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	-x1+3/4,-x2+3/4,x3,-x4,+1	{ 2₀₀₁ \| 3/4 3/4 0 0 }
3	-x1+3/4,x2,-x3+3/4,-x4+1/2,+1	{ 2₀₁₀ \| 3/4 0 3/4 1/2 }
4	x1,-x2+3/4,-x3+3/4,x4+1/2,+1	{ 2₁₀₀ \| 0 3/4 3/4 1/2 }
5	-x1+1/2,-x2+1/2,-x3,-x4,+1	{ -1 \| 1/2 1/2 0 0 }
6	x1+1/4,x2+1/4,-x3,x4,+1	{ m₀₀₁ \| 1/4 1/4 0 0 }
7	x1+1/4,-x2,x3+1/4,x4+1/2,+1	{ m₀₁₀ \| 1/4 0 1/4 1/2 }
8	-x1+1/2,x2+3/4,x3+1/4,-x4+1/2,+1	{ m₁₀₀ \| 1/2 3/4 1/4 1/2 }
(0,1/2,1/2,0) + set click here to show and hide
9	x1,x2+1/2,x3+1/2,x4,+1	{ 1 \| 0 1/2 1/2 0 }
10	-x1+3/4,-x2+1/4,x3+1/2,-x4,+1	{ 2₀₀₁ \| 3/4 1/4 1/2 0 }
11	-x1+3/4,x2+1/2,-x3+1/4,-x4+1/2,+1	{ 2₀₁₀ \| 3/4 1/2 1/4 1/2 }
12	x1,-x2+1/4,-x3+1/4,x4+1/2,+1	{ 2₁₀₀ \| 0 1/4 1/4 1/2 }
13	-x1+1/2,-x2,-x3+1/2,-x4,+1	{ -1 \| 1/2 0 1/2 0 }
14	x1+1/4,x2+3/4,-x3+1/2,x4,+1	{ m₀₀₁ \| 1/4 3/4 1/2 0 }
15	x1+1/4,-x2+1/2,x3+3/4,x4+1/2,+1	{ m₀₁₀ \| 1/4 1/2 3/4 1/2 }
16	-x1+1/2,x2+1/4,x3+3/4,-x4+1/2,+1	{ m₁₀₀ \| 1/2 1/4 3/4 1/2 }
(1/2,0,1/2,0) + set click here to show and hide
17	x1+1/2,x2,x3+1/2,x4,+1	{ 1 \| 1/2 0 1/2 0 }
18	-x1+1/4,-x2+3/4,x3+1/2,-x4,+1	{ 2₀₀₁ \| 1/4 3/4 1/2 0 }
19	-x1+1/4,x2,-x3+1/4,-x4+1/2,+1	{ 2₀₁₀ \| 1/4 0 1/4 1/2 }
20	x1+1/2,-x2+3/4,-x3+1/4,x4+1/2,+1	{ 2₁₀₀ \| 1/2 3/4 1/4 1/2 }
21	-x1,-x2+1/2,-x3+1/2,-x4,+1	{ -1 \| 0 1/2 1/2 0 }
22	x1+3/4,x2+1/4,-x3+1/2,x4,+1	{ m₀₀₁ \| 3/4 1/4 1/2 0 }
23	x1+3/4,-x2,x3+3/4,x4+1/2,+1	{ m₀₁₀ \| 3/4 0 3/4 1/2 }
24	-x1,x2+3/4,x3+3/4,-x4+1/2,+1	{ m₁₀₀ \| 0 3/4 3/4 1/2 }
(1/2,1/2,0,0) + set click here to show and hide
25	x1+1/2,x2+1/2,x3,x4,+1	{ 1 \| 1/2 1/2 0 0 }
26	-x1+1/4,-x2+1/4,x3,-x4,+1	{ 2₀₀₁ \| 1/4 1/4 0 0 }
27	-x1+1/4,x2+1/2,-x3+3/4,-x4+1/2,+1	{ 2₀₁₀ \| 1/4 1/2 3/4 1/2 }
28	x1+1/2,-x2+1/4,-x3+3/4,x4+1/2,+1	{ 2₁₀₀ \| 1/2 1/4 3/4 1/2 }
29	-x1,-x2,-x3,-x4,+1	{ -1 \| 0 }
30	x1+3/4,x2+3/4,-x3,x4,+1	{ m₀₀₁ \| 3/4 3/4 0 0 }
31	x1+3/4,-x2+1/2,x3+1/4,x4+1/2,+1	{ m₀₁₀ \| 3/4 1/2 1/4 1/2 }
32	-x1,x2+1/4,x3+1/4,-x4+1/2,+1	{ m₁₀₀ \| 0 1/4 1/4 1/2 }
(0,0,0,1/2)' + set click here to show and hide
