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	5.2	0.0	0.0	5.20

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	0.1503	-0.0311	0.0513	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	5.20000	0.00000	0.00000
2	0.75000	0.87500	0.00000	0,m_x,0	0.00000	5.20000	0.00000
3	0.00000	0.75000	0.87500	0,0,m_x	0.00000	0.00000	5.20000
4	0.50000	0.75000	0.12500	0,0,-m_x	0.00000	0.00000	-5.20000
5	0.75000	0.12500	0.50000	0,-m_x,0	0.00000	-5.20000	0.00000
6	0.12500	0.50000	0.75000	-m_x,0,0	-5.20000	0.00000	0.00000
7	0.37500	0.00000	0.75000	-m_x,0,0	-5.20000	0.00000	0.00000
8	0.00000	0.25000	0.12500	0,0,m_x	0.00000	0.00000	5.20000
9	0.25000	0.12500	0.00000	0,m_x,0	0.00000	5.20000	0.00000
10	0.37500	0.50000	0.25000	m_x,0,0	5.20000	0.00000	0.00000
11	0.75000	0.37500	0.00000	0,-m_x,0	0.00000	-5.20000	0.00000
12	0.00000	0.75000	0.37500	0,0,-m_x	0.00000	0.00000	-5.20000
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13	0.62500	0.50000	0.75000	m_x,0,0	5.20000	0.00000	0.00000
14	0.25000	0.37500	0.50000	0,m_x,0	0.00000	5.20000	0.00000
15	0.50000	0.25000	0.37500	0,0,m_x	0.00000	0.00000	5.20000
16	0.00000	0.25000	0.62500	0,0,-m_x	0.00000	0.00000	-5.20000
17	0.25000	0.62500	0.00000	0,-m_x,0	0.00000	-5.20000	0.00000
18	0.62500	0.00000	0.25000	-m_x,0,0	-5.20000	0.00000	0.00000
19	0.87500	0.50000	0.25000	-m_x,0,0	-5.20000	0.00000	0.00000
20	0.50000	0.75000	0.62500	0,0,m_x	0.00000	0.00000	5.20000
21	0.75000	0.62500	0.50000	0,m_x,0	0.00000	5.20000	0.00000
22	0.87500	0.00000	0.75000	m_x,0,0	5.20000	0.00000	0.00000
23	0.25000	0.87500	0.50000	0,-m_x,0	0.00000	-5.20000	0.00000
24	0.50000	0.25000	0.87500	0,0,-m_x	0.00000	0.00000	-5.20000

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	0.15030	0.96890	0.05130
2	0.94870	0.84970	0.03110
3	0.03110	0.94870	0.84970
4	0.46890	0.94870	0.15030
5	0.94870	0.15030	0.46890
6	0.05130	0.65030	0.03110
7	0.96890	0.55130	0.84970
8	0.03110	0.05130	0.65030
9	0.55130	0.84970	0.96890
10	0.15030	0.46890	0.94870
11	0.15030	0.03110	0.44870
12	0.34970	0.96890	0.94870
13	0.19870	0.28110	0.09970
14	0.28110	0.09970	0.19870
15	0.40030	0.30130	0.21890
16	0.21890	0.09970	0.80130
17	0.71890	0.40030	0.19870
18	0.09970	0.30130	0.78110
19	0.19870	0.71890	0.40030
20	0.69870	0.28110	0.40030
21	0.59970	0.19870	0.21890
22	0.09970	0.80130	0.21890
23	0.30130	0.28110	0.90030
24	0.28110	0.90030	0.30130
25	0.84970	0.03110	0.94870
26	0.05130	0.15030	0.96890
27	0.96890	0.05130	0.15030
28	0.53110	0.05130	0.84970
29	0.05130	0.84970	0.53110
30	0.94870	0.34970	0.96890
31	0.03110	0.44870	0.15030
32	0.96890	0.94870	0.34970
33	0.44870	0.15030	0.03110
34	0.84970	0.53110	0.05130
35	0.84970	0.96890	0.55130
36	0.65030	0.03110	0.05130
37	0.80130	0.71890	0.90030
38	0.71890	0.90030	0.80130
39	0.59970	0.69870	0.78110
40	0.78110	0.90030	0.19870
41	0.28110	0.59970	0.80130
42	0.90030	0.69870	0.21890
43	0.80130	0.28110	0.59970
44	0.30130	0.71890	0.59970
45	0.40030	0.80130	0.78110
46	0.90030	0.19870	0.78110
47	0.69870	0.71890	0.09970
48	0.71890	0.09970	0.69870
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49	0.65030	0.46890	0.55130
50	0.44870	0.34970	0.53110
51	0.53110	0.44870	0.34970
52	0.96890	0.44870	0.65030
53	0.44870	0.65030	0.96890
54	0.55130	0.15030	0.53110
55	0.46890	0.05130	0.34970
56	0.53110	0.55130	0.15030
57	0.05130	0.34970	0.46890
58	0.65030	0.96890	0.44870
59	0.65030	0.53110	0.94870
60	0.84970	0.46890	0.44870
61	0.69870	0.78110	0.59970
62	0.78110	0.59970	0.69870
63	0.90030	0.80130	0.71890
64	0.71890	0.59970	0.30130
65	0.21890	0.90030	0.69870
66	0.59970	0.80130	0.28110
67	0.69870	0.21890	0.90030
68	0.19870	0.78110	0.90030
69	0.09970	0.69870	0.71890
70	0.59970	0.30130	0.71890
71	0.80130	0.78110	0.40030
72	0.78110	0.40030	0.80130
73	0.34970	0.53110	0.44870
74	0.55130	0.65030	0.46890
75	0.46890	0.55130	0.65030
76	0.03110	0.55130	0.34970
77	0.55130	0.34970	0.03110
78	0.44870	0.84970	0.46890
79	0.53110	0.94870	0.65030
80	0.46890	0.44870	0.84970
81	0.94870	0.65030	0.53110
82	0.34970	0.03110	0.55130
83	0.34970	0.46890	0.05130
84	0.15030	0.53110	0.55130
85	0.30130	0.21890	0.40030
86	0.21890	0.40030	0.30130
87	0.09970	0.19870	0.28110
88	0.28110	0.40030	0.69870
89	0.78110	0.09970	0.30130
90	0.40030	0.19870	0.71890
91	0.30130	0.78110	0.09970
92	0.80130	0.21890	0.09970
93	0.90030	0.30130	0.28110
94	0.40030	0.69870	0.28110
95	0.19870	0.21890	0.59970
96	0.21890	0.59970	0.19870

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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	5.2	0.0	0.0	5.20

[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

Ho₃Al₅O₁₂ (#0.743)

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

Ho3Al5O12 (#0.743)

Ho₃Al₅O₁₂ (#0.743)