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,+1	{ 3⁺₀₀₁ \| 0 0 0 1/3 }
3	-x1+x2,-x1,x3,x4+2/3,+1	{ 3^-₀₀₁ \| 0 0 0 2/3 }
(2/3,1/3,1/3,0) + set click here to show and hide
4	x1+2/3,x2+1/3,x3+1/3,x4,+1	{ 1 \| 2/3 1/3 1/3 0 }
5	-x2+2/3,x1-x2+1/3,x3+1/3,x4+1/3,+1	{ 3⁺₀₀₁ \| 2/3 1/3 1/3 1/3 }
6	-x1+x2+2/3,-x1+1/3,x3+1/3,x4+2/3,+1	{ 3^-₀₀₁ \| 2/3 1/3 1/3 2/3 }
(1/3,2/3,2/3,0) + set click here to show and hide
7	x1+1/3,x2+2/3,x3+2/3,x4,+1	{ 1 \| 1/3 2/3 2/3 0 }
8	-x2+1/3,x1-x2+2/3,x3+2/3,x4+1/3,+1	{ 3⁺₀₀₁ \| 1/3 2/3 2/3 1/3 }
9	-x1+x2+1/3,-x1+2/3,x3+2/3,x4+2/3,+1	{ 3^-₀₀₁ \| 1/3 2/3 2/3 2/3 }
(0,0,0,1/2)' + set click here to show and hide
10	x1,x2,x3,x4+1/2,-1	{ 1' \| 0 0 0 1/2 }
11	-x2,x1-x2,x3,x4+5/6,-1	{ 3'⁺₀₀₁ \| 0 0 0 5/6 }
12	-x1+x2,-x1,x3,x4+1/6,-1	{ 3'^-₀₀₁ \| 0 0 0 1/6 }
(2/3,1/3,1/3,1/2)' + set click here to show and hide
13	x1+2/3,x2+1/3,x3+1/3,x4+1/2,-1	{ 1' \| 2/3 1/3 1/3 1/2 }
14	-x2+2/3,x1-x2+1/3,x3+1/3,x4+5/6,-1	{ 3'⁺₀₀₁ \| 2/3 1/3 1/3 5/6 }
15	-x1+x2+2/3,-x1+1/3,x3+1/3,x4+1/6,-1	{ 3'^-₀₀₁ \| 2/3 1/3 1/3 1/6 }
(1/3,2/3,2/3,1/2)' + set click here to show and hide
16	x1+1/3,x2+2/3,x3+2/3,x4+1/2,-1	{ 1' \| 1/3 2/3 2/3 1/2 }
17	-x2+1/3,x1-x2+2/3,x3+2/3,x4+5/6,-1	{ 3'⁺₀₀₁ \| 1/3 2/3 2/3 5/6 }
18	-x1+x2+1/3,-x1+2/3,x3+2/3,x4+1/6,-1	{ 3'^-₀₀₁ \| 1/3 2/3 2/3 1/6 }

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
1' + set click here to show and hide
4	x,y,z,-1	1'
5	-y,x-y,z,-1	3'⁺₀₀₁
6	-x+y,-x,z,-1	3'^-₀₀₁

Label	Atom type	x	y	z	Occupancy	Multiplicity
Sb1_1	Sb	0	0	0.3486	0.5	3
Sb1_2	Sb	0	0	-0.3486	0.5	3
O1_1	O	0.2897	-0.0211	0.2562	1	9
O1_2	O	-0.2897	0.0211	-0.2562	1	9

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
Mn1_1	-0.57735M_xsin1+1.1547M_ysin1	-1.1547M_xsin1+0.57735M_ysin1	0	2.771282	5.542563	0.0	M_xsin1	M_ysin1	0	-4.8	0.0	0.0
Mn1_2	-0.57735M_xsin1+1.1547M_ysin1	-1.1547M_xsin1+0.57735M_ysin1	0	-1.991858	3.481423	0.0	M_xsin1	M_ysin1	0	-5.17	-4.31	0.0
Fe1_1	-0.57735M_xsin1+1.1547M_ysin1	-1.1547M_xsin1+0.57735M_ysin1	0	-2.713547	-5.427093	0.0	M_xsin1	M_ysin1	0	4.7	0.0	0.0
Fe1_2	-0.57735M_xsin1+1.1547M_ysin1	-1.1547M_xsin1+0.57735M_ysin1	0	1.951443	-3.406367	0.0	M_xsin1	M_ysin1	0	5.06	4.22	0.0

Atom	x	y	z
1	0.00000	0.00000	0.13840
(2/3,1/3,1/3,0) + set click here to show and hide
2	0.66667	0.33333	0.47173
(1/3,2/3,2/3,0) + set click here to show and hide
3	0.33333	0.66667	0.80507

