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	-x,-y,-z,+1	{ -1 \| 0 }
5	-z,-x,-y,+1	{ -3⁺₁₁₁ \| 0 }
6	-y,-z,-x,+1	{ -3^-₁₁₁ \| 0 }
7	-z,-y,-x,-1	{ 2'_-101 \| 0 }
8	-x,-z,-y,-1	{ 2'_01-1 \| 0 }
9	-y,-x,-z,-1	{ 2'_1-10 \| 0 }
10	z,y,x,-1	{ m'_-101 \| 0 }
11	x,z,y,-1	{ m'_01-1 \| 0 }
12	y,x,z,-1	{ m'_1-10 \| 0 }
(0,1/2,1/2) + set click here to show and hide
13	x,y+1/2,z+1/2,+1	{ 1 \| 0 1/2 1/2 }
14	z,x+1/2,y+1/2,+1	{ 3⁺₁₁₁ \| 0 1/2 1/2 }
15	y,z+1/2,x+1/2,+1	{ 3^-₁₁₁ \| 0 1/2 1/2 }
16	-x,-y+1/2,-z+1/2,+1	{ -1 \| 0 1/2 1/2 }
17	-z,-x+1/2,-y+1/2,+1	{ -3⁺₁₁₁ \| 0 1/2 1/2 }
18	-y,-z+1/2,-x+1/2,+1	{ -3^-₁₁₁ \| 0 1/2 1/2 }
19	-z,-y+1/2,-x+1/2,-1	{ 2'_-101 \| 0 1/2 1/2 }
20	-x,-z+1/2,-y+1/2,-1	{ 2'_01-1 \| 0 1/2 1/2 }
21	-y,-x+1/2,-z+1/2,-1	{ 2'_1-10 \| 0 1/2 1/2 }
22	z,y+1/2,x+1/2,-1	{ m'_-101 \| 0 1/2 1/2 }
23	x,z+1/2,y+1/2,-1	{ m'_01-1 \| 0 1/2 1/2 }
24	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
25	x+1/2,y,z+1/2,+1	{ 1 \| 1/2 0 1/2 }
26	z+1/2,x,y+1/2,+1	{ 3⁺₁₁₁ \| 1/2 0 1/2 }
27	y+1/2,z,x+1/2,+1	{ 3^-₁₁₁ \| 1/2 0 1/2 }
28	-x+1/2,-y,-z+1/2,+1	{ -1 \| 1/2 0 1/2 }
29	-z+1/2,-x,-y+1/2,+1	{ -3⁺₁₁₁ \| 1/2 0 1/2 }
30	-y+1/2,-z,-x+1/2,+1	{ -3^-₁₁₁ \| 1/2 0 1/2 }
31	-z+1/2,-y,-x+1/2,-1	{ 2'_-101 \| 1/2 0 1/2 }
32	-x+1/2,-z,-y+1/2,-1	{ 2'_01-1 \| 1/2 0 1/2 }
33	-y+1/2,-x,-z+1/2,-1	{ 2'_1-10 \| 1/2 0 1/2 }
34	z+1/2,y,x+1/2,-1	{ m'_-101 \| 1/2 0 1/2 }
35	x+1/2,z,y+1/2,-1	{ m'_01-1 \| 1/2 0 1/2 }
36	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
37	x+1/2,y+1/2,z,+1	{ 1 \| 1/2 1/2 0 }
38	z+1/2,x+1/2,y,+1	{ 3⁺₁₁₁ \| 1/2 1/2 0 }
39	y+1/2,z+1/2,x,+1	{ 3^-₁₁₁ \| 1/2 1/2 0 }
40	-x+1/2,-y+1/2,-z,+1	{ -1 \| 1/2 1/2 0 }
41	-z+1/2,-x+1/2,-y,+1	{ -3⁺₁₁₁ \| 1/2 1/2 0 }
42	-y+1/2,-z+1/2,-x,+1	{ -3^-₁₁₁ \| 1/2 1/2 0 }
43	-z+1/2,-y+1/2,-x,-1	{ 2'_-101 \| 1/2 1/2 0 }
44	-x+1/2,-z+1/2,-y,-1	{ 2'_01-1 \| 1/2 1/2 0 }
45	-y+1/2,-x+1/2,-z,-1	{ 2'_1-10 \| 1/2 1/2 0 }
46	z+1/2,y+1/2,x,-1	{ m'_-101 \| 1/2 1/2 0 }
47	x+1/2,z+1/2,y,-1	{ m'_01-1 \| 1/2 1/2 0 }
48	y+1/2,x+1/2,z,-1	{ m'_1-10 \| 1/2 1/2 0 }

