MAGNDATA - Collection of Magnetic Structures

Transformation matrix from the setting of the parent structure (a_p,b_p,c_p) to the working setting (a,b,c):

a	b	c
1	-1	1/2	a_p
0	1	1/2	b_p
-1	0	1/2	c_p

origin shift
0	a_p
0	b_p
0	c_p

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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,x-y,z,+1	{ 3⁺₀₀₁ \| 0 }
3	-x+y,-x,z,+1	{ 3^-₀₀₁ \| 0 }
4	-x+y,y,z+1/2,+1	{ m₁₀₀ \| 0 0 1/2 }
5	-y,-x,z+1/2,+1	{ m₁₁₀ \| 0 0 1/2 }
6	x,x-y,z+1/2,+1	{ m₀₁₀ \| 0 0 1/2 }
7	x-y,-y,-z+1/2,-1	{ 2'₁₀₀ \| 0 0 1/2 }
8	y,x,-z+1/2,-1	{ 2'₁₁₀ \| 0 0 1/2 }
9	-x,-x+y,-z+1/2,-1	{ 2'₀₁₀ \| 0 0 1/2 }
10	-x,-y,-z,-1	{ -1' \| 0 }
11	y,-x+y,-z,-1	{ -3'⁺₀₀₁ \| 0 }
12	x-y,x,-z,-1	{ -3'^-₀₀₁ \| 0 }
(2/3,1/3,1/3) + set click here to show and hide
13	x+2/3,y+1/3,z+1/3,+1	{ 1 \| 2/3 1/3 1/3 }
14	-y+2/3,x-y+1/3,z+1/3,+1	{ 3⁺₀₀₁ \| 2/3 1/3 1/3 }
15	-x+y+2/3,-x+1/3,z+1/3,+1	{ 3^-₀₀₁ \| 2/3 1/3 1/3 }
16	-x+y+2/3,y+1/3,z+5/6,+1	{ m₁₀₀ \| 2/3 1/3 5/6 }
17	-y+2/3,-x+1/3,z+5/6,+1	{ m₁₁₀ \| 2/3 1/3 5/6 }
18	x+2/3,x-y+1/3,z+5/6,+1	{ m₀₁₀ \| 2/3 1/3 5/6 }
19	x-y+2/3,-y+1/3,-z+5/6,-1	{ 2'₁₀₀ \| 2/3 1/3 5/6 }
20	y+2/3,x+1/3,-z+5/6,-1	{ 2'₁₁₀ \| 2/3 1/3 5/6 }
21	-x+2/3,-x+y+1/3,-z+5/6,-1	{ 2'₀₁₀ \| 2/3 1/3 5/6 }
22	-x+2/3,-y+1/3,-z+1/3,-1	{ -1' \| 2/3 1/3 1/3 }
23	y+2/3,-x+y+1/3,-z+1/3,-1	{ -3'⁺₀₀₁ \| 2/3 1/3 1/3 }
24	x-y+2/3,x+1/3,-z+1/3,-1	{ -3'^-₀₀₁ \| 2/3 1/3 1/3 }
(1/3,2/3,2/3) + set click here to show and hide
25	x+1/3,y+2/3,z+2/3,+1	{ 1 \| 1/3 2/3 2/3 }
26	-y+1/3,x-y+2/3,z+2/3,+1	{ 3⁺₀₀₁ \| 1/3 2/3 2/3 }
27	-x+y+1/3,-x+2/3,z+2/3,+1	{ 3^-₀₀₁ \| 1/3 2/3 2/3 }
28	-x+y+1/3,y+2/3,z+1/6,+1	{ m₁₀₀ \| 1/3 2/3 1/6 }
29	-y+1/3,-x+2/3,z+1/6,+1	{ m₁₁₀ \| 1/3 2/3 1/6 }
30	x+1/3,x-y+2/3,z+1/6,+1	{ m₀₁₀ \| 1/3 2/3 1/6 }
31	x-y+1/3,-y+2/3,-z+1/6,-1	{ 2'₁₀₀ \| 1/3 2/3 1/6 }
32	y+1/3,x+2/3,-z+1/6,-1	{ 2'₁₁₀ \| 1/3 2/3 1/6 }
33	-x+1/3,-x+y+2/3,-z+1/6,-1	{ 2'₀₁₀ \| 1/3 2/3 1/6 }
34	-x+1/3,-y+2/3,-z+2/3,-1	{ -1' \| 1/3 2/3 2/3 }
35	y+1/3,-x+y+2/3,-z+2/3,-1	{ -3'⁺₀₀₁ \| 1/3 2/3 2/3 }
36	x-y+1/3,x+2/3,-z+2/3,-1	{ -3'^-₀₀₁ \| 1/3 2/3 2/3 }