33	x1,x2,x3,x4+1/2,-1	{ 1' \| 0 0 0 1/2 }
34	-x1+3/4,-x2+3/4,x3,-x4+1/2,-1	{ 2'₀₀₁ \| 3/4 3/4 0 1/2 }
35	-x1+3/4,x2,-x3+3/4,-x4,-1	{ 2'₀₁₀ \| 3/4 0 3/4 0 }
36	x1,-x2+3/4,-x3+3/4,x4,-1	{ 2'₁₀₀ \| 0 3/4 3/4 0 }
37	-x1+1/2,-x2+1/2,-x3,-x4+1/2,-1	{ -1' \| 1/2 1/2 0 1/2 }
38	x1+1/4,x2+1/4,-x3,x4+1/2,-1	{ m'₀₀₁ \| 1/4 1/4 0 1/2 }
39	x1+1/4,-x2,x3+1/4,x4,-1	{ m'₀₁₀ \| 1/4 0 1/4 0 }
40	-x1+1/2,x2+3/4,x3+1/4,-x4,-1	{ m'₁₀₀ \| 1/2 3/4 1/4 0 }
(0,1/2,1/2,1/2)' + set click here to show and hide
41	x1,x2+1/2,x3+1/2,x4+1/2,-1	{ 1' \| 0 1/2 1/2 1/2 }
42	-x1+3/4,-x2+1/4,x3+1/2,-x4+1/2,-1	{ 2'₀₀₁ \| 3/4 1/4 1/2 1/2 }
43	-x1+3/4,x2+1/2,-x3+1/4,-x4,-1	{ 2'₀₁₀ \| 3/4 1/2 1/4 0 }
44	x1,-x2+1/4,-x3+1/4,x4,-1	{ 2'₁₀₀ \| 0 1/4 1/4 0 }
45	-x1+1/2,-x2,-x3+1/2,-x4+1/2,-1	{ -1' \| 1/2 0 1/2 1/2 }
46	x1+1/4,x2+3/4,-x3+1/2,x4+1/2,-1	{ m'₀₀₁ \| 1/4 3/4 1/2 1/2 }
47	x1+1/4,-x2+1/2,x3+3/4,x4,-1	{ m'₀₁₀ \| 1/4 1/2 3/4 0 }
48	-x1+1/2,x2+1/4,x3+3/4,-x4,-1	{ m'₁₀₀ \| 1/2 1/4 3/4 0 }
(1/2,0,1/2,1/2)' + set click here to show and hide
49	x1+1/2,x2,x3+1/2,x4+1/2,-1	{ 1' \| 1/2 0 1/2 1/2 }
50	-x1+1/4,-x2+3/4,x3+1/2,-x4+1/2,-1	{ 2'₀₀₁ \| 1/4 3/4 1/2 1/2 }
51	-x1+1/4,x2,-x3+1/4,-x4,-1	{ 2'₀₁₀ \| 1/4 0 1/4 0 }
52	x1+1/2,-x2+3/4,-x3+1/4,x4,-1	{ 2'₁₀₀ \| 1/2 3/4 1/4 0 }
53	-x1,-x2+1/2,-x3+1/2,-x4+1/2,-1	{ -1' \| 0 1/2 1/2 1/2 }
54	x1+3/4,x2+1/4,-x3+1/2,x4+1/2,-1	{ m'₀₀₁ \| 3/4 1/4 1/2 1/2 }
55	x1+3/4,-x2,x3+3/4,x4,-1	{ m'₀₁₀ \| 3/4 0 3/4 0 }
56	-x1,x2+3/4,x3+3/4,-x4,-1	{ m'₁₀₀ \| 0 3/4 3/4 0 }
(1/2,1/2,0,1/2)' + set click here to show and hide
57	x1+1/2,x2+1/2,x3,x4+1/2,-1	{ 1' \| 1/2 1/2 0 1/2 }
58	-x1+1/4,-x2+1/4,x3,-x4+1/2,-1	{ 2'₀₀₁ \| 1/4 1/4 0 1/2 }
59	-x1+1/4,x2+1/2,-x3+3/4,-x4,-1	{ 2'₀₁₀ \| 1/4 1/2 3/4 0 }
60	x1+1/2,-x2+1/4,-x3+3/4,x4,-1	{ 2'₁₀₀ \| 1/2 1/4 3/4 0 }
61	-x1,-x2,-x3,-x4+1/2,-1	{ -1' \| 0 0 0 1/2 }
62	x1+3/4,x2+3/4,-x3,x4+1/2,-1	{ m'₀₀₁ \| 3/4 3/4 0 1/2 }
63	x1+3/4,-x2+1/2,x3+1/4,x4,-1	{ m'₀₁₀ \| 3/4 1/2 1/4 0 }
64	-x1,x2+1/4,x3+1/4,-x4,-1	{ m'₁₀₀ \| 0 1/4 1/4 0 }