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	-0.57735M_xsin1+1.15470M_ysin1	-1.15470M_xsin1+0.57735M_ysin1	0	2.77128	5.54256	0.0	M_xsin1	M_ysin1	0	-4.80000	0.0	0.0
(2/3,1/3,1/3,0) + set click here to show and hide
2	-0.57735M_xsin1+1.15470M_ysin1	-1.15470M_xsin1+0.57735M_ysin1	0	2.77128	5.54256	0.0	M_xsin1	M_ysin1	0	-4.80000	0.0	0.0
(1/3,2/3,2/3,0) + set click here to show and hide
3	-0.57735M_xsin1+1.15470M_ysin1	-1.15470M_xsin1+0.57735M_ysin1	0	2.77128	5.54256	0.0	M_xsin1	M_ysin1	0	-4.80000	0.0	0.0

Atom	x	y	z
1	0.00000	0.00000	0.86160
(2/3,1/3,1/3,0) + set click here to show and hide
2	0.66667	0.33333	0.19493
(1/3,2/3,2/3,0) + set click here to show and hide
3	0.33333	0.66667	0.52827

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	-0.57735M_xsin1+1.15470M_ysin1	-1.15470M_xsin1+0.57735M_ysin1	0	-1.99186	3.48142	0.0	M_xsin1	M_ysin1	0	-5.17000	-4.31000	0.0
(2/3,1/3,1/3,0) + set click here to show and hide
2	-0.57735M_xsin1+1.15470M_ysin1	-1.15470M_xsin1+0.57735M_ysin1	0	-1.99186	3.48142	0.0	M_xsin1	M_ysin1	0	-5.17000	-4.31000	0.0
(1/3,2/3,2/3,0) + set click here to show and hide
3	-0.57735M_xsin1+1.15470M_ysin1	-1.15470M_xsin1+0.57735M_ysin1	0	-1.99186	3.48142	0.0	M_xsin1	M_ysin1	0	-5.17000	-4.31000	0.0

Atom	x	y	z
1	0.00000	0.00000	0.34860
(2/3,1/3,1/3,0) + set click here to show and hide
2	0.66667	0.33333	0.68193
(1/3,2/3,2/3,0) + set click here to show and hide
3	0.33333	0.66667	0.01527

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	-0.57735M_xsin1+1.15470M_ysin1	-1.15470M_xsin1+0.57735M_ysin1	0	-2.71355	-5.42709	0.0	M_xsin1	M_ysin1	0	4.70000	0.0	0.0
(2/3,1/3,1/3,0) + set click here to show and hide
2	-0.57735M_xsin1+1.15470M_ysin1	-1.15470M_xsin1+0.57735M_ysin1	0	-2.71355	-5.42709	0.0	M_xsin1	M_ysin1	0	4.70000	0.0	0.0
(1/3,2/3,2/3,0) + set click here to show and hide
3	-0.57735M_xsin1+1.15470M_ysin1	-1.15470M_xsin1+0.57735M_ysin1	0	-2.71355	-5.42709	0.0	M_xsin1	M_ysin1	0	4.70000	0.0	0.0

Atom	x	y	z
1	0.00000	0.00000	0.65140
(2/3,1/3,1/3,0) + set click here to show and hide
2	0.66667	0.33333	0.98473
(1/3,2/3,2/3,0) + set click here to show and hide
3	0.33333	0.66667	0.31807

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	-0.57735M_xsin1+1.15470M_ysin1	-1.15470M_xsin1+0.57735M_ysin1	0	1.95144	-3.40637	0.0	M_xsin1	M_ysin1	0	5.06000	4.22000	0.0
(2/3,1/3,1/3,0) + set click here to show and hide
2	-0.57735M_xsin1+1.15470M_ysin1	-1.15470M_xsin1+0.57735M_ysin1	0	1.95144	-3.40637	0.0	M_xsin1	M_ysin1	0	5.06000	4.22000	0.0
(1/3,2/3,2/3,0) + set click here to show and hide
3	-0.57735M_xsin1+1.15470M_ysin1	-1.15470M_xsin1+0.57735M_ysin1	0	1.95144	-3.40637	0.0	M_xsin1	M_ysin1	0	5.06000	4.22000	0.0

Atom	x	y	z
1	0.00000	0.00000	0.34860
(2/3,1/3,1/3,0) + set click here to show and hide
2	0.66667	0.33333	0.68193
(1/3,2/3,2/3,0) + set click here to show and hide
3	0.33333	0.66667	0.01527

Atom	x	y	z
1	0.00000	0.00000	0.65140
(2/3,1/3,1/3,0) + set click here to show and hide
2	0.66667	0.33333	0.98473
(1/3,2/3,2/3,0) + set click here to show and hide
3	0.33333	0.66667	0.31807