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Transformation matrix from the working setting (a,b,c) to the standard setting of the magnetic space group (a_s,b_s,c_s):

a_s	b_s	c_s
1	0	0	a
0	1	0	b
0	0	1	c

origin shift
0	a
0	b
0	c

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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-y,z,+1	3⁺₀₀₁
3	-x+y,-x,z,+1	3^-₀₀₁
4	-x+y,y,z,+1	m₁₀₀
5	-y,-x,z,+1	m₁₁₀
6	x,x-y,z,+1	m₀₁₀
7	x-y,-y,-z,-1	2'₁₀₀
8	y,x,-z,-1	2'₁₁₀
9	-x,-x+y,-z,-1	2'₀₁₀
10	-x,-y,-z,-1	-1'
11	y,-x+y,-z,-1	-3'⁺₀₀₁
12	x-y,x,-z,-1	-3'^-₀₀₁

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Magnetic atoms:

Label	Atom type	x	y	z	Occupancy	Multiplicity	Symmetry constraints on M	M_x	M_y	M_z	\|M\|
Fe1	Fe	0.16667	0.70833	0.08333	1.	1	m_x,m_y,m_z	-0.1(6),	3.3(3),	0.2(4)	3.36

Non-magnetic atoms:

Label	Atom type	x	y	z	Occupancy	Multiplicity
Ca1_1	Ca	0.12500	0.00000	0.25000	0.66667	18
Ca1_2	Ca	0.62500	0.00000	0.25000	0.66667	18
La1_1	La	0.12500	0.00000	0.25000	0.33333	18
La1_2	La	0.62500	0.00000	0.25000	0.33333	18
Zr1_1	Zr	0.00000	0.00000	0.00000	1.	6
Zr1_2	Zr	0.50000	0.00000	0.00000	1.	18
O1_1	O	0.086(2)	0.089(2)	0.116(2)	1.	36
O1_2	O	0.116(2)	0.256(2)	0.178(2)	1.	36
O1_3	O	0.614(1)	0.710(1)	0.288(2)	1.	36
O1_4	O	0.507(2)	0.613(1)	0.089(2)	1.	36

[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 Fe1:

Atom	x	y	z	Symmetry constraints on M	M_x	M_y	M_z
1

Non-magnetic atoms:

Set of atoms in the unit cell related by symmetry with the atom Ca1_1:

Atom	x	y	z
1	0.12500	0.00000	0.25000
2	0.00000	0.12500	0.25000
3	0.87500	0.87500	0.25000
4	0.87500	0.00000	0.75000
5	0.00000	0.87500	0.75000
6	0.12500	0.12500	0.75000
(2/3,1/3,1/3) + set click here to show and hide
7	0.79167	0.33333	0.58333
8	0.66667	0.45833	0.58333
9	0.54167	0.20833	0.58333
10	0.54167	0.33333	0.08333
11	0.66667	0.20833	0.08333
12	0.79167	0.45833	0.08333
(1/3,2/3,2/3) + set click here to show and hide
13	0.45833	0.66667	0.91667
14	0.33333	0.79167	0.91667
15	0.20833	0.54167	0.91667
16	0.20833	0.66667	0.41667
17	0.33333	0.54167	0.41667
18	0.45833	0.79167	0.41667

