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	y+1/4,-x+1/2,z+3/4,+1	{ 4^-₀₀₁ \| 1/4 1/2 3/4 }
3	-y,x+3/4,z+3/4,+1	{ 4⁺₀₀₁ \| 0 3/4 3/4 }
4	-x+1/4,-y+1/4,z,+1	{ 2₀₀₁ \| 1/4 1/4 0 }
5	-x,-y,-z,+1	{ -1 \| 0 }
6	-y+3/4,x+1/2,-z+1/4,+1	{ -4^-₀₀₁ \| 3/4 1/2 1/4 }
7	y,-x+1/4,-z+1/4,+1	{ -4⁺₀₀₁ \| 0 1/4 1/4 }
8	x+1/4,y+1/4,-z,+1	{ m₀₀₁ \| 1/4 1/4 0 }
9	-y,-x,-z,-1	{ 2'_1-10 \| 0 }
10	y+1/4,x+1/4,-z,-1	{ 2'₁₁₀ \| 1/4 1/4 0 }
11	-x+3/4,y+1/2,-z+1/4,-1	{ 2'₀₁₀ \| 3/4 1/2 1/4 }
12	x,-y+1/4,-z+1/4,-1	{ 2'₁₀₀ \| 0 1/4 1/4 }
13	y,x,z,-1	{ m'_1-10 \| 0 }
14	-y+1/4,-x+1/4,z,-1	{ m'₁₁₀ \| 1/4 1/4 0 }
15	x+1/4,-y+1/2,z+3/4,-1	{ m'₀₁₀ \| 1/4 1/2 3/4 }
16	-x,y+3/4,z+3/4,-1	{ m'₁₀₀ \| 0 3/4 3/4 }
(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	y+1/4,-x,z+1/4,+1	{ 4^-₀₀₁ \| 1/4 0 1/4 }
19	-y,x+1/4,z+1/4,+1	{ 4⁺₀₀₁ \| 0 1/4 1/4 }
20	-x+1/4,-y+3/4,z+1/2,+1	{ 2₀₀₁ \| 1/4 3/4 1/2 }
21	-x,-y+1/2,-z+1/2,+1	{ -1 \| 0 1/2 1/2 }
22	-y+3/4,x,-z+3/4,+1	{ -4^-₀₀₁ \| 3/4 0 3/4 }
23	y,-x+3/4,-z+3/4,+1	{ -4⁺₀₀₁ \| 0 3/4 3/4 }
24	x+1/4,y+3/4,-z+1/2,+1	{ m₀₀₁ \| 1/4 3/4 1/2 }
25	-y,-x+1/2,-z+1/2,-1	{ 2'_1-10 \| 0 1/2 1/2 }
26	y+1/4,x+3/4,-z+1/2,-1	{ 2'₁₁₀ \| 1/4 3/4 1/2 }
27	-x+3/4,y,-z+3/4,-1	{ 2'₀₁₀ \| 3/4 0 3/4 }
28	x,-y+3/4,-z+3/4,-1	{ 2'₁₀₀ \| 0 3/4 3/4 }
29	y,x+1/2,z+1/2,-1	{ m'_1-10 \| 0 1/2 1/2 }
30	-y+1/4,-x+3/4,z+1/2,-1	{ m'₁₁₀ \| 1/4 3/4 1/2 }
31	x+1/4,-y,z+1/4,-1	{ m'₀₁₀ \| 1/4 0 1/4 }
32	-x,y+1/4,z+1/4,-1	{ m'₁₀₀ \| 0 1/4 1/4 }
(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	y+3/4,-x+1/2,z+1/4,+1	{ 4^-₀₀₁ \| 3/4 1/2 1/4 }
35	-y+1/2,x+3/4,z+1/4,+1	{ 4⁺₀₀₁ \| 1/2 3/4 1/4 }
36	-x+3/4,-y+1/4,z+1/2,+1	{ 2₀₀₁ \| 3/4 1/4 1/2 }
37	-x+1/2,-y,-z+1/2,+1	{ -1 \| 1/2 0 1/2 }
38	-y+1/4,x+1/2,-z+3/4,+1	{ -4^-₀₀₁ \| 1/4 1/2 3/4 }
39	y+1/2,-x+1/4,-z+3/4,+1	{ -4⁺₀₀₁ \| 1/2 1/4 3/4 }
40	x+3/4,y+1/4,-z+1/2,+1	{ m₀₀₁ \| 3/4 1/4 1/2 }
41	-y+1/2,-x,-z+1/2,-1	{ 2'_1-10 \| 1/2 0 1/2 }
42	y+3/4,x+1/4,-z+1/2,-1	{ 2'₁₁₀ \| 3/4 1/4 1/2 }
43	-x+1/4,y+1/2,-z+3/4,-1	{ 2'₀₁₀ \| 1/4 1/2 3/4 }
44	x+1/2,-y+1/4,-z+3/4,-1	{ 2'₁₀₀ \| 1/2 1/4 3/4 }
45	y+1/2,x,z+1/2,-1	{ m'_1-10 \| 1/2 0 1/2 }
46	-y+3/4,-x+1/4,z+1/2,-1	{ m'₁₁₀ \| 3/4 1/4 1/2 }
47	x+3/4,-y+1/2,z+1/4,-1	{ m'₀₁₀ \| 3/4 1/2 1/4 }
48	-x+1/2,y+3/4,z+1/4,-1	{ m'₁₀₀ \| 1/2 3/4 1/4 }
(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	y+3/4,-x,z+3/4,+1	{ 4^-₀₀₁ \| 3/4 0 3/4 }
51	-y+1/2,x+1/4,z+3/4,+1	{ 4⁺₀₀₁ \| 1/2 1/4 3/4 }
52	-x+3/4,-y+3/4,z,+1	{ 2₀₀₁ \| 3/4 3/4 0 }
53	-x+1/2,-y+1/2,-z,+1	{ -1 \| 1/2 1/2 0 }
54	-y+1/4,x,-z+1/4,+1	{ -4^-₀₀₁ \| 1/4 0 1/4 }
55	y+1/2,-x+3/4,-z+1/4,+1	{ -4⁺₀₀₁ \| 1/2 3/4 1/4 }
56	x+3/4,y+3/4,-z,+1	{ m₀₀₁ \| 3/4 3/4 0 }
57	-y+1/2,-x+1/2,-z,-1	{ 2'_1-10 \| 1/2 1/2 0 }
58	y+3/4,x+3/4,-z,-1	{ 2'₁₁₀ \| 3/4 3/4 0 }
59	-x+1/4,y,-z+1/4,-1	{ 2'₀₁₀ \| 1/4 0 1/4 }
60	x+1/2,-y+3/4,-z+1/4,-1	{ 2'₁₀₀ \| 1/2 3/4 1/4 }
61	y+1/2,x+1/2,z,-1	{ m'_1-10 \| 1/2 1/2 0 }
62	-y+3/4,-x+3/4,z,-1	{ m'₁₁₀ \| 3/4 3/4 0 }
63	x+3/4,-y,z+3/4,-1	{ m'₀₁₀ \| 3/4 0 3/4 }
64	-x+1/2,y+1/4,z+3/4,-1	{ m'₁₀₀ \| 1/2 1/4 3/4 }

