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	-x+1/4,-y+1/4,z,+1	{ 2₀₀₁ \| 1/4 1/4 0 }
3	-x+3/4,y+1/2,-z+1/4,+1	{ 2₀₁₀ \| 3/4 1/2 1/4 }
4	x,-y+1/4,-z+1/4,+1	{ 2₁₀₀ \| 0 1/4 1/4 }
5	-x+1/2,-y,-z+1/2,+1	{ -1 \| 1/2 0 1/2 }
6	x+3/4,y+1/4,-z+1/2,+1	{ m₀₀₁ \| 3/4 1/4 1/2 }
7	x+3/4,-y+1/2,z+1/4,+1	{ m₀₁₀ \| 3/4 1/2 1/4 }
8	-x+1/2,y+3/4,z+1/4,+1	{ m₁₀₀ \| 1/2 3/4 1/4 }
9	-y,x+1/4,z+1/4,-1	{ 4'⁺₀₀₁ \| 0 1/4 1/4 }
10	y+1/4,-x,z+1/4,-1	{ 4'^-₀₀₁ \| 1/4 0 1/4 }
11	y+1/4,x+3/4,-z+1/2,-1	{ 2'₁₁₀ \| 1/4 3/4 1/2 }
12	-y,-x+1/2,-z+1/2,-1	{ 2'_1-10 \| 0 1/2 1/2 }
13	y+1/2,-x+3/4,-z+1/4,-1	{ -4'⁺₀₀₁ \| 1/2 3/4 1/4 }
14	-y+1/4,x,-z+1/4,-1	{ -4'^-₀₀₁ \| 1/4 0 1/4 }
15	-y+1/4,-x+1/4,z,-1	{ m'₁₁₀ \| 1/4 1/4 0 }
16	y,x,z,-1	{ m'_1-10 \| 0 }
(0,1/2,1/2) + set click here to show and hide
17	x,y+1/2,z+1/2,+1	{ 1 \| 0 1/2 1/2 }
18	-x+1/4,-y+3/4,z+1/2,+1	{ 2₀₀₁ \| 1/4 3/4 1/2 }
19	-x+3/4,y,-z+3/4,+1	{ 2₀₁₀ \| 3/4 0 3/4 }
20	x,-y+3/4,-z+3/4,+1	{ 2₁₀₀ \| 0 3/4 3/4 }
21	-x+1/2,-y+1/2,-z,+1	{ -1 \| 1/2 1/2 0 }
22	x+3/4,y+3/4,-z,+1	{ m₀₀₁ \| 3/4 3/4 0 }
23	x+3/4,-y,z+3/4,+1	{ m₀₁₀ \| 3/4 0 3/4 }
24	-x+1/2,y+1/4,z+3/4,+1	{ m₁₀₀ \| 1/2 1/4 3/4 }
25	-y,x+3/4,z+3/4,-1	{ 4'⁺₀₀₁ \| 0 3/4 3/4 }
26	y+1/4,-x+1/2,z+3/4,-1	{ 4'^-₀₀₁ \| 1/4 1/2 3/4 }
27	y+1/4,x+1/4,-z,-1	{ 2'₁₁₀ \| 1/4 1/4 0 }
28	-y,-x,-z,-1	{ 2'_1-10 \| 0 }
29	y+1/2,-x+1/4,-z+3/4,-1	{ -4'⁺₀₀₁ \| 1/2 1/4 3/4 }
30	-y+1/4,x+1/2,-z+3/4,-1	{ -4'^-₀₀₁ \| 1/4 1/2 3/4 }
31	-y+1/4,-x+3/4,z+1/2,-1	{ m'₁₁₀ \| 1/4 3/4 1/2 }
32	y,x+1/2,z+1/2,-1	{ m'_1-10 \| 0 1/2 1/2 }
(1/2,0,1/2) + set click here to show and hide