Set of atoms in the unit cell related by symmetry with the atom Ca1_2:

Atom	x	y	z
1	0.62500	0.00000	0.25000
2	0.00000	0.62500	0.25000
3	0.37500	0.37500	0.25000
4	0.37500	0.00000	0.75000
5	0.00000	0.37500	0.75000
6	0.62500	0.62500	0.75000
(2/3,1/3,1/3) + set click here to show and hide
7	0.29167	0.33333	0.58333
8	0.66667	0.95833	0.58333
9	0.04167	0.70833	0.58333
10	0.04167	0.33333	0.08333
11	0.66667	0.70833	0.08333
12	0.29167	0.95833	0.08333
(1/3,2/3,2/3) + set click here to show and hide
13	0.95833	0.66667	0.91667
14	0.33333	0.29167	0.91667
15	0.70833	0.04167	0.91667
16	0.70833	0.66667	0.41667
17	0.33333	0.04167	0.41667
18	0.95833	0.29167	0.41667

Set of atoms in the unit cell related by symmetry with the atom La1_1:

Atom	x	y	z
1	0.12500	0.00000	0.25000
2	0.00000	0.12500	0.25000
3	0.87500	0.87500	0.25000
4	0.87500	0.00000	0.75000
5	0.00000	0.87500	0.75000
6	0.12500	0.12500	0.75000
(2/3,1/3,1/3) + set click here to show and hide
7	0.79167	0.33333	0.58333
8	0.66667	0.45833	0.58333
9	0.54167	0.20833	0.58333
10	0.54167	0.33333	0.08333
11	0.66667	0.20833	0.08333
12	0.79167	0.45833	0.08333
(1/3,2/3,2/3) + set click here to show and hide
13	0.45833	0.66667	0.91667
14	0.33333	0.79167	0.91667
15	0.20833	0.54167	0.91667
16	0.20833	0.66667	0.41667
17	0.33333	0.54167	0.41667
18	0.45833	0.79167	0.41667

Set of atoms in the unit cell related by symmetry with the atom La1_2:

Atom	x	y	z
1	0.62500	0.00000	0.25000
2	0.00000	0.62500	0.25000
3	0.37500	0.37500	0.25000
4	0.37500	0.00000	0.75000
5	0.00000	0.37500	0.75000
6	0.62500	0.62500	0.75000
(2/3,1/3,1/3) + set click here to show and hide
7	0.29167	0.33333	0.58333
8	0.66667	0.95833	0.58333
9	0.04167	0.70833	0.58333
10	0.04167	0.33333	0.08333
11	0.66667	0.70833	0.08333
12	0.29167	0.95833	0.08333
(1/3,2/3,2/3) + set click here to show and hide
13	0.95833	0.66667	0.91667
14	0.33333	0.29167	0.91667
15	0.70833	0.04167	0.91667
16	0.70833	0.66667	0.41667
17	0.33333	0.04167	0.41667
18	0.95833	0.29167	0.41667

Set of atoms in the unit cell related by symmetry with the atom Zr1_1:

Atom	x	y	z
1	0.00000	0.00000	0.00000
2	0.00000	0.00000	0.50000
(2/3,1/3,1/3) + set click here to show and hide
3	0.66667	0.33333	0.33333
4	0.66667	0.33333	0.83333
(1/3,2/3,2/3) + set click here to show and hide
5	0.33333	0.66667	0.66667
6	0.33333	0.66667	0.16667

Set of atoms in the unit cell related by symmetry with the atom Zr1_2:

Atom	x	y	z
1	0.50000	0.00000	0.00000
2	0.00000	0.50000	0.00000
3	0.50000	0.50000	0.00000
4	0.50000	0.00000	0.50000
5	0.00000	0.50000	0.50000
6	0.50000	0.50000	0.50000
(2/3,1/3,1/3) + set click here to show and hide
7	0.16667	0.33333	0.33333
8	0.66667	0.83333	0.33333
9	0.16667	0.83333	0.33333
10	0.16667	0.33333	0.83333
11	0.66667	0.83333	0.83333
12	0.16667	0.83333	0.83333
(1/3,2/3,2/3) + set click here to show and hide
13	0.83333	0.66667	0.66667
14	0.33333	0.16667	0.66667
15	0.83333	0.16667	0.66667
16	0.83333	0.66667	0.16667
17	0.33333	0.16667	0.16667
18	0.83333	0.16667	0.16667

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

Atom	x	y	z
1	0.08600	0.08900	0.11600
2	0.91100	0.99700	0.11600
3	0.00300	0.91400	0.11600
4	0.00300	0.08900	0.61600
5	0.91100	0.91400	0.61600
6	0.08600	0.99700	0.61600
7	0.99700	0.91100	0.38400
8	0.08900	0.08600	0.38400
9	0.91400	0.00300	0.38400
10	0.91400	0.91100	0.88400
11	0.08900	0.00300	0.88400
12	0.99700	0.08600	0.88400
(2/3,1/3,1/3) + set click here to show and hide
13	0.75267	0.42233	0.44933
14	0.57767	0.33033	0.44933
15	0.66967	0.24733	0.44933
16	0.66967	0.42233	0.94933
17	0.57767	0.24733	0.94933
18	0.75267	0.33033	0.94933
19	0.66367	0.24433	0.71733
20	0.75567	0.41933	0.71733
21	0.58067	0.33633	0.71733
22	0.58067	0.24433	0.21733
23	0.75567	0.33633	0.21733
24	0.66367	0.41933	0.21733
(1/3,2/3,2/3) + set click here to show and hide
25	0.41933	0.75567	0.78267
26	0.24433	0.66367	0.78267
27	0.33633	0.58067	0.78267
28	0.33633	0.75567	0.28267
29	0.24433	0.58067	0.28267
30	0.41933	0.66367	0.28267
31	0.33033	0.57767	0.05067
32	0.42233	0.75267	0.05067
33	0.24733	0.66967	0.05067
34	0.24733	0.57767	0.55067
35	0.42233	0.66967	0.55067
36	0.33033	0.75267	0.55067

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

Atom	x	y	z
1	0.11600	0.25600	0.17800
2	0.74400	0.86000	0.17800
3	0.14000	0.88400	0.17800
4	0.14000	0.25600	0.67800
5	0.74400	0.88400	0.67800
6	0.11600	0.86000	0.67800
7	0.86000	0.74400	0.32200
8	0.25600	0.11600	0.32200
9	0.88400	0.14000	0.32200
10	0.88400	0.74400	0.82200
11	0.25600	0.14000	0.82200
12	0.86000	0.11600	0.82200
(2/3,1/3,1/3) + set click here to show and hide
13	0.78267	0.58933	0.51133
14	0.41067	0.19333	0.51133
15	0.80667	0.21733	0.51133
16	0.80667	0.58933	0.01133
17	0.41067	0.21733	0.01133
18	0.78267	0.19333	0.01133
19	0.52667	0.07733	0.65533
20	0.92267	0.44933	0.65533
21	0.55067	0.47333	0.65533
22	0.55067	0.07733	0.15533
23	0.92267	0.47333	0.15533
24	0.52667	0.44933	0.15533
(1/3,2/3,2/3) + set click here to show and hide
25	0.44933	0.92267	0.84467
26	0.07733	0.52667	0.84467
27	0.47333	0.55067	0.84467
28	0.47333	0.92267	0.34467
29	0.07733	0.55067	0.34467
30	0.44933	0.52667	0.34467
31	0.19333	0.41067	0.98867
32	0.58933	0.78267	0.98867
33	0.21733	0.80667	0.98867
34	0.21733	0.41067	0.48867
35	0.58933	0.80667	0.48867
36	0.19333	0.78267	0.48867

Set of atoms in the unit cell related by symmetry with the atom O1_3:

Atom	x	y	z
1	0.61400	0.71000	0.28800
2	0.29000	0.90400	0.28800
3	0.09600	0.38600	0.28800
4	0.09600	0.71000	0.78800
5	0.29000	0.38600	0.78800
6	0.61400	0.90400	0.78800
7	0.90400	0.29000	0.21200
8	0.71000	0.61400	0.21200
9	0.38600	0.09600	0.21200
10	0.38600	0.29000	0.71200
11	0.71000	0.09600	0.71200
12	0.90400	0.61400	0.71200
(2/3,1/3,1/3) + set click here to show and hide
13	0.28067	0.04333	0.62133
14	0.95667	0.23733	0.62133
15	0.76267	0.71933	0.62133
16	0.76267	0.04333	0.12133
17	0.95667	0.71933	0.12133
18	0.28067	0.23733	0.12133
19	0.57067	0.62333	0.54533
20	0.37667	0.94733	0.54533
21	0.05267	0.42933	0.54533
22	0.05267	0.62333	0.04533
23	0.37667	0.42933	0.04533
24	0.57067	0.94733	0.04533
(1/3,2/3,2/3) + set click here to show and hide
25	0.94733	0.37667	0.95467
26	0.62333	0.57067	0.95467
27	0.42933	0.05267	0.95467
28	0.42933	0.37667	0.45467
29	0.62333	0.05267	0.45467
30	0.94733	0.57067	0.45467
31	0.23733	0.95667	0.87867
32	0.04333	0.28067	0.87867
33	0.71933	0.76267	0.87867
34	0.71933	0.95667	0.37867
35	0.04333	0.76267	0.37867
36	0.23733	0.28067	0.37867

Set of atoms in the unit cell related by symmetry with the atom O1_4:

Atom	x	y	z
1	0.50700	0.61300	0.08900
2	0.38700	0.89400	0.08900
3	0.10600	0.49300	0.08900
4	0.10600	0.61300	0.58900
5	0.38700	0.49300	0.58900
6	0.50700	0.89400	0.58900
7	0.89400	0.38700	0.41100
8	0.61300	0.50700	0.41100
9	0.49300	0.10600	0.41100
10	0.49300	0.38700	0.91100
11	0.61300	0.10600	0.91100
12	0.89400	0.50700	0.91100
(2/3,1/3,1/3) + set click here to show and hide
13	0.17367	0.94633	0.42233
14	0.05367	0.22733	0.42233
15	0.77267	0.82633	0.42233
16	0.77267	0.94633	0.92233
17	0.05367	0.82633	0.92233
18	0.17367	0.22733	0.92233
19	0.56067	0.72033	0.74433
20	0.27967	0.84033	0.74433
21	0.15967	0.43933	0.74433
22	0.15967	0.72033	0.24433
23	0.27967	0.43933	0.24433
24	0.56067	0.84033	0.24433
(1/3,2/3,2/3) + set click here to show and hide
25	0.84033	0.27967	0.75567
26	0.72033	0.56067	0.75567
27	0.43933	0.15967	0.75567
28	0.43933	0.27967	0.25567
29	0.72033	0.15967	0.25567
30	0.84033	0.56067	0.25567
31	0.22733	0.05367	0.07767
32	0.94633	0.17367	0.07767
33	0.82633	0.77267	0.07767
34	0.82633	0.05367	0.57767
35	0.94633	0.77267	0.57767
36	0.22733	0.17367	0.57767

[Hide]

Label	Atom type	x	y	z	Multiplicity	Symmetry constraints on M	M_x	M_y	M_z	\|M\|
Fe1	Fe	0.16667	0.70833	0.08333	1	m_x,m_y,m_z	-0.1(6),	3.3(3),	0.2(4)	3.36

[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

Ca₂LaZr₂Fe₃O₁₂ (#0.754)

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

Ca2LaZr2Fe3O12 (#0.754)

Ca₂LaZr₂Fe₃O₁₂ (#0.754)