MAGNDATA - Collection of Magnetic Structures

Magnetic structure with only magnetic atoms

N	(x,y,z)	Seitz notation
1	x1,x2,x3,x4,+1	{ 1 \| 0 }
2	-x2,x1-x2,x3,x4,+1	{ 3⁺₀₀₁ \| 0 }
3	-x1+x2,-x1,x3,x4,+1	{ 3^-₀₀₁ \| 0 }
4	x2,x1,-x3+1/2,-x4,+1	{ 2₁₁₀ \| 0 0 1/2 0 }
5	x1-x2,-x2,-x3+1/2,-x4,+1	{ 2₁₀₀ \| 0 0 1/2 0 }
6	-x1,-x1+x2,-x3+1/2,-x4,+1	{ 2₀₁₀ \| 0 0 1/2 0 }
7	-x1,-x2,-x3,-x4,+1	{ -1 \| 0 }
8	x2,-x1+x2,-x3,-x4,+1	{ -3⁺₀₀₁ \| 0 }
9	x1-x2,x1,-x3,-x4,+1	{ -3^-₀₀₁ \| 0 }
10	-x2,-x1,x3+1/2,x4,+1	{ m₁₁₀ \| 0 0 1/2 0 }
11	-x1+x2,x2,x3+1/2,x4,+1	{ m₁₀₀ \| 0 0 1/2 0 }
12	x1,x1-x2,x3+1/2,x4,+1	{ m₀₁₀ \| 0 0 1/2 0 }
(2/3,1/3,1/3,0) + set click here to show and hide
13	x1+2/3,x2+1/3,x3+1/3,x4,+1	{ 1 \| 2/3 1/3 1/3 0 }
14	-x2+2/3,x1-x2+1/3,x3+1/3,x4,+1	{ 3⁺₀₀₁ \| 2/3 1/3 1/3 0 }
15	-x1+x2+2/3,-x1+1/3,x3+1/3,x4,+1	{ 3^-₀₀₁ \| 2/3 1/3 1/3 0 }
16	x2+2/3,x1+1/3,-x3+5/6,-x4,+1	{ 2₁₁₀ \| 2/3 1/3 5/6 0 }
17	x1-x2+2/3,-x2+1/3,-x3+5/6,-x4,+1	{ 2₁₀₀ \| 2/3 1/3 5/6 0 }
18	-x1+2/3,-x1+x2+1/3,-x3+5/6,-x4,+1	{ 2₀₁₀ \| 2/3 1/3 5/6 0 }
19	-x1+2/3,-x2+1/3,-x3+1/3,-x4,+1	{ -1 \| 2/3 1/3 1/3 0 }
20	x2+2/3,-x1+x2+1/3,-x3+1/3,-x4,+1	{ -3⁺₀₀₁ \| 2/3 1/3 1/3 0 }
21	x1-x2+2/3,x1+1/3,-x3+1/3,-x4,+1	{ -3^-₀₀₁ \| 2/3 1/3 1/3 0 }
22	-x2+2/3,-x1+1/3,x3+5/6,x4,+1	{ m₁₁₀ \| 2/3 1/3 5/6 0 }
23	-x1+x2+2/3,x2+1/3,x3+5/6,x4,+1	{ m₁₀₀ \| 2/3 1/3 5/6 0 }
24	x1+2/3,x1-x2+1/3,x3+5/6,x4,+1	{ m₀₁₀ \| 2/3 1/3 5/6 0 }
(1/3,2/3,2/3,0) + set click here to show and hide
25	x1+1/3,x2+2/3,x3+2/3,x4,+1	{ 1 \| 1/3 2/3 2/3 0 }
