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	0	0	a_p
0	1	0	b_p
0	0	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	x-y,x,z,+1	{ 6⁺₀₀₁ \| 0 }
3	-y,x-y,z,+1	{ 3⁺₀₀₁ \| 0 }
4	-x,-y,z,+1	{ 2₀₀₁ \| 0 }
5	-x+y,-x,z,+1	{ 3^-₀₀₁ \| 0 }
6	y,-x+y,z,+1	{ 6^-₀₀₁ \| 0 }
7	x-y,-y,-z+1/2,+1	{ 2₁₀₀ \| 0 0 1/2 }
8	y,x,-z+1/2,+1	{ 2₁₁₀ \| 0 0 1/2 }
9	-x,-x+y,-z+1/2,+1	{ 2₀₁₀ \| 0 0 1/2 }
10	x,x-y,-z+1/2,+1	{ 2₂₁₀ \| 0 0 1/2 }
11	-x+y,y,-z+1/2,+1	{ 2₁₂₀ \| 0 0 1/2 }
12	-y,-x,-z+1/2,+1	{ 2_1-10 \| 0 0 1/2 }
13	-x,-y,-z,+1	{ -1 \| 0 }
14	-x+y,-x,-z,+1	{ -6⁺₀₀₁ \| 0 }
15	y,-x+y,-z,+1	{ -3⁺₀₀₁ \| 0 }
16	x,y,-z,+1	{ m₀₀₁ \| 0 }
17	x-y,x,-z,+1	{ -3^-₀₀₁ \| 0 }
18	-y,x-y,-z,+1	{ -6^-₀₀₁ \| 0 }
19	-x+y,y,z+1/2,+1	{ m₁₀₀ \| 0 0 1/2 }
20	-y,-x,z+1/2,+1	{ m₁₁₀ \| 0 0 1/2 }
21	x,x-y,z+1/2,+1	{ m₀₁₀ \| 0 0 1/2 }
22	-x,-x+y,z+1/2,+1	{ m₂₁₀ \| 0 0 1/2 }
23	x-y,-y,z+1/2,+1	{ m₁₂₀ \| 0 0 1/2 }
24	y,x,z+1/2,+1	{ m_1-10 \| 0 0 1/2 }
(0,0,1/2)' + set click here to show and hide
25	x,y,z+1/2,-1	{ 1' \| 0 0 1/2 }
26	x-y,x,z+1/2,-1	{ 6'⁺₀₀₁ \| 0 0 1/2 }
27	-y,x-y,z+1/2,-1	{ 3'⁺₀₀₁ \| 0 0 1/2 }
28	-x,-y,z+1/2,-1	{ 2'₀₀₁ \| 0 0 1/2 }
29	-x+y,-x,z+1/2,-1	{ 3'^-₀₀₁ \| 0 0 1/2 }
30	y,-x+y,z+1/2,-1	{ 6'^-₀₀₁ \| 0 0 1/2 }
31	x-y,-y,-z,-1	{ 2'₁₀₀ \| 0 }
32	y,x,-z,-1	{ 2'₁₁₀ \| 0 }
33	-x,-x+y,-z,-1	{ 2'₀₁₀ \| 0 }
34	x,x-y,-z,-1	{ 2'₂₁₀ \| 0 }
35	-x+y,y,-z,-1	{ 2'₁₂₀ \| 0 }
36	-y,-x,-z,-1	{ 2'_1-10 \| 0 }
37	-x,-y,-z+1/2,-1	{ -1' \| 0 0 1/2 }
38	-x+y,-x,-z+1/2,-1	{ -6'⁺₀₀₁ \| 0 0 1/2 }
39	y,-x+y,-z+1/2,-1	{ -3'⁺₀₀₁ \| 0 0 1/2 }
40	x,y,-z+1/2,-1	{ m'₀₀₁ \| 0 0 1/2 }
41	x-y,x,-z+1/2,-1	{ -3'^-₀₀₁ \| 0 0 1/2 }
42	-y,x-y,-z+1/2,-1	{ -6'^-₀₀₁ \| 0 0 1/2 }
43	-x+y,y,z,-1	{ m'₁₀₀ \| 0 }
44	-y,-x,z,-1	{ m'₁₁₀ \| 0 }
45	x,x-y,z,-1	{ m'₀₁₀ \| 0 }
46	-x,-x+y,z,-1	{ m'₂₁₀ \| 0 }
47	x-y,-y,z,-1	{ m'₁₂₀ \| 0 }
48	y,x,z,-1	{ m'_1-10 \| 0 }

