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\|
Er1	Er	0.12500	0.00000	0.25000	24	m_x,0,0	5.24(4)	0.0	0.0	5.24

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	0.0266	0.0567	0.6511	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 Er1:

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	5.24000	0.00000	0.00000
2	0.75000	0.87500	0.00000	0,m_x,0	0.00000	5.24000	0.00000
3	0.00000	0.75000	0.87500	0,0,m_x	0.00000	0.00000	5.24000
4	0.50000	0.75000	0.12500	0,0,-m_x	0.00000	0.00000	-5.24000
5	0.75000	0.12500	0.50000	0,-m_x,0	0.00000	-5.24000	0.00000
6	0.12500	0.50000	0.75000	-m_x,0,0	-5.24000	0.00000	0.00000
7	0.37500	0.00000	0.75000	-m_x,0,0	-5.24000	0.00000	0.00000
8	0.00000	0.25000	0.12500	0,0,m_x	0.00000	0.00000	5.24000
9	0.25000	0.12500	0.00000	0,m_x,0	0.00000	5.24000	0.00000
10	0.37500	0.50000	0.25000	m_x,0,0	5.24000	0.00000	0.00000
11	0.75000	0.37500	0.00000	0,-m_x,0	0.00000	-5.24000	0.00000
12	0.00000	0.75000	0.37500	0,0,-m_x	0.00000	0.00000	-5.24000
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13	0.62500	0.50000	0.75000	m_x,0,0	5.24000	0.00000	0.00000
14	0.25000	0.37500	0.50000	0,m_x,0	0.00000	5.24000	0.00000
15	0.50000	0.25000	0.37500	0,0,m_x	0.00000	0.00000	5.24000
16	0.00000	0.25000	0.62500	0,0,-m_x	0.00000	0.00000	-5.24000
17	0.25000	0.62500	0.00000	0,-m_x,0	0.00000	-5.24000	0.00000
18	0.62500	0.00000	0.25000	-m_x,0,0	-5.24000	0.00000	0.00000
19	0.87500	0.50000	0.25000	-m_x,0,0	-5.24000	0.00000	0.00000
20	0.50000	0.75000	0.62500	0,0,m_x	0.00000	0.00000	5.24000
21	0.75000	0.62500	0.50000	0,m_x,0	0.00000	5.24000	0.00000
22	0.87500	0.00000	0.75000	m_x,0,0	5.24000	0.00000	0.00000
23	0.25000	0.87500	0.50000	0,-m_x,0	0.00000	-5.24000	0.00000
24	0.50000	0.25000	0.87500	0,0,-m_x	0.00000	0.00000	-5.24000

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	0.02660	0.05670	0.65110
2	0.34890	0.97340	0.94330
3	0.94330	0.34890	0.97340
4	0.55670	0.34890	0.02660
5	0.34890	0.02660	0.55670
6	0.65110	0.52660	0.94330
7	0.05670	0.15110	0.97340
8	0.94330	0.65110	0.52660
9	0.15110	0.97340	0.05670
10	0.02660	0.55670	0.34890
11	0.02660	0.94330	0.84890
12	0.47340	0.05670	0.34890
13	0.59890	0.19330	0.22340
14	0.19330	0.22340	0.59890
15	0.27660	0.90110	0.30670
16	0.30670	0.22340	0.40110
17	0.80670	0.27660	0.59890
18	0.22340	0.90110	0.69330
19	0.59890	0.80670	0.27660
20	0.09890	0.19330	0.27660
21	0.72340	0.59890	0.30670
22	0.22340	0.40110	0.30670
23	0.90110	0.19330	0.77660
24	0.19330	0.77660	0.90110
25	0.97340	0.94330	0.34890
26	0.65110	0.02660	0.05670
27	0.05670	0.65110	0.02660
28	0.44330	0.65110	0.97340
29	0.65110	0.97340	0.44330
30	0.34890	0.47340	0.05670
31	0.94330	0.84890	0.02660
32	0.05670	0.34890	0.47340
33	0.84890	0.02660	0.94330
34	0.97340	0.44330	0.65110
35	0.97340	0.05670	0.15110
36	0.52660	0.94330	0.65110
37	0.40110	0.80670	0.77660
38	0.80670	0.77660	0.40110
39	0.72340	0.09890	0.69330
40	0.69330	0.77660	0.59890
41	0.19330	0.72340	0.40110
42	0.77660	0.09890	0.30670
43	0.40110	0.19330	0.72340
44	0.90110	0.80670	0.72340
45	0.27660	0.40110	0.69330
46	0.77660	0.59890	0.69330
47	0.09890	0.80670	0.22340
48	0.80670	0.22340	0.09890
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49	0.52660	0.55670	0.15110
50	0.84890	0.47340	0.44330
51	0.44330	0.84890	0.47340
52	0.05670	0.84890	0.52660
53	0.84890	0.52660	0.05670
54	0.15110	0.02660	0.44330
55	0.55670	0.65110	0.47340
56	0.44330	0.15110	0.02660
57	0.65110	0.47340	0.55670
58	0.52660	0.05670	0.84890
59	0.52660	0.44330	0.34890
60	0.97340	0.55670	0.84890
61	0.09890	0.69330	0.72340
62	0.69330	0.72340	0.09890
63	0.77660	0.40110	0.80670
64	0.80670	0.72340	0.90110
65	0.30670	0.77660	0.09890
66	0.72340	0.40110	0.19330
67	0.09890	0.30670	0.77660
68	0.59890	0.69330	0.77660
69	0.22340	0.09890	0.80670
70	0.72340	0.90110	0.80670
71	0.40110	0.69330	0.27660
72	0.69330	0.27660	0.40110
73	0.47340	0.44330	0.84890
74	0.15110	0.52660	0.55670
75	0.55670	0.15110	0.52660
76	0.94330	0.15110	0.47340
77	0.15110	0.47340	0.94330
78	0.84890	0.97340	0.55670
79	0.44330	0.34890	0.52660
80	0.55670	0.84890	0.97340
81	0.34890	0.52660	0.44330
82	0.47340	0.94330	0.15110
83	0.47340	0.55670	0.65110
84	0.02660	0.44330	0.15110
85	0.90110	0.30670	0.27660
86	0.30670	0.27660	0.90110
87	0.22340	0.59890	0.19330
88	0.19330	0.27660	0.09890
89	0.69330	0.22340	0.90110
90	0.27660	0.59890	0.80670
91	0.90110	0.69330	0.22340
92	0.40110	0.30670	0.22340
93	0.77660	0.90110	0.19330
94	0.27660	0.09890	0.19330
95	0.59890	0.30670	0.72340
96	0.30670	0.72340	0.59890

[Hide]

Label	Atom type	x	y	z	Multiplicity	Symmetry constraints on M	M_x	M_y	M_z	\|M\|
Er1	Er	0.12500	0.00000	0.25000	24	m_x,0,0	5.24(4)	0.0	0.0	5.24

[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

Er₃Ga₅O₁₂ (#0.741)

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

Er3Ga5O12 (#0.741)

Er₃Ga₅O₁₂ (#0.741)