26	-x2+1/3,x1-x2+2/3,x3+2/3,x4,+1	{ 3⁺₀₀₁ \| 1/3 2/3 2/3 0 }
27	-x1+x2+1/3,-x1+2/3,x3+2/3,x4,+1	{ 3^-₀₀₁ \| 1/3 2/3 2/3 0 }
28	x2+1/3,x1+2/3,-x3+1/6,-x4,+1	{ 2₁₁₀ \| 1/3 2/3 1/6 0 }
29	x1-x2+1/3,-x2+2/3,-x3+1/6,-x4,+1	{ 2₁₀₀ \| 1/3 2/3 1/6 0 }
30	-x1+1/3,-x1+x2+2/3,-x3+1/6,-x4,+1	{ 2₀₁₀ \| 1/3 2/3 1/6 0 }
31	-x1+1/3,-x2+2/3,-x3+2/3,-x4,+1	{ -1 \| 1/3 2/3 2/3 0 }
32	x2+1/3,-x1+x2+2/3,-x3+2/3,-x4,+1	{ -3⁺₀₀₁ \| 1/3 2/3 2/3 0 }
33	x1-x2+1/3,x1+2/3,-x3+2/3,-x4,+1	{ -3^-₀₀₁ \| 1/3 2/3 2/3 0 }
34	-x2+1/3,-x1+2/3,x3+1/6,x4,+1	{ m₁₁₀ \| 1/3 2/3 1/6 0 }
35	-x1+x2+1/3,x2+2/3,x3+1/6,x4,+1	{ m₁₀₀ \| 1/3 2/3 1/6 0 }
36	x1+1/3,x1-x2+2/3,x3+1/6,x4,+1	{ m₀₁₀ \| 1/3 2/3 1/6 0 }
(0,0,0,1/2)' + set click here to show and hide
37	x1,x2,x3,x4+1/2,-1	{ 1' \| 0 0 0 1/2 }
38	-x2,x1-x2,x3,x4+1/2,-1	{ 3'⁺₀₀₁ \| 0 0 0 1/2 }
39	-x1+x2,-x1,x3,x4+1/2,-1	{ 3'^-₀₀₁ \| 0 0 0 1/2 }
40	x2,x1,-x3+1/2,-x4+1/2,-1	{ 2'₁₁₀ \| 0 0 1/2 1/2 }
41	x1-x2,-x2,-x3+1/2,-x4+1/2,-1	{ 2'₁₀₀ \| 0 0 1/2 1/2 }
42	-x1,-x1+x2,-x3+1/2,-x4+1/2,-1	{ 2'₀₁₀ \| 0 0 1/2 1/2 }
43	-x1,-x2,-x3,-x4+1/2,-1	{ -1' \| 0 0 0 1/2 }
44	x2,-x1+x2,-x3,-x4+1/2,-1	{ -3'⁺₀₀₁ \| 0 0 0 1/2 }
45	x1-x2,x1,-x3,-x4+1/2,-1	{ -3'^-₀₀₁ \| 0 0 0 1/2 }
46	-x2,-x1,x3+1/2,x4+1/2,-1	{ m'₁₁₀ \| 0 0 1/2 1/2 }
47	-x1+x2,x2,x3+1/2,x4+1/2,-1	{ m'₁₀₀ \| 0 0 1/2 1/2 }
48	x1,x1-x2,x3+1/2,x4+1/2,-1	{ m'₀₁₀ \| 0 0 1/2 1/2 }
(2/3,1/3,1/3,1/2)' + set click here to show and hide
49	x1+2/3,x2+1/3,x3+1/3,x4+1/2,-1	{ 1' \| 2/3 1/3 1/3 1/2 }
50	-x2+2/3,x1-x2+1/3,x3+1/3,x4+1/2,-1	{ 3'⁺₀₀₁ \| 2/3 1/3 1/3 1/2 }
