	0.84920	0.97290	0.55530
79	0.44470	0.34920	0.52710
80	0.55530	0.84920	0.97290
81	0.34920	0.52710	0.44470
82	0.47290	0.94470	0.15080
83	0.47290	0.55530	0.65080
84	0.02710	0.44470	0.15080
85	0.90080	0.30530	0.27710
86	0.30530	0.27710	0.90080
87	0.22290	0.59920	0.19470
88	0.19470	0.27710	0.09920
89	0.69470	0.22290	0.90080
90	0.27710	0.59920	0.80530
91	0.90080	0.69470	0.22290
92	0.40080	0.30530	0.22290
93	0.77710	0.90080	0.19470
94	0.27710	0.09920	0.19470
95	0.59920	0.30530	0.72290
96	0.30530	0.72290	0.59920

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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	4.	0.0	0.0	4.00

[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

Tb₃Ga₅O₁₂ (#0.746)

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

Tb3Ga5O12 (#0.746)

Tb₃Ga₅O₁₂ (#0.746)