N	(x,y,z)	Seitz notation
1	x,y,z,+1	1
2	-x,-y,z,+1	2₀₀₁
3	-x,y,-z,+1	2₀₁₀
4	x,-y,-z,+1	2₁₀₀
5	-x,-y,-z,+1	-1
6	x,y,-z,+1	m₀₀₁
7	x,-y,z,+1	m₀₁₀
8	-x,y,z,+1	m₁₀₀
1' + set click here to show and hide
9	x,y,z,-1	1'
10	-x,-y,z,-1	2'₀₀₁
11	-x,y,-z,-1	2'₀₁₀
12	x,-y,-z,-1	2'₁₀₀
13	-x,-y,-z,-1	-1'
14	x,y,-z,-1	m'₀₀₁
15	x,-y,z,-1	m'₀₁₀
16	-x,y,z,-1	m'₁₀₀

Label	Atom type	x	y	z	Multiplicity
Li1	Li	0.125	0.125	0.04167	16
Li2	Li	0.125	0.125	0.875	16
O1	O	0.855(7)	0.125	0.125	16
O2	O	0.621(8)	0.3669	0.0384(7)	32

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
Ir1	0	0	M_zcos1	0.0	0.0	0.47(1)	M_xsin1	M_ysin1	0	0.21(1)	0.31(1)	0.0

Atom	x	y	z
1	0.12500	0.12500	0.70845
2	0.62500	0.62500	0.70845
3	0.62500	0.12500	0.04155
4	0.12500	0.62500	0.04155
(0,1/2,1/2,0) + set click here to show and hide
5	0.37500	0.37500	0.29155
6	0.37500	0.87500	0.95845
7	0.12500	0.62500	0.20845
8	0.62500	0.12500	0.20845
(1/2,0,1/2,0) + set click here to show and hide
9	0.62500	0.62500	0.54155
10	0.12500	0.12500	0.54155
11	0.37500	0.87500	0.79155
12	0.37500	0.37500	0.45845
(1/2,1/2,0,0) + set click here to show and hide
13	0.87500	0.37500	0.79155
14	0.87500	0.87500	0.45845
15	0.87500	0.87500	0.29155
16	0.87500	0.37500	0.95845

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	0.47000	M_xsin1	M_ysin1	0	0.21000	0.31000	0.0
2	0	0	M_zcos1	0.0	0.0	0.47000	M_xsin1	M_ysin1	0	0.21000	0.31000	0.0
3	0	0	M_zcos1	0.0	0.0	0.47000	-M_xsin1	M_ysin1	0	-0.21000	0.31000	0.0
4	0	0	M_zcos1	0.0	0.0	0.47000	-M_xsin1	M_ysin1	0	-0.21000	0.31000	0.0
(0,1/2,1/2,0) + set click here to show and hide
5	0	0	M_zcos1	0.0	0.0	0.47000	-M_xsin1	-M_ysin1	0	-0.21000	-0.31000	0.0
6	0	0	M_zcos1	0.0	0.0	0.47000	M_xsin1	-M_ysin1	0	0.21000	-0.31000	0.0
7	0	0	M_zcos1	0.0	0.0	0.47000	M_xsin1	M_ysin1	0	0.21000	0.31000	0.0
8	0	0	M_zcos1	0.0	0.0	0.47000	M_xsin1	M_ysin1	0	0.21000	0.31000	0.0
(1/2,0,1/2,0) + set click here to show and hide
9	0	0	M_zcos1	0.0	0.0	0.47000	-M_xsin1	M_ysin1	0	-0.21000	0.31000	0.0
10	0	0	M_zcos1	0.0	0.0	0.47000	-M_xsin1	M_ysin1	0	-0.21000	0.31000	0.0
11	0	0	M_zcos1	0.0	0.0	0.47000	-M_xsin1	-M_ysin1	0	-0.21000	-0.31000	0.0
12	0	0	M_zcos1	0.0	0.0	0.47000	M_xsin1	-M_ysin1	0	0.21000	-0.31000	0.0
(1/2,1/2,0,0) + set click here to show and hide
13	0	0	M_zcos1	0.0	0.0	0.47000	-M_xsin1	-M_ysin1	0	-0.21000	-0.31000	0.0
14	0	0	M_zcos1	0.0	0.0	0.47000	M_xsin1	-M_ysin1	0	0.21000	-0.31000	0.0
15	0	0	M_zcos1	0.0	0.0	0.47000	-M_xsin1	-M_ysin1	0	-0.21000	-0.31000	0.0
16	0	0	M_zcos1	0.0	0.0	0.47000	M_xsin1	-M_ysin1	0	0.21000	-0.31000	0.0