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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	x-y,x,z,+1	6⁺₀₀₁
3	-y,x-y,z,+1	3⁺₀₀₁
4	-x,-y,z,+1	2₀₀₁
5	-x+y,-x,z,+1	3^-₀₀₁
6	y,-x+y,z,+1	6^-₀₀₁
7	x-y,-y,-z,+1	2₁₀₀
8	y,x,-z,+1	2₁₁₀
9	-x,-x+y,-z,+1	2₀₁₀
10	x,x-y,-z,+1	2₂₁₀
11	-x+y,y,-z,+1	2₁₂₀
12	-y,-x,-z,+1	2_1-10
13	-x,-y,-z,+1	-1
14	-x+y,-x,-z,+1	-6⁺₀₀₁
15	y,-x+y,-z,+1	-3⁺₀₀₁
16	x,y,-z,+1	m₀₀₁
17	x-y,x,-z,+1	-3^-₀₀₁
18	-y,x-y,-z,+1	-6^-₀₀₁
19	-x+y,y,z,+1	m₁₀₀
20	-y,-x,z,+1	m₁₁₀
21	x,x-y,z,+1	m₀₁₀
22	-x,-x+y,z,+1	m₂₁₀
23	x-y,-y,z,+1	m₁₂₀
24	y,x,z,+1	m_1-10
1' + set click here to show and hide
25	x,y,z,-1	1'
26	x-y,x,z,-1	6'⁺₀₀₁
27	-y,x-y,z,-1	3'⁺₀₀₁
28	-x,-y,z,-1	2'₀₀₁
29	-x+y,-x,z,-1	3'^-₀₀₁
30	y,-x+y,z,-1	6'^-₀₀₁
31	x-y,-y,-z,-1	2'₁₀₀
32	y,x,-z,-1	2'₁₁₀
33	-x,-x+y,-z,-1	2'₀₁₀
34	x,x-y,-z,-1	2'₂₁₀
35	-x+y,y,-z,-1	2'₁₂₀
36	-y,-x,-z,-1	2'_1-10
37	-x,-y,-z,-1	-1'
38	-x+y,-x,-z,-1	-6'⁺₀₀₁
39	y,-x+y,-z,-1	-3'⁺₀₀₁
40	x,y,-z,-1	m'₀₀₁
41	x-y,x,-z,-1	-3'^-₀₀₁
42	-y,x-y,-z,-1	-6'^-₀₀₁
43	-x+y,y,z,-1	m'₁₀₀
44	-y,-x,z,-1	m'₁₁₀
45	x,x-y,z,-1	m'₀₁₀
46	-x,-x+y,z,-1	m'₂₁₀
47	x-y,-y,z,-1	m'₁₂₀
48	y,x,z,-1	m'_1-10

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Magnetic atoms:

Label	Atom type	x	y	z	Multiplicity	Symmetry constraints on M	M_x	M_y	M_z	\|M\|
Fe1	Fe	0.50000	0.00000	0.00000	6	0,0,m_z	0.0	0.0	1.67(5)	1.67

Non-magnetic atoms:

Label	Atom type	x	y	z	Multiplicity
Ge1	Ge	0.00000	0.00000	0.00000	2
Ge2	Ge	0.33333	0.66667	0.25000	4

Atom	x	y	z	Symmetry constraints on M	M_x	M_y	M_z
1	0.50000	0.00000	0.00000	0,0,m_z	0.00000	0.00000	1.67000
2	0.50000	0.50000	0.00000	0,0,m_z	0.00000	0.00000	1.67000
3	0.00000	0.50000	0.00000	0,0,m_z	0.00000	0.00000	1.67000
(0,0,1/2)' + set click here to show and hide
4	0.50000	0.00000	0.50000	0,0,-m_z	0.00000	0.00000	-1.67000
5	0.50000	0.50000	0.50000	0,0,-m_z	0.00000	0.00000	-1.67000
6	0.00000	0.50000	0.50000	0,0,-m_z	0.00000	0.00000	-1.67000

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

Atom	x	y	z
1	0.33333	0.66667	0.25000
2	0.66666	0.33333	0.25000
(0,0,1/2)' + set click here to show and hide
3	0.33333	0.66667	0.75000
4	0.66666	0.33333	0.75000

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

Label	Atom type	x	y	z	Multiplicity	Symmetry constraints on M	M_x	M_y	M_z	\|M\|
Fe1	Fe	0.50000	0.00000	0.00000	6	0,0,m_z	0.0	0.0	1.67(5)	1.67

Atom	x	y	z	Symmetry constraints on M	M_x	M_y	M_z
1	0.50000	0.00000	0.00000	0,0,m_z	0.00000	0.00000	1.67000
2	0.50000	0.50000	0.00000	0,0,m_z	0.00000	0.00000	1.67000
3	0.00000	0.50000	0.00000	0,0,m_z	0.00000	0.00000	1.67000
(0,0,1/2)' + set click here to show and hide
4	0.50000	0.00000	0.50000	0,0,-m_z	0.00000	0.00000	-1.67000
5	0.50000	0.50000	0.50000	0,0,-m_z	0.00000	0.00000	-1.67000
6	0.00000	0.50000	0.50000	0,0,-m_z	0.00000	0.00000	-1.67000

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

label	dim. small irrep	dim. full irrep	action	number of modes
mA2+	1	1	primary	1

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

FeGe (#1.629)