33	x+1/2,y,z+1/2,+1	{ 1 \| 1/2 0 1/2 }
34	-x+3/4,-y+1/4,z+1/2,+1	{ 2₀₀₁ \| 3/4 1/4 1/2 }
35	-x+1/4,y+1/2,-z+3/4,+1	{ 2₀₁₀ \| 1/4 1/2 3/4 }
36	x+1/2,-y+1/4,-z+3/4,+1	{ 2₁₀₀ \| 1/2 1/4 3/4 }
37	-x,-y,-z,+1	{ -1 \| 0 }
38	x+1/4,y+1/4,-z,+1	{ m₀₀₁ \| 1/4 1/4 0 }
39	x+1/4,-y+1/2,z+3/4,+1	{ m₀₁₀ \| 1/4 1/2 3/4 }
40	-x,y+3/4,z+3/4,+1	{ m₁₀₀ \| 0 3/4 3/4 }
41	-y+1/2,x+1/4,z+3/4,-1	{ 4'⁺₀₀₁ \| 1/2 1/4 3/4 }
42	y+3/4,-x,z+3/4,-1	{ 4'^-₀₀₁ \| 3/4 0 3/4 }
43	y+3/4,x+3/4,-z,-1	{ 2'₁₁₀ \| 3/4 3/4 0 }
44	-y+1/2,-x+1/2,-z,-1	{ 2'_1-10 \| 1/2 1/2 0 }
45	y,-x+3/4,-z+3/4,-1	{ -4'⁺₀₀₁ \| 0 3/4 3/4 }
46	-y+3/4,x,-z+3/4,-1	{ -4'^-₀₀₁ \| 3/4 0 3/4 }
47	-y+3/4,-x+1/4,z+1/2,-1	{ m'₁₁₀ \| 3/4 1/4 1/2 }
48	y+1/2,x,z+1/2,-1	{ m'_1-10 \| 1/2 0 1/2 }
(1/2,1/2,0) + set click here to show and hide
49	x+1/2,y+1/2,z,+1	{ 1 \| 1/2 1/2 0 }
50	-x+3/4,-y+3/4,z,+1	{ 2₀₀₁ \| 3/4 3/4 0 }
51	-x+1/4,y,-z+1/4,+1	{ 2₀₁₀ \| 1/4 0 1/4 }
52	x+1/2,-y+3/4,-z+1/4,+1	{ 2₁₀₀ \| 1/2 3/4 1/4 }
53	-x,-y+1/2,-z+1/2,+1	{ -1 \| 0 1/2 1/2 }
54	x+1/4,y+3/4,-z+1/2,+1	{ m₀₀₁ \| 1/4 3/4 1/2 }
55	x+1/4,-y,z+1/4,+1	{ m₀₁₀ \| 1/4 0 1/4 }
56	-x,y+1/4,z+1/4,+1	{ m₁₀₀ \| 0 1/4 1/4 }
57	-y+1/2,x+3/4,z+1/4,-1	{ 4'⁺₀₀₁ \| 1/2 3/4 1/4 }
58	y+3/4,-x+1/2,z+1/4,-1	{ 4'^-₀₀₁ \| 3/4 1/2 1/4 }
59	y+3/4,x+1/4,-z+1/2,-1	{ 2'₁₁₀ \| 3/4 1/4 1/2 }
60	-y+1/2,-x,-z+1/2,-1	{ 2'_1-10 \| 1/2 0 1/2 }
61	y,-x+1/4,-z+1/4,-1	{ -4'⁺₀₀₁ \| 0 1/4 1/4 }
62	-y+3/4,x+1/2,-z+1/4,-1	{ -4'^-₀₀₁ \| 3/4 1/2 1/4 }
63	-y+3/4,-x+3/4,z,-1	{ m'₁₁₀ \| 3/4 3/4 0 }
64	y+1/2,x+1/2,z,-1	{ m'_1-10 \| 1/2 1/2 0 }