51	-x1+x2+2/3,-x1+1/3,x3+1/3,x4+1/2,-1	{ 3'^-₀₀₁ \| 2/3 1/3 1/3 1/2 }
52	x2+2/3,x1+1/3,-x3+5/6,-x4+1/2,-1	{ 2'₁₁₀ \| 2/3 1/3 5/6 1/2 }
53	x1-x2+2/3,-x2+1/3,-x3+5/6,-x4+1/2,-1	{ 2'₁₀₀ \| 2/3 1/3 5/6 1/2 }
54	-x1+2/3,-x1+x2+1/3,-x3+5/6,-x4+1/2,-1	{ 2'₀₁₀ \| 2/3 1/3 5/6 1/2 }
55	-x1+2/3,-x2+1/3,-x3+1/3,-x4+1/2,-1	{ -1' \| 2/3 1/3 1/3 1/2 }
56	x2+2/3,-x1+x2+1/3,-x3+1/3,-x4+1/2,-1	{ -3'⁺₀₀₁ \| 2/3 1/3 1/3 1/2 }
57	x1-x2+2/3,x1+1/3,-x3+1/3,-x4+1/2,-1	{ -3'^-₀₀₁ \| 2/3 1/3 1/3 1/2 }
58	-x2+2/3,-x1+1/3,x3+5/6,x4+1/2,-1	{ m'₁₁₀ \| 2/3 1/3 5/6 1/2 }
59	-x1+x2+2/3,x2+1/3,x3+5/6,x4+1/2,-1	{ m'₁₀₀ \| 2/3 1/3 5/6 1/2 }
60	x1+2/3,x1-x2+1/3,x3+5/6,x4+1/2,-1	{ m'₀₁₀ \| 2/3 1/3 5/6 1/2 }
(1/3,2/3,2/3,1/2)' + set click here to show and hide
61	x1+1/3,x2+2/3,x3+2/3,x4+1/2,-1	{ 1' \| 1/3 2/3 2/3 1/2 }
62	-x2+1/3,x1-x2+2/3,x3+2/3,x4+1/2,-1	{ 3'⁺₀₀₁ \| 1/3 2/3 2/3 1/2 }
63	-x1+x2+1/3,-x1+2/3,x3+2/3,x4+1/2,-1	{ 3'^-₀₀₁ \| 1/3 2/3 2/3 1/2 }
64	x2+1/3,x1+2/3,-x3+1/6,-x4+1/2,-1	{ 2'₁₁₀ \| 1/3 2/3 1/6 1/2 }
65	x1-x2+1/3,-x2+2/3,-x3+1/6,-x4+1/2,-1	{ 2'₁₀₀ \| 1/3 2/3 1/6 1/2 }
66	-x1+1/3,-x1+x2+2/3,-x3+1/6,-x4+1/2,-1	{ 2'₀₁₀ \| 1/3 2/3 1/6 1/2 }
67	-x1+1/3,-x2+2/3,-x3+2/3,-x4+1/2,-1	{ -1' \| 1/3 2/3 2/3 1/2 }
68	x2+1/3,-x1+x2+2/3,-x3+2/3,-x4+1/2,-1	{ -3'⁺₀₀₁ \| 1/3 2/3 2/3 1/2 }
69	x1-x2+1/3,x1+2/3,-x3+2/3,-x4+1/2,-1	{ -3'^-₀₀₁ \| 1/3 2/3 2/3 1/2 }
70	-x2+1/3,-x1+2/3,x3+1/6,x4+1/2,-1	{ m'₁₁₀ \| 1/3 2/3 1/6 1/2 }
71	-x1+x2+1/3,x2+2/3,x3+1/6,x4+1/2,-1	{ m'₁₀₀ \| 1/3 2/3 1/6 1/2 }
72	x1+1/3,x1-x2+2/3,x3+1/6,x4+1/2,-1	{ m'₀₁₀ \| 1/3 2/3 1/6 1/2 }