Atom	x	y	z
1	0.12500	0.12500	0.04167
2	0.62500	0.12500	0.70833
3	0.37500	0.37500	0.95833
4	0.37500	0.87500	0.29167
(0,1/2,1/2,0) + set click here to show and hide
5	0.12500	0.62500	0.54167
6	0.62500	0.62500	0.20833
7	0.37500	0.87500	0.45833
8	0.37500	0.37500	0.79167
(1/2,0,1/2,0) + set click here to show and hide
9	0.62500	0.12500	0.54167
10	0.12500	0.12500	0.20833
11	0.87500	0.37500	0.45833
12	0.87500	0.87500	0.79167
(1/2,1/2,0,0) + set click here to show and hide
13	0.62500	0.62500	0.04167
14	0.12500	0.62500	0.70833
15	0.87500	0.87500	0.95833
16	0.87500	0.37500	0.29167

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

Atom	x	y	z
1	0.85500	0.12500	0.12500
2	0.89500	0.62500	0.12500
3	0.64500	0.37500	0.87500
4	0.10500	0.37500	0.87500
(0,1/2,1/2,0) + set click here to show and hide
5	0.85500	0.62500	0.62500
6	0.89500	0.12500	0.62500
7	0.64500	0.87500	0.37500
8	0.10500	0.87500	0.37500
(1/2,0,1/2,0) + set click here to show and hide
9	0.35500	0.12500	0.62500
10	0.39500	0.62500	0.62500
11	0.14500	0.37500	0.37500
12	0.60500	0.37500	0.37500
(1/2,1/2,0,0) + set click here to show and hide
13	0.35500	0.62500	0.12500
14	0.39500	0.12500	0.12500
15	0.14500	0.87500	0.87500
16	0.60500	0.87500	0.87500

Atom	x	y	z
1	0.62100	0.36690	0.03840
2	0.12900	0.38310	0.03840
3	0.12900	0.36690	0.71160
4	0.62100	0.38310	0.71160
5	0.87900	0.13310	0.96160
6	0.87100	0.61690	0.96160
7	0.87100	0.63310	0.28840
8	0.87900	0.11690	0.28840
(0,1/2,1/2,0) + set click here to show and hide
9	0.62100	0.86690	0.53840
10	0.12900	0.88310	0.53840
11	0.12900	0.86690	0.21160
12	0.62100	0.88310	0.21160
13	0.87900	0.63310	0.46160
14	0.87100	0.11690	0.46160
15	0.87100	0.13310	0.78840
16	0.87900	0.61690	0.78840
(1/2,0,1/2,0) + set click here to show and hide
17	0.12100	0.36690	0.53840
18	0.62900	0.38310	0.53840
19	0.62900	0.36690	0.21160
20	0.12100	0.38310	0.21160
21	0.37900	0.13310	0.46160
22	0.37100	0.61690	0.46160
23	0.37100	0.63310	0.78840
24	0.37900	0.11690	0.78840
(1/2,1/2,0,0) + set click here to show and hide
25	0.12100	0.86690	0.03840
26	0.62900	0.88310	0.03840
27	0.62900	0.86690	0.71160
28	0.12100	0.88310	0.71160
29	0.37900	0.63310	0.96160
30	0.37100	0.11690	0.96160
31	0.37100	0.13310	0.28840
32	0.37900	0.61690	0.28840

Reference: Biffin, A. et al., PHYSICAL REVIEW B (2014) 90 205116
DOI: 10.1103/PhysRevB.90.205116
Atomic positions from: same reference

Parent space group (paramagnetic phase): Fddd (#70)
Propagation vector: k1 (0.5768(3), 0.000000, 0.000000)

Transition Temperature: 38 K

Lattice parameters of the basic unit cell:
5.8903(2) 8.4261(3) 17.7924(7) 90 90 90
Transformation from parent structure: (a,b,c;0,0,0)
    [View matrix form]