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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	-x,-y,z,+1	2₀₀₁
3	-x,y,-z,+1	2₀₁₀
4	x,-y,-z,+1	2₁₀₀
5	-x,-y,-z,+1	-1
6	x,y,-z,+1	m₀₀₁
7	x,-y,z,+1	m₀₁₀
8	-x,y,z,+1	m₁₀₀
9	-y,-x,-z,-1	2'_1-10
10	y,x,-z,-1	2'₁₁₀
11	-y,x,z,-1	4'⁺₀₀₁
12	y,-x,z,-1	4'^-₀₀₁
13	y,x,z,-1	m'_1-10
14	-y,-x,z,-1	m'₁₁₀
15	y,-x,-z,-1	-4'⁺₀₀₁
16	-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	0.00000	0.00000	0.00000	16	m_x,m_x,m_z	1.325	1.325	-2.65	3.25

Non-magnetic atoms:

Label	Atom type	x	y	z	Multiplicity
Ti1	Ti	0.00000	0.00000	0.50000	16
O1	O	0.62500	0.62500	0.12500	8
O2_1	O	0.58000	0.87500	0.87500	32
O2_2	O	0.87500	0.87500	0.58000	16

[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	0.00000	0.00000	0.00000	m_x,m_x,m_z	1.32500	1.32500	-2.65000
2	0.25000	0.25000	0.00000	-m_x,-m_x,m_z	-1.32500	-1.32500	-2.65000
3	0.75000	0.50000	0.25000	-m_x,m_x,-m_z	-1.32500	1.32500	2.65000
4	0.00000	0.25000	0.25000	m_x,-m_x,-m_z	1.32500	-1.32500	2.65000
(0,1/2,1/2) + set click here to show and hide
5	0.00000	0.50000	0.50000	m_x,m_x,m_z	1.32500	1.32500	-2.65000
6	0.25000	0.75000	0.50000	-m_x,-m_x,m_z	-1.32500	-1.32500	-2.65000
7	0.75000	0.00000	0.75000	-m_x,m_x,-m_z	-1.32500	1.32500	2.65000
8	0.00000	0.75000	0.75000	m_x,-m_x,-m_z	1.32500	-1.32500	2.65000
(1/2,0,1/2) + set click here to show and hide
9	0.50000	0.00000	0.50000	m_x,m_x,m_z	1.32500	1.32500	-2.65000
10	0.75000	0.25000	0.50000	-m_x,-m_x,m_z	-1.32500	-1.32500	-2.65000
11	0.25000	0.50000	0.75000	-m_x,m_x,-m_z	-1.32500	1.32500	2.65000
12	0.50000	0.25000	0.75000	m_x,-m_x,-m_z	1.32500	-1.32500	2.65000
(1/2,1/2,0) + set click here to show and hide
13	0.50000	0.50000	0.00000	m_x,m_x,m_z	1.32500	1.32500	-2.65000
14	0.75000	0.75000	0.00000	-m_x,-m_x,m_z	-1.32500	-1.32500	-2.65000
15	0.25000	0.00000	0.25000	-m_x,m_x,-m_z	-1.32500	1.32500	2.65000
16	0.50000	0.75000	0.25000	m_x,-m_x,-m_z	1.32500	-1.32500	2.65000

Non-magnetic atoms:

Set of atoms in the unit cell related by symmetry with the atom Ti1:

Atom	x	y	z
1	0.00000	0.00000	0.50000
2	0.25000	0.25000	0.50000
3	0.75000	0.50000	0.75000
4	0.00000	0.25000	0.75000
(0,1/2,1/2) + set click here to show and hide
5	0.00000	0.50000	0.00000
6	0.25000	0.75000	0.00000
7	0.75000	0.00000	0.25000
8	0.00000	0.75000	0.25000
(1/2,0,1/2) + set click here to show and hide
9	0.50000	0.00000	0.00000
10	0.75000	0.25000	0.00000
11	0.25000	0.50000	0.25000
12	0.50000	0.25000	0.25000
(1/2,1/2,0) + set click here to show and hide
13	0.50000	0.50000	0.50000
14	0.75000	0.75000	0.50000
15	0.25000	0.00000	0.75000
16	0.50000	0.75000	0.75000