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	y,x,-z,+1	2₁₁₀
5	x-y,-y,-z,+1	2₁₀₀
6	-x,-x+y,-z,+1	2₀₁₀
7	-x,-y,-z,+1	-1
8	y,-x+y,-z,+1	-3⁺₀₀₁
9	x-y,x,-z,+1	-3^-₀₀₁
10	-y,-x,z,+1	m₁₁₀
11	-x+y,y,z,+1	m₁₀₀
12	x,x-y,z,+1	m₀₁₀
1' + set click here to show and hide
13	x,y,z,-1	1'
14	-y,x-y,z,-1	3'⁺₀₀₁
15	-x+y,-x,z,-1	3'^-₀₀₁
16	y,x,-z,-1	2'₁₁₀
17	x-y,-y,-z,-1	2'₁₀₀
18	-x,-x+y,-z,-1	2'₀₁₀
19	-x,-y,-z,-1	-1'
20	y,-x+y,-z,-1	-3'⁺₀₀₁
21	x-y,x,-z,-1	-3'^-₀₀₁
22	-y,-x,z,-1	m'₁₁₀
23	-x+y,y,z,-1	m'₁₀₀
24	x,x-y,z,-1	m'₀₁₀

Label	Atom type	x	y	z	Multiplicity
Ca1	Ca	0.36940(10)	0	0.25	18
O1	O	0.1768(3)	0.0246(4)	0.1138(3)	36

Atom	Magnetic moment Fourier Cos coeffs	Magnetic moment Fourier Sin coeffs
Symmetry constraints	Numerical values	Symmetry constraints	Numerical values
x	y	z	x	y	z	x	y	z	x	y	z
Co1	0	0	M_zcos1	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0
Co2	0	0	0	0.0	0.0	0.0	0	0	M_zsin1	0.0	0.0	5.0(1)

Atom	x	y	z
1	0.00000	0.00000	0.00000
2	0.00000	0.00000	0.50000
(2/3,1/3,1/3,0) + set click here to show and hide
3	0.66667	0.33333	0.33333
4	0.66667	0.33333	0.83333
(1/3,2/3,2/3,0) + set click here to show and hide
5	0.33333	0.66667	0.66667
6	0.33333	0.66667	0.16667

Atom	Magnetic moment Fourier Cos coeffs	Magnetic moment Fourier Sin coeffs
Symmetry constraints	Numerical values	Symmetry constraints	Numerical values
x	y	z	x	y	z	x	y	z	x	y	z
1	0	0	M_zcos1	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0
2	0	0	-M_zcos1	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0
(2/3,1/3,1/3,0) + set click here to show and hide
3	0	0	M_zcos1	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0
4	0	0	-M_zcos1	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0
(1/3,2/3,2/3,0) + set click here to show and hide
5	0	0	M_zcos1	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0
6	0	0	-M_zcos1	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0

Atom	x	y	z
1	0.00000	0.00000	0.25000
2	0.00000	0.00000	0.75000
(2/3,1/3,1/3,0) + set click here to show and hide
3	0.66667	0.33333	0.58333
4	0.66667	0.33333	0.08333
(1/3,2/3,2/3,0) + set click here to show and hide
5	0.33333	0.66667	0.91667
6	0.33333	0.66667	0.41667

Atom	Magnetic moment Fourier Cos coeffs	Magnetic moment Fourier Sin coeffs
Symmetry constraints	Numerical values	Symmetry constraints	Numerical values
x	y	z	x	y	z	x	y	z	x	y	z
1	0	0	0	0.0	0.0	0.0	0	0	M_zsin1	0.0	0.0	5.00000
2	0	0	0	0.0	0.0	0.0	0	0	-M_zsin1	0.0	0.0	-5.00000
(2/3,1/3,1/3,0) + set click here to show and hide
3	0	0	0	0.0	0.0	0.0	0	0	M_zsin1	0.0	0.0	5.00000
4	0	0	0	0.0	0.0	0.0	0	0	-M_zsin1	0.0	0.0	-5.00000
(1/3,2/3,2/3,0) + set click here to show and hide
5	0	0	0	0.0	0.0	0.0	0	0	M_zsin1	0.0	0.0	5.00000
6	0	0	0	0.0	0.0	0.0	0	0	-M_zsin1	0.0	0.0	-5.00000