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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	-x,-y,-z,+1	-1
5	-z,-x,-y,+1	-3⁺₁₁₁
6	-y,-z,-x,+1	-3^-₁₁₁
7	-z,-y,-x,-1	2'_-101
8	-x,-z,-y,-1	2'_01-1
9	-y,-x,-z,-1	2'_1-10
10	z,y,x,-1	m'_-101
11	x,z,y,-1	m'_01-1
12	y,x,z,-1	m'_1-10

Magnetic atoms:

Label	Atom type	x	y	z	Multiplicity	Symmetry constraints on M	M_x	M_y	M_z	\|M\|
Tb1_1	Tb	0.50000	0.50000	0.50000	4	m_x,m_x,m_x	3.2	3.2	3.2	5.54
Tb1_2	Tb	0.25000	0.75000	0.00000	12	m_x,m_x,m_z	1.9	1.9	-2.3	3.54

Non-magnetic atoms:

Label	Atom type	x	y	z	Multiplicity
Ti1_1	Ti	0.00000	0.00000	0.00000	4
Ti1_2	Ti	0.75000	0.25000	0.50000	12
O1_1	O	0.32850	0.12500	0.12500	24
O1_2	O	0.42150	0.12500	0.62500	24
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 Tb1_1:

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_x	3.20000	3.20000	3.20000
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2	0.50000	0.00000	0.00000	m_x,m_x,m_x	3.20000	3.20000	3.20000
(1/2,0,1/2) + set click here to show and hide
3	0.00000	0.50000	0.00000	m_x,m_x,m_x	3.20000	3.20000	3.20000
(1/2,1/2,0) + set click here to show and hide
4	0.00000	0.00000	0.50000	m_x,m_x,m_x	3.20000	3.20000	3.20000

Set of atoms in the unit cell related by symmetry with the magnetic atom Tb1_2:

Atom	x	y	z	Symmetry constraints on M	M_x	M_y	M_z
1	0.25000	0.75000	0.00000	m_x,m_x,m_z	1.90000	1.90000	-2.30000
2	0.00000	0.25000	0.75000	m_z,m_x,m_x	-2.30000	1.90000	1.90000
3	0.75000	0.00000	0.25000	m_x,m_z,m_x	1.90000	-2.30000	1.90000
(0,1/2,1/2) + set click here to show and hide
4	0.25000	0.25000	0.50000	m_x,m_x,m_z	1.90000	1.90000	-2.30000
5	0.00000	0.75000	0.25000	m_z,m_x,m_x	-2.30000	1.90000	1.90000
6	0.75000	0.50000	0.75000	m_x,m_z,m_x	1.90000	-2.30000	1.90000
(1/2,0,1/2) + set click here to show and hide
7	0.75000	0.75000	0.50000	m_x,m_x,m_z	1.90000	1.90000	-2.30000
8	0.50000	0.25000	0.25000	m_z,m_x,m_x	-2.30000	1.90000	1.90000
9	0.25000	0.00000	0.75000	m_x,m_z,m_x	1.90000	-2.30000	1.90000
(1/2,1/2,0) + set click here to show and hide
10	0.75000	0.25000	0.00000	m_x,m_x,m_z	1.90000	1.90000	-2.30000
11	0.50000	0.75000	0.75000	m_z,m_x,m_x	-2.30000	1.90000	1.90000
12	0.25000	0.50000	0.25000	m_x,m_z,m_x	1.90000	-2.30000	1.90000

