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\|
Ho1	Ho	0.12500	0.00000	0.25000	24	m_x,0,0	3.9	0.0	0.0	3.90

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	-0.0274	0.0552	0.1502	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 Ho1:

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	3.90000	0.00000	0.00000
2	0.75000	0.87500	0.00000	0,m_x,0	0.00000	3.90000	0.00000
3	0.00000	0.75000	0.87500	0,0,m_x	0.00000	0.00000	3.90000
4	0.50000	0.75000	0.12500	0,0,-m_x	0.00000	0.00000	-3.90000
5	0.75000	0.12500	0.50000	0,-m_x,0	0.00000	-3.90000	0.00000
6	0.12500	0.50000	0.75000	-m_x,0,0	-3.90000	0.00000	0.00000
7	0.37500	0.00000	0.75000	-m_x,0,0	-3.90000	0.00000	0.00000
8	0.00000	0.25000	0.12500	0,0,m_x	0.00000	0.00000	3.90000
9	0.25000	0.12500	0.00000	0,m_x,0	0.00000	3.90000	0.00000
10	0.37500	0.50000	0.25000	m_x,0,0	3.90000	0.00000	0.00000
11	0.75000	0.37500	0.00000	0,-m_x,0	0.00000	-3.90000	0.00000
12	0.00000	0.75000	0.37500	0,0,-m_x	0.00000	0.00000	-3.90000
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13	0.62500	0.50000	0.75000	m_x,0,0	3.90000	0.00000	0.00000
14	0.25000	0.37500	0.50000	0,m_x,0	0.00000	3.90000	0.00000
15	0.50000	0.25000	0.37500	0,0,m_x	0.00000	0.00000	3.90000
16	0.00000	0.25000	0.62500	0,0,-m_x	0.00000	0.00000	-3.90000
17	0.25000	0.62500	0.00000	0,-m_x,0	0.00000	-3.90000	0.00000
18	0.62500	0.00000	0.25000	-m_x,0,0	-3.90000	0.00000	0.00000
19	0.87500	0.50000	0.25000	-m_x,0,0	-3.90000	0.00000	0.00000
20	0.50000	0.75000	0.62500	0,0,m_x	0.00000	0.00000	3.90000
21	0.75000	0.62500	0.50000	0,m_x,0	0.00000	3.90000	0.00000
22	0.87500	0.00000	0.75000	m_x,0,0	3.90000	0.00000	0.00000
23	0.25000	0.87500	0.50000	0,-m_x,0	0.00000	-3.90000	0.00000
24	0.50000	0.25000	0.87500	0,0,-m_x	0.00000	0.00000	-3.90000

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	0.97260	0.05520	0.15020
2	0.84980	0.02740	0.94480
3	0.94480	0.84980	0.02740
4	0.55520	0.84980	0.97260
5	0.84980	0.97260	0.55520
6	0.15020	0.47260	0.94480
7	0.05520	0.65020	0.02740
8	0.94480	0.15020	0.47260
9	0.65020	0.02740	0.05520
10	0.97260	0.55520	0.84980
11	0.97260	0.94480	0.34980
12	0.52740	0.05520	0.84980
13	0.09980	0.19480	0.27740
14	0.19480	0.27740	0.09980
15	0.22260	0.40020	0.30520
16	0.30520	0.27740	0.90020
17	0.80520	0.22260	0.09980
18	0.27740	0.40020	0.69480
19	0.09980	0.80520	0.22260
20	0.59980	0.19480	0.22260
21	0.77740	0.09980	0.30520
22	0.27740	0.90020	0.30520
23	0.40020	0.19480	0.72260
24	0.19480	0.72260	0.40020
25	0.02740	0.94480	0.84980
26	0.15020	0.97260	0.05520
27	0.05520	0.15020	0.97260
28	0.44480	0.15020	0.02740
29	0.15020	0.02740	0.44480
30	0.84980	0.52740	0.05520
31	0.94480	0.34980	0.97260
32	0.05520	0.84980	0.52740
33	0.34980	0.97260	0.94480
34	0.02740	0.44480	0.15020
35	0.02740	0.05520	0.65020
36	0.47260	0.94480	0.15020
37	0.90020	0.80520	0.72260
38	0.80520	0.72260	0.90020
39	0.77740	0.59980	0.69480
40	0.69480	0.72260	0.09980
41	0.19480	0.77740	0.90020
42	0.72260	0.59980	0.30520
43	0.90020	0.19480	0.77740
44	0.40020	0.80520	0.77740
45	0.22260	0.90020	0.69480
46	0.72260	0.09980	0.69480
47	0.59980	0.80520	0.27740
48	0.80520	0.27740	0.59980
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49	0.47260	0.55520	0.65020
50	0.34980	0.52740	0.44480
51	0.44480	0.34980	0.52740
52	0.05520	0.34980	0.47260
53	0.34980	0.47260	0.05520
54	0.65020	0.97260	0.44480
55	0.55520	0.15020	0.52740
56	0.44480	0.65020	0.97260
57	0.15020	0.52740	0.55520
58	0.47260	0.05520	0.34980
59	0.47260	0.44480	0.84980
60	0.02740	0.55520	0.34980
61	0.59980	0.69480	0.77740
62	0.69480	0.77740	0.59980
63	0.72260	0.90020	0.80520
64	0.80520	0.77740	0.40020
65	0.30520	0.72260	0.59980
66	0.77740	0.90020	0.19480
67	0.59980	0.30520	0.72260
68	0.09980	0.69480	0.72260
69	0.27740	0.59980	0.80520
70	0.77740	0.40020	0.80520
71	0.90020	0.69480	0.22260
72	0.69480	0.22260	0.90020
73	0.52740	0.44480	0.34980
74	0.65020	0.47260	0.55520
75	0.55520	0.65020	0.47260
76	0.94480	0.65020	0.52740
77	0.65020	0.52740	0.94480
78	0.34980	0.02740	0.55520
79	0.44480	0.84980	0.47260
80	0.55520	0.34980	0.02740
81	0.84980	0.47260	0.44480
82	0.52740	0.94480	0.65020
83	0.52740	0.55520	0.15020
84	0.97260	0.44480	0.65020
85	0.40020	0.30520	0.22260
86	0.30520	0.22260	0.40020
87	0.27740	0.09980	0.19480
88	0.19480	0.22260	0.59980
89	0.69480	0.27740	0.40020
90	0.22260	0.09980	0.80520
91	0.40020	0.69480	0.27740
92	0.90020	0.30520	0.27740
93	0.72260	0.40020	0.19480
94	0.22260	0.59980	0.19480
95	0.09980	0.30520	0.77740
96	0.30520	0.77740	0.09980

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Label	Atom type	x	y	z	Multiplicity	Symmetry constraints on M	M_x	M_y	M_z	\|M\|
Ho1	Ho	0.12500	0.00000	0.25000	24	m_x,0,0	3.9	0.0	0.0	3.90

[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

Ho₃Ga₅O₁₂ (#0.745)

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

Ho3Ga5O12 (#0.745)

Ho₃Ga₅O₁₂ (#0.745)