Atom	x	y	z
1	0.28970	0.97890	0.25620
2	0.02110	0.31080	0.25620
3	0.68920	0.71030	0.25620
(2/3,1/3,1/3,0) + set click here to show and hide
4	0.95637	0.31223	0.58953
5	0.68777	0.64413	0.58953
6	0.35587	0.04363	0.58953
(1/3,2/3,2/3,0) + set click here to show and hide
7	0.62303	0.64557	0.92287
8	0.35443	0.97747	0.92287
9	0.02253	0.37697	0.92287

Atom	x	y	z
1	0.71030	0.02110	0.74380
2	0.97890	0.68920	0.74380
3	0.31080	0.28970	0.74380
(2/3,1/3,1/3,0) + set click here to show and hide
4	0.37697	0.35443	0.07713
5	0.64557	0.02253	0.07713
6	0.97747	0.62303	0.07713
(1/3,2/3,2/3,0) + set click here to show and hide
7	0.04363	0.68777	0.41047
8	0.31223	0.35587	0.41047
9	0.64413	0.95637	0.41047

Reference: A.J. Dosâ€…santos-Garcia, E. Solana-Madruga, C. Ritter, A. Andrada-Chacon, J. Sanchez-Benitez, F.J. Mompean, M. Garcia-Hernandez, R. Saez-Puche and R. Schmidt, Angewandte Chemie International Edition (2017) 56 4438-4442.
DOI: 10.1002/anie.201609762
Atomic positions from: same reference

Parent space group (paramagnetic phase): (#148)
Propagation vector: k1 (0.000000, 0.000000, 0.070000)

Transition Temperature: 50 K
Experiment Temperature: 4 K

Lattice parameters of the basic unit cell:
5.2321 5.2321 14.3722 90 90 120
Transformation from parent structure: (a,b,c;0,0,0)
    [View matrix form]

Magnetic Superspace Group: R31'(00γ)ts
    [View symmetry operations]

Magnetic Point Group: 31' (16.2.61)
    [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	z	Occupancy	Multiplicity
Mn1_1	Mn	0.1384	1	3
Mn1_2	Mn	-0.1384	1	3
Fe1_1	Fe	0.3486	0.5	3
Fe1_2	Fe	-0.3486	0.5	3

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
Mn1_1	-0.57735M_xsin1+1.1547M_ysin1	-1.1547M_xsin1+0.57735M_ysin1	0	2.771282	5.542563	0.0	M_xsin1	M_ysin1	0	-4.8	0.0	0.0
Mn1_2	-0.57735M_xsin1+1.1547M_ysin1	-1.1547M_xsin1+0.57735M_ysin1	0	-1.991858	3.481423	0.0	M_xsin1	M_ysin1	0	-5.17	-4.31	0.0
Fe1_1	-0.57735M_xsin1+1.1547M_ysin1	-1.1547M_xsin1+0.57735M_ysin1	0	-2.713547	-5.427093	0.0	M_xsin1	M_ysin1	0	4.7	0.0	0.0
Fe1_2	-0.57735M_xsin1+1.1547M_ysin1	-1.1547M_xsin1+0.57735M_ysin1	0	1.951443	-3.406367	0.0	M_xsin1	M_ysin1	0	5.06	4.22	0.0

Atom	x	y	z
1	0.00000	0.00000	0.13840
(2/3,1/3,1/3,0) + set click here to show and hide
2	0.66667	0.33333	0.47173
(1/3,2/3,2/3,0) + set click here to show and hide
3	0.33333	0.66667	0.80507

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	-0.57735M_xsin1+1.15470M_ysin1	-1.15470M_xsin1+0.57735M_ysin1	0	2.77128	5.54256	0.0	M_xsin1	M_ysin1	0	-4.80000	0.0	0.0
(2/3,1/3,1/3,0) + set click here to show and hide
2	-0.57735M_xsin1+1.15470M_ysin1	-1.15470M_xsin1+0.57735M_ysin1	0	2.77128	5.54256	0.0	M_xsin1	M_ysin1	0	-4.80000	0.0	0.0
(1/3,2/3,2/3,0) + set click here to show and hide
3	-0.57735M_xsin1+1.15470M_ysin1	-1.15470M_xsin1+0.57735M_ysin1	0	2.77128	5.54256	0.0	M_xsin1	M_ysin1	0	-4.80000	0.0	0.0

Atom	x	y	z
1	0.00000	0.00000	0.86160
(2/3,1/3,1/3,0) + set click here to show and hide
2	0.66667	0.33333	0.19493
(1/3,2/3,2/3,0) + set click here to show and hide
3	0.33333	0.66667	0.52827