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

Atom	x	y	z
1	0.62500	0.62500	0.12500
2	0.87500	0.37500	0.37500
(0,1/2,1/2) + set click here to show and hide
3	0.62500	0.12500	0.62500
4	0.87500	0.87500	0.87500
(1/2,0,1/2) + set click here to show and hide
5	0.12500	0.62500	0.62500
6	0.37500	0.37500	0.87500
(1/2,1/2,0) + set click here to show and hide
7	0.12500	0.12500	0.12500
8	0.37500	0.87500	0.37500

Set of atoms in the unit cell related by symmetry with the atom O2_1:

Atom	x	y	z
1	0.58000	0.87500	0.87500
2	0.67000	0.37500	0.87500
3	0.92000	0.12500	0.62500
4	0.33000	0.12500	0.62500
5	0.12500	0.83000	0.12500
6	0.12500	0.42000	0.12500
7	0.37500	0.17000	0.37500
8	0.37500	0.58000	0.37500
(0,1/2,1/2) + set click here to show and hide
9	0.58000	0.37500	0.37500
10	0.67000	0.87500	0.37500
11	0.92000	0.62500	0.12500
12	0.33000	0.62500	0.12500
13	0.12500	0.33000	0.62500
14	0.12500	0.92000	0.62500
15	0.37500	0.67000	0.87500
16	0.37500	0.08000	0.87500
(1/2,0,1/2) + set click here to show and hide
17	0.08000	0.87500	0.37500
18	0.17000	0.37500	0.37500
19	0.42000	0.12500	0.12500
20	0.83000	0.12500	0.12500
21	0.62500	0.83000	0.62500
22	0.62500	0.42000	0.62500
23	0.87500	0.17000	0.87500
24	0.87500	0.58000	0.87500
(1/2,1/2,0) + set click here to show and hide
25	0.08000	0.37500	0.87500
26	0.17000	0.87500	0.87500
27	0.42000	0.62500	0.62500
28	0.83000	0.62500	0.62500
29	0.62500	0.33000	0.12500
30	0.62500	0.92000	0.12500
31	0.87500	0.67000	0.37500
32	0.87500	0.08000	0.37500

Set of atoms in the unit cell related by symmetry with the atom O2_2:

Atom	x	y	z
1	0.87500	0.87500	0.58000
2	0.87500	0.37500	0.67000
3	0.62500	0.12500	0.92000
4	0.62500	0.62500	0.83000
(0,1/2,1/2) + set click here to show and hide
5	0.87500	0.37500	0.08000
6	0.87500	0.87500	0.17000
7	0.62500	0.62500	0.42000
8	0.62500	0.12500	0.33000
(1/2,0,1/2) + set click here to show and hide
9	0.37500	0.87500	0.08000
10	0.37500	0.37500	0.17000
11	0.12500	0.12500	0.42000
12	0.12500	0.62500	0.33000
(1/2,1/2,0) + set click here to show and hide
13	0.37500	0.37500	0.58000
14	0.37500	0.87500	0.67000
15	0.12500	0.62500	0.92000
16	0.12500	0.12500	0.83000

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Label	Atom type	x	y	z	Multiplicity	Symmetry constraints on M	M_x	M_y	M_z	\|M\|
Er1	Er	0.00000	0.00000	0.00000	16	m_x,m_x,m_z	1.325	1.325	-2.65	3.25

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

label	dim. full irrep	dim. small irrep	direction	action
mGM3+	2	2	'special'	'primary'
mGM2+	1	1		'secondary'

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

Er₂Ti₂O₇ (#0.29)

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

Er2Ti2O7 (#0.29)

Er₂Ti₂O₇ (#0.29)