Atom	x	y	z
1	0.36940	0.00000	0.25000
2	0.00000	0.36940	0.25000
3	0.63060	0.63060	0.25000
4	0.63060	0.00000	0.75000
5	0.00000	0.63060	0.75000
6	0.36940	0.36940	0.75000
(2/3,1/3,1/3,0) + set click here to show and hide
7	0.03607	0.33333	0.58333
8	0.66667	0.70273	0.58333
9	0.29727	0.96393	0.58333
10	0.29727	0.33333	0.08333
11	0.66667	0.96393	0.08333
12	0.03607	0.70273	0.08333
(1/3,2/3,2/3,0) + set click here to show and hide
13	0.70273	0.66667	0.91667
14	0.33333	0.03607	0.91667
15	0.96393	0.29727	0.91667
16	0.96393	0.66667	0.41667
17	0.33333	0.29727	0.41667
18	0.70273	0.03607	0.41667

Atom	x	y	z
1	0.17680	0.02460	0.11380
2	0.97540	0.15220	0.11380
3	0.84780	0.82320	0.11380
4	0.02460	0.17680	0.38620
5	0.15220	0.97540	0.38620
6	0.82320	0.84780	0.38620
7	0.82320	0.97540	0.88620
8	0.02460	0.84780	0.88620
9	0.15220	0.17680	0.88620
10	0.97540	0.82320	0.61380
11	0.84780	0.02460	0.61380
12	0.17680	0.15220	0.61380
(2/3,1/3,1/3,0) + set click here to show and hide
13	0.84347	0.35793	0.44713
14	0.64207	0.48553	0.44713
15	0.51447	0.15653	0.44713
16	0.69127	0.51013	0.71953
17	0.81887	0.30873	0.71953
18	0.48987	0.18113	0.71953
19	0.48987	0.30873	0.21953
20	0.69127	0.18113	0.21953
21	0.81887	0.51013	0.21953
22	0.64207	0.15653	0.94713
23	0.51447	0.35793	0.94713
24	0.84347	0.48553	0.94713
(1/3,2/3,2/3,0) + set click here to show and hide
25	0.51013	0.69127	0.78047
26	0.30873	0.81887	0.78047
27	0.18113	0.48987	0.78047
28	0.35793	0.84347	0.05287
29	0.48553	0.64207	0.05287
30	0.15653	0.51447	0.05287
31	0.15653	0.64207	0.55287
32	0.35793	0.51447	0.55287
33	0.48553	0.84347	0.55287
34	0.30873	0.48987	0.28047
35	0.18113	0.69127	0.28047
36	0.51013	0.81887	0.28047

Reference: S. Agrestini, L.C. Chapon, A. Daoud-Aladine, J. Schefer, A. Gukasov, C. Mazzoli, M.R. Lees and O.A. Petrenko, Physical Review Letters (2008) 101 097207.
DOI: 10.1103/physrevlett.101.097207
Atomic positions from: ICSD #153193

Parent space group (paramagnetic phase): R-3c (#167)
Propagation vector: k1 (0.000000, 0.000000, 1.020000)

Transition Temperature: 25 K
Experiment Temperature: 20 K

Lattice parameters of the basic unit cell:
9.0729(3) 9.0729(3) 10.3759(2) 90 90 120
Transformation from parent structure: (a,b,c;0,0,0)
    [View matrix form]

Magnetic Superspace Group: R-3c1'(00γ)00s
    [View symmetry operations]

Magnetic Point Group: -3m1' (20.2.72)
    [View symmetry operations]
Symmetry-adapted form of material tensors via