Non-magnetic atoms:

Set of atoms in the unit cell related by symmetry with the atom Ti1_1:

Atom	x	y	z
1	0.00000	0.00000	0.00000
(0,1/2,1/2) + set click here to show and hide
2	0.00000	0.50000	0.50000
(1/2,0,1/2) + set click here to show and hide
3	0.50000	0.00000	0.50000
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4	0.50000	0.50000	0.00000

Set of atoms in the unit cell related by symmetry with the atom Ti1_2:

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

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

Atom	x	y	z
1	0.32850	0.12500	0.12500
2	0.12500	0.32850	0.12500
3	0.12500	0.12500	0.32850
4	0.67150	0.87500	0.87500
5	0.87500	0.67150	0.87500
6	0.87500	0.87500	0.67150
(0,1/2,1/2) + set click here to show and hide
7	0.32850	0.62500	0.62500
8	0.12500	0.82850	0.62500
9	0.12500	0.62500	0.82850
10	0.67150	0.37500	0.37500
11	0.87500	0.17150	0.37500
12	0.87500	0.37500	0.17150
(1/2,0,1/2) + set click here to show and hide
13	0.82850	0.12500	0.62500
14	0.62500	0.32850	0.62500
15	0.62500	0.12500	0.82850
16	0.17150	0.87500	0.37500
17	0.37500	0.67150	0.37500
18	0.37500	0.87500	0.17150
(1/2,1/2,0) + set click here to show and hide
19	0.82850	0.62500	0.12500
20	0.62500	0.82850	0.12500
21	0.62500	0.62500	0.32850
22	0.17150	0.37500	0.87500
23	0.37500	0.17150	0.87500
24	0.37500	0.37500	0.67150

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

Atom	x	y	z
1	0.42150	0.12500	0.62500
2	0.62500	0.42150	0.12500
3	0.12500	0.62500	0.42150
4	0.57850	0.87500	0.37500
5	0.37500	0.57850	0.87500
6	0.87500	0.37500	0.57850
(0,1/2,1/2) + set click here to show and hide
7	0.42150	0.62500	0.12500
8	0.62500	0.92150	0.62500
9	0.12500	0.12500	0.92150
10	0.57850	0.37500	0.87500
11	0.37500	0.07850	0.37500
12	0.87500	0.87500	0.07850
(1/2,0,1/2) + set click here to show and hide
13	0.92150	0.12500	0.12500
14	0.12500	0.42150	0.62500
15	0.62500	0.62500	0.92150
16	0.07850	0.87500	0.87500
17	0.87500	0.57850	0.37500
18	0.37500	0.37500	0.07850
(1/2,1/2,0) + set click here to show and hide
19	0.92150	0.62500	0.62500
20	0.12500	0.92150	0.12500
21	0.62500	0.12500	0.42150
22	0.07850	0.37500	0.37500
23	0.87500	0.07850	0.87500
24	0.37500	0.87500	0.57850

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

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Label	Atom type	x	y	z	Multiplicity	Symmetry constraints on M	M_x	M_y	M_z	\|M\|
Tb1_1	Tb	0.50000	0.50000	0.50000	4	m_x,m_x,m_x	3.2	3.2	3.2	5.54
Tb1_2	Tb	0.25000	0.75000	0.00000	12	m_x,m_x,m_z	1.9	1.9	-2.3	3.54

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

label	dim. full irrep	dim. small irrep	direction	action	number of modes	presence
mGM4+	3	3	special	primary	2
mGM2+	1	1		secondary	1	yes

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

Tb₂Ti₂O₇ (#0.77)

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

Tb2Ti2O7 (#0.77)

Tb₂Ti₂O₇ (#0.77)