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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	y,-x,z,+1	4^-₀₀₁
3	-y,x,z,+1	4⁺₀₀₁
4	-x,-y,z,+1	2₀₀₁
5	-x,-y,-z,+1	-1
6	-y,x,-z,+1	-4^-₀₀₁
7	y,-x,-z,+1	-4⁺₀₀₁
8	x,y,-z,+1	m₀₀₁
9	-y,-x,-z,-1	2'_1-10
10	y,x,-z,-1	2'₁₁₀
11	-x,y,-z,-1	2'₀₁₀
12	x,-y,-z,-1	2'₁₀₀
13	y,x,z,-1	m'_1-10
14	-y,-x,z,-1	m'₁₁₀
15	x,-y,z,-1	m'₀₁₀
16	-x,y,z,-1	m'₁₀₀

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Magnetic atoms:

Label	Atom type	x	y	z	Multiplicity	Symmetry constraints on M	M_x	M_y	M_z	\|M\|
Yb1	Yb	0.50000	0.50000	0.50000	16	m_x,m_x,m_z	0.15	0.15	0.87	0.90

Non-magnetic atoms:

Label	Atom type	x	y	z	Multiplicity
Ti1	Ti	0.00000	0.00000	0.00000	16
O1_1	O	0.3309	0.12500	0.12500	32
O1_2	O	0.12500	0.12500	0.3309	16
O2	O	0.37500	0.37500	0.37500	8

[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 Yb1:

Atom	x	y	z	Symmetry constraints on M	M_x	M_y	M_z
1	0.50000	0.50000	0.50000	m_x,m_x,m_z	0.15000	0.15000	0.87000
2	0.75000	0.00000	0.25000	m_x,-m_x,m_z	0.15000	-0.15000	0.87000
3	0.50000	0.25000	0.25000	-m_x,m_x,m_z	-0.15000	0.15000	0.87000
4	0.75000	0.75000	0.50000	-m_x,-m_x,m_z	-0.15000	-0.15000	0.87000
(0,1/2,1/2) + set click here to show and hide
5	0.50000	0.00000	0.00000	m_x,m_x,m_z	0.15000	0.15000	0.87000
6	0.75000	0.50000	0.75000	m_x,-m_x,m_z	0.15000	-0.15000	0.87000
7	0.50000	0.75000	0.75000	-m_x,m_x,m_z	-0.15000	0.15000	0.87000
8	0.75000	0.25000	0.00000	-m_x,-m_x,m_z	-0.15000	-0.15000	0.87000
(1/2,0,1/2) + set click here to show and hide
9	0.00000	0.50000	0.00000	m_x,m_x,m_z	0.15000	0.15000	0.87000
10	0.25000	0.00000	0.75000	m_x,-m_x,m_z	0.15000	-0.15000	0.87000
11	0.00000	0.25000	0.75000	-m_x,m_x,m_z	-0.15000	0.15000	0.87000
12	0.25000	0.75000	0.00000	-m_x,-m_x,m_z	-0.15000	-0.15000	0.87000
(1/2,1/2,0) + set click here to show and hide
13	0.00000	0.00000	0.50000	m_x,m_x,m_z	0.15000	0.15000	0.87000
14	0.25000	0.50000	0.25000	m_x,-m_x,m_z	0.15000	-0.15000	0.87000
15	0.00000	0.75000	0.25000	-m_x,m_x,m_z	-0.15000	0.15000	0.87000
16	0.25000	0.25000	0.50000	-m_x,-m_x,m_z	-0.15000	-0.15000	0.87000

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

Set of atoms in the unit cell related by symmetry with the atom O1_1:

Atom	x	y	z
1	0.33090	0.12500	0.12500
2	0.37500	0.16910	0.87500
3	0.87500	0.08090	0.87500
4	0.91910	0.12500	0.12500
5	0.66910	0.87500	0.87500
6	0.62500	0.83090	0.12500
7	0.12500	0.91910	0.12500
8	0.58090	0.37500	0.87500
(0,1/2,1/2) + set click here to show and hide
9	0.33090	0.62500	0.62500
10	0.37500	0.66910	0.37500
11	0.87500	0.58090	0.37500
12	0.91910	0.62500	0.62500
13	0.66910	0.37500	0.37500
14	0.62500	0.33090	0.62500
15	0.12500	0.41910	0.62500
16	0.58090	0.87500	0.37500
(1/2,0,1/2) + set click here to show and hide
17	0.83090	0.12500	0.62500
18	0.87500	0.16910	0.37500
19	0.37500	0.08090	0.37500
20	0.41910	0.12500	0.62500
21	0.16910	0.87500	0.37500
22	0.12500	0.83090	0.62500
23	0.62500	0.91910	0.62500
24	0.08090	0.37500	0.37500
(1/2,1/2,0) + set click here to show and hide
25	0.83090	0.62500	0.12500
26	0.87500	0.66910	0.87500
27	0.37500	0.58090	0.87500
28	0.41910	0.62500	0.12500
29	0.16910	0.37500	0.87500
30	0.12500	0.33090	0.12500
31	0.62500	0.41910	0.12500
32	0.08090	0.87500	0.87500

Set of atoms in the unit cell related by symmetry with the atom O1_2:

Atom	x	y	z
1	0.12500	0.12500	0.33090
2	0.37500	0.37500	0.08090
3	0.87500	0.87500	0.66910
4	0.62500	0.62500	0.91910
(0,1/2,1/2) + set click here to show and hide
5	0.12500	0.62500	0.83090
6	0.37500	0.87500	0.58090
7	0.87500	0.37500	0.16910
8	0.62500	0.12500	0.41910
(1/2,0,1/2) + set click here to show and hide
9	0.62500	0.12500	0.83090
10	0.87500	0.37500	0.58090
11	0.37500	0.87500	0.16910
12	0.12500	0.62500	0.41910
(1/2,1/2,0) + set click here to show and hide
13	0.62500	0.62500	0.33090
14	0.87500	0.87500	0.08090
15	0.37500	0.37500	0.66910
16	0.12500	0.12500	0.91910

Set of atoms in the unit cell related by symmetry with the atom O2:

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

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Label	Atom type	x	y	z	Multiplicity	Symmetry constraints on M	M_x	M_y	M_z	\|M\|
Yb1	Yb	0.50000	0.50000	0.50000	16	m_x,m_x,m_z	0.15	0.15	0.87	0.90

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

label	dim. full irrep	dim. small irrep	direction	action	number of modes
mGM4+	3	3	special	primary	2

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

Yb₂Ti₂O₇ (#0.158)

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

Yb2Ti2O7 (#0.158)

Yb₂Ti₂O₇ (#0.158)