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	-0.57735M_xsin1+1.15470M_ysin1	-1.15470M_xsin1+0.57735M_ysin1	0	-1.99186	3.48142	0.0	M_xsin1	M_ysin1	0	-5.17000	-4.31000	0.0
(2/3,1/3,1/3,0) + set click here to show and hide
2	-0.57735M_xsin1+1.15470M_ysin1	-1.15470M_xsin1+0.57735M_ysin1	0	-1.99186	3.48142	0.0	M_xsin1	M_ysin1	0	-5.17000	-4.31000	0.0
(1/3,2/3,2/3,0) + set click here to show and hide
3	-0.57735M_xsin1+1.15470M_ysin1	-1.15470M_xsin1+0.57735M_ysin1	0	-1.99186	3.48142	0.0	M_xsin1	M_ysin1	0	-5.17000	-4.31000	0.0

Atom	x	y	z
1	0.00000	0.00000	0.34860
(2/3,1/3,1/3,0) + set click here to show and hide
2	0.66667	0.33333	0.68193
(1/3,2/3,2/3,0) + set click here to show and hide
3	0.33333	0.66667	0.01527

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	-0.57735M_xsin1+1.15470M_ysin1	-1.15470M_xsin1+0.57735M_ysin1	0	-2.71355	-5.42709	0.0	M_xsin1	M_ysin1	0	4.70000	0.0	0.0
(2/3,1/3,1/3,0) + set click here to show and hide
2	-0.57735M_xsin1+1.15470M_ysin1	-1.15470M_xsin1+0.57735M_ysin1	0	-2.71355	-5.42709	0.0	M_xsin1	M_ysin1	0	4.70000	0.0	0.0
(1/3,2/3,2/3,0) + set click here to show and hide
3	-0.57735M_xsin1+1.15470M_ysin1	-1.15470M_xsin1+0.57735M_ysin1	0	-2.71355	-5.42709	0.0	M_xsin1	M_ysin1	0	4.70000	0.0	0.0

Atom	x	y	z
1	0.00000	0.00000	0.65140
(2/3,1/3,1/3,0) + set click here to show and hide
2	0.66667	0.33333	0.98473
(1/3,2/3,2/3,0) + set click here to show and hide
3	0.33333	0.66667	0.31807

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	-0.57735M_xsin1+1.15470M_ysin1	-1.15470M_xsin1+0.57735M_ysin1	0	1.95144	-3.40637	0.0	M_xsin1	M_ysin1	0	5.06000	4.22000	0.0
(2/3,1/3,1/3,0) + set click here to show and hide
2	-0.57735M_xsin1+1.15470M_ysin1	-1.15470M_xsin1+0.57735M_ysin1	0	1.95144	-3.40637	0.0	M_xsin1	M_ysin1	0	5.06000	4.22000	0.0
(1/3,2/3,2/3,0) + set click here to show and hide
3	-0.57735M_xsin1+1.15470M_ysin1	-1.15470M_xsin1+0.57735M_ysin1	0	1.95144	-3.40637	0.0	M_xsin1	M_ysin1	0	5.06000	4.22000	0.0

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

Active Irreps:

label	dim. small irrep	dim. full irrep	direction	action	number of modes
mLD2LD3	2	4	special	primary	7

Comments:

NPD
Refinement was not sensitive to the phase shift between Mn1_1 and Fe1_1 modulations, and it can be considered undetermined. This phase shift was set to zero in the original reference using the FullProf parameterization with (k.R). Here, for simplicity the two modulations are also set in phase but in the (k.(R+ri)) superspace parameterization that is used here.
The reported model forced the same phase shift between the modulations of the split sites Mn1_1 and Mn1_2, and of Fe1_1 and Fe1_2, but in principle these two phase shifts are independent.
Some of the modulation amplitudes include here non-significant digits, as obtained by the symmetry constraints between sine and cosine amplitudes in the oblique trigonal basis, forcing a spiral modulation of all the spin mpdulations.
The MSSG does not fix an origin along x4 and the global phase origin of all the modulations is arbitrary. Therefore, the phase of one of the modulations can be chosen arbitrarily (here the mysin1 component of Mn1_1 is set arbitrarily to zero).
At least some of the figures in the original reference seem inconsistent with the reported phase shifts between the modulations.

Comments (symmetry):

1k incommensurate magnetic structure
k-maximal symmetry
Single physically irreducible 4-dim irrep involved, but along a special direction of higher symmetry.
The spiral-type of spin modulations of all magnetic sites is forced by the MSSG
Polar along z. Centrosymmetry broken by the magnetic ordering. Multiferroic of type II.

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

Mn₂FeSbO₆ (#1.1.50)

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

Mn2FeSbO6 (#1.1.50)

Mn₂FeSbO₆ (#1.1.50)