Average positions, magnetic moments and magnetic modulations of symmetry independent atoms:
From now on, magnetic atoms are in boldface and colored in red. Magnetic moments are expressed in units of μB

     [Show only magnetic atoms]
     [Show all the atoms]

Average atomic positions of symmetry independent atoms

Label	Atom type	x	y	z	Multiplicity
Co1	Co	0	0	0	6
Co2	Co	0	0	0.25	6

Magnetic moment modulation parameters of symmetry independent atoms

Wave vector 1

Atom	Magnetic moment Fourier Cos coeffs						Magnetic moment Fourier Sin coeffs
	Symmetry constraints			Numerical values			Symmetry constraints			Numerical values
	x	y	z	x	y	z	x	y	z	x	y	z
Co1	0	0	M_zcos1	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0
Co2	0	0	0	0.0	0.0	0.0	0	0	M_zsin1	0.0	0.0	5.0(1)

Atom	x	y	z
1	0.00000	0.00000	0.00000
2	0.00000	0.00000	0.50000
(2/3,1/3,1/3,0) + set click here to show and hide
3	0.66667	0.33333	0.33333
4	0.66667	0.33333	0.83333
(1/3,2/3,2/3,0) + set click here to show and hide
5	0.33333	0.66667	0.66667
6	0.33333	0.66667	0.16667

Atom	Magnetic moment Fourier Cos coeffs	Magnetic moment Fourier Sin coeffs
Symmetry constraints	Numerical values	Symmetry constraints	Numerical values
x	y	z	x	y	z	x	y	z	x	y	z
1	0	0	M_zcos1	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0
2	0	0	-M_zcos1	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0
(2/3,1/3,1/3,0) + set click here to show and hide
3	0	0	M_zcos1	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0
4	0	0	-M_zcos1	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0
(1/3,2/3,2/3,0) + set click here to show and hide
5	0	0	M_zcos1	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0
6	0	0	-M_zcos1	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0

Atom	x	y	z
1	0.00000	0.00000	0.25000
2	0.00000	0.00000	0.75000
(2/3,1/3,1/3,0) + set click here to show and hide
3	0.66667	0.33333	0.58333
4	0.66667	0.33333	0.08333
(1/3,2/3,2/3,0) + set click here to show and hide
5	0.33333	0.66667	0.91667
6	0.33333	0.66667	0.41667

Atom	Magnetic moment Fourier Cos coeffs	Magnetic moment Fourier Sin coeffs
Symmetry constraints	Numerical values	Symmetry constraints	Numerical values
x	y	z	x	y	z	x	y	z	x	y	z
1	0	0	0	0.0	0.0	0.0	0	0	M_zsin1	0.0	0.0	5.00000
2	0	0	0	0.0	0.0	0.0	0	0	-M_zsin1	0.0	0.0	-5.00000
(2/3,1/3,1/3,0) + set click here to show and hide
3	0	0	0	0.0	0.0	0.0	0	0	M_zsin1	0.0	0.0	5.00000
4	0	0	0	0.0	0.0	0.0	0	0	-M_zsin1	0.0	0.0	-5.00000
(1/3,2/3,2/3,0) + set click here to show and hide
5	0	0	0	0.0	0.0	0.0	0	0	M_zsin1	0.0	0.0	5.00000
6	0	0	0	0.0	0.0	0.0	0	0	-M_zsin1	0.0	0.0	-5.00000

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

Active Irreps:

label	dim. small irrep	dim. full irrep	action	number of modes
mLD1	1	2	primary	1

Comments:

NPD
Co1 has null spin

Comments (symmetry):

1k incommensurate magnetic structure
k-maximal superspace magnetic symmetry
2-dim irrep active

Bilbao Crystallographic Server
http://www.cryst.ehu.es

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

Ca₃Co₂O₆ (#1.1.39)

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

Ca3Co2O6 (#1.1.39)

Ca₃Co₂O₆ (#1.1.39)