Magnetic Superspace Group: Fddd1'(α00)0s0s
    [View symmetry operations]

Magnetic Point Group: mmm1' (8.2.25)
    [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
Ir1	Ir	0.125	0.125	0.70845(7)	16

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
Ir1	0	0	M_zcos1	0.0	0.0	0.47(1)	M_xsin1	M_ysin1	0	0.21(1)	0.31(1)	0.0

Atom	x	y	z
1	0.12500	0.12500	0.70845
2	0.62500	0.62500	0.70845
3	0.62500	0.12500	0.04155
4	0.12500	0.62500	0.04155
(0,1/2,1/2,0) + set click here to show and hide
5	0.37500	0.37500	0.29155
6	0.37500	0.87500	0.95845
7	0.12500	0.62500	0.20845
8	0.62500	0.12500	0.20845
(1/2,0,1/2,0) + set click here to show and hide
9	0.62500	0.62500	0.54155
10	0.12500	0.12500	0.54155
11	0.37500	0.87500	0.79155
12	0.37500	0.37500	0.45845
(1/2,1/2,0,0) + set click here to show and hide
13	0.87500	0.37500	0.79155
14	0.87500	0.87500	0.45845
15	0.87500	0.87500	0.29155
16	0.87500	0.37500	0.95845

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	0.47000	M_xsin1	M_ysin1	0	0.21000	0.31000	0.0
2	0	0	M_zcos1	0.0	0.0	0.47000	M_xsin1	M_ysin1	0	0.21000	0.31000	0.0
3	0	0	M_zcos1	0.0	0.0	0.47000	-M_xsin1	M_ysin1	0	-0.21000	0.31000	0.0
4	0	0	M_zcos1	0.0	0.0	0.47000	-M_xsin1	M_ysin1	0	-0.21000	0.31000	0.0
(0,1/2,1/2,0) + set click here to show and hide
5	0	0	M_zcos1	0.0	0.0	0.47000	-M_xsin1	-M_ysin1	0	-0.21000	-0.31000	0.0
6	0	0	M_zcos1	0.0	0.0	0.47000	M_xsin1	-M_ysin1	0	0.21000	-0.31000	0.0
7	0	0	M_zcos1	0.0	0.0	0.47000	M_xsin1	M_ysin1	0	0.21000	0.31000	0.0
8	0	0	M_zcos1	0.0	0.0	0.47000	M_xsin1	M_ysin1	0	0.21000	0.31000	0.0
(1/2,0,1/2,0) + set click here to show and hide
9	0	0	M_zcos1	0.0	0.0	0.47000	-M_xsin1	M_ysin1	0	-0.21000	0.31000	0.0
10	0	0	M_zcos1	0.0	0.0	0.47000	-M_xsin1	M_ysin1	0	-0.21000	0.31000	0.0
11	0	0	M_zcos1	0.0	0.0	0.47000	-M_xsin1	-M_ysin1	0	-0.21000	-0.31000	0.0
12	0	0	M_zcos1	0.0	0.0	0.47000	M_xsin1	-M_ysin1	0	0.21000	-0.31000	0.0
(1/2,1/2,0,0) + set click here to show and hide
13	0	0	M_zcos1	0.0	0.0	0.47000	-M_xsin1	-M_ysin1	0	-0.21000	-0.31000	0.0
14	0	0	M_zcos1	0.0	0.0	0.47000	M_xsin1	-M_ysin1	0	0.21000	-0.31000	0.0
15	0	0	M_zcos1	0.0	0.0	0.47000	-M_xsin1	-M_ysin1	0	-0.21000	-0.31000	0.0
16	0	0	M_zcos1	0.0	0.0	0.47000	M_xsin1	-M_ysin1	0	0.21000	-0.31000	0.0

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

Active Irreps:

label	dim. small irrep	dim. full irrep	action	number of modes
mSM4	1	2	primary	3

Comments:

NPD and magnetic X-ray resonant diffraction
Positional structure from a 100K measurement
beta-polymorph

Comments (symmetry):

1k magnetic structure
k maximal magnetic symmetry (4 possible)
2-dim active irrep, which implies a one to one correspondence with the MSSG, but less free parameters than in the usual representation approach, due to the inclusion of the symmetry properties for operations changing k into -k. The original reference included these additional restrictions in referring to ISODISTORT, but without mentioning the associated superspace symmetry that this program provides.

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

For comments, please mail to
cryst@wm.lc.ehu.es

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

Li₂IrO₃ (#1.1.20)

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

Li2IrO3 (#1.1.20)

Li₂IrO₃ (#1.1.20)