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 }
4	x2,x1,-x3,-x4+1/3,+1	{ 2₁₁₀ \| 0 0 0 1/3 }
5	x1-x2,-x2,-x3,-x4,+1	{ 2₁₀₀ \| 0 }
6	-x1,-x1+x2,-x3,-x4+2/3,+1	{ 2₀₁₀ \| 0 0 0 2/3 }
(2/3,1/3,1/3,0) + set click here to show and hide
7	x1+2/3,x2+1/3,x3+1/3,x4,+1	{ 1 \| 2/3 1/3 1/3 0 }
8	-x2+2/3,x1-x2+1/3,x3+1/3,x4+1/3,+1	{ 3⁺₀₀₁ \| 2/3 1/3 1/3 1/3 }
9	-x1+x2+2/3,-x1+1/3,x3+1/3,x4+2/3,+1	{ 3^-₀₀₁ \| 2/3 1/3 1/3 2/3 }
10	x2+2/3,x1+1/3,-x3+1/3,-x4+1/3,+1	{ 2₁₁₀ \| 2/3 1/3 1/3 1/3 }
11	x1-x2+2/3,-x2+1/3,-x3+1/3,-x4,+1	{ 2₁₀₀ \| 2/3 1/3 1/3 0 }
12	-x1+2/3,-x1+x2+1/3,-x3+1/3,-x4+2/3,+1	{ 2₀₁₀ \| 2/3 1/3 1/3 2/3 }
(1/3,2/3,2/3,0) + set click here to show and hide
13	x1+1/3,x2+2/3,x3+2/3,x4,+1	{ 1 \| 1/3 2/3 2/3 0 }
14	-x2+1/3,x1-x2+2/3,x3+2/3,x4+1/3,+1	{ 3⁺₀₀₁ \| 1/3 2/3 2/3 1/3 }
15	-x1+x2+1/3,-x1+2/3,x3+2/3,x4+2/3,+1	{ 3^-₀₀₁ \| 1/3 2/3 2/3 2/3 }
16	x2+1/3,x1+2/3,-x3+2/3,-x4+1/3,+1	{ 2₁₁₀ \| 1/3 2/3 2/3 1/3 }
17	x1-x2+1/3,-x2+2/3,-x3+2/3,-x4,+1	{ 2₁₀₀ \| 1/3 2/3 2/3 0 }
18	-x1+1/3,-x1+x2+2/3,-x3+2/3,-x4+2/3,+1	{ 2₀₁₀ \| 1/3 2/3 2/3 2/3 }
(0,0,0,1/2)' + set click here to show and hide
19	x1,x2,x3,x4+1/2,-1	{ 1' \| 0 0 0 1/2 }
20	-x2,x1-x2,x3,x4+5/6,-1	{ 3'⁺₀₀₁ \| 0 0 0 5/6 }
21	-x1+x2,-x1,x3,x4+1/6,-1	{ 3'^-₀₀₁ \| 0 0 0 1/6 }
22	x2,x1,-x3,-x4+5/6,-1	{ 2'₁₁₀ \| 0 0 0 5/6 }
23	x1-x2,-x2,-x3,-x4+1/2,-1	{ 2'₁₀₀ \| 0 0 0 1/2 }
24	-x1,-x1+x2,-x3,-x4+1/6,-1	{ 2'₀₁₀ \| 0 0 0 1/6 }
(2/3,1/3,1/3,1/2)' + set click here to show and hide
25	x1+2/3,x2+1/3,x3+1/3,x4+1/2,-1	{ 1' \| 2/3 1/3 1/3 1/2 }
26	-x2+2/3,x1-x2+1/3,x3+1/3,x4+5/6,-1	{ 3'⁺₀₀₁ \| 2/3 1/3 1/3 5/6 }
27	-x1+x2+2/3,-x1+1/3,x3+1/3,x4+1/6,-1	{ 3'^-₀₀₁ \| 2/3 1/3 1/3 1/6 }
28	x2+2/3,x1+1/3,-x3+1/3,-x4+5/6,-1	{ 2'₁₁₀ \| 2/3 1/3 1/3 5/6 }
29	x1-x2+2/3,-x2+1/3,-x3+1/3,-x4+1/2,-1	{ 2'₁₀₀ \| 2/3 1/3 1/3 1/2 }
30	-x1+2/3,-x1+x2+1/3,-x3+1/3,-x4+1/6,-1	{ 2'₀₁₀ \| 2/3 1/3 1/3 1/6 }
(1/3,2/3,2/3,1/2)' + set click here to show and hide
31	x1+1/3,x2+2/3,x3+2/3,x4+1/2,-1	{ 1' \| 1/3 2/3 2/3 1/2 }
32	-x2+1/3,x1-x2+2/3,x3+2/3,x4+5/6,-1	{ 3'⁺₀₀₁ \| 1/3 2/3 2/3 5/6 }
33	-x1+x2+1/3,-x1+2/3,x3+2/3,x4+1/6,-1	{ 3'^-₀₀₁ \| 1/3 2/3 2/3 1/6 }
34	x2+1/3,x1+2/3,-x3+2/3,-x4+5/6,-1	{ 2'₁₁₀ \| 1/3 2/3 2/3 5/6 }
35	x1-x2+1/3,-x2+2/3,-x3+2/3,-x4+1/2,-1	{ 2'₁₀₀ \| 1/3 2/3 2/3 1/2 }
36	-x1+1/3,-x1+x2+2/3,-x3+2/3,-x4+1/6,-1	{ 2'₀₁₀ \| 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
4	y,x,-z,+1	2₁₁₀
5	x-y,-y,-z,+1	2₁₀₀
6	-x,-x+y,-z,+1	2₀₁₀
1' + set click here to show and hide
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	2'₁₁₀
11	x-y,-y,-z,-1	2'₁₀₀
12	-x,-x+y,-z,-1	2'₀₁₀

Label	Atom type	x	y	z	Multiplicity
B1	B	0	0	0.5	3
B2	B	0.4468(5)	0	0.5	9
O1	O	0.8586(8)	0	0.5	9
O2	O	0.5903(6)	0	0.5	9
O3	O	0.4533(5)	0.1448(5)	0.5182(4)	18

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
Nd1	√3M_xsin1	0	0	1.08(9)	0.0	0.0	M_xsin1	2M_xsin1	0	0.623	1.246	0.0
Fe1	M_xcos1	0	0	4.17(4)	0.0	0.0	M_xsin1	2M_xsin1	M_zsin1	2.41	4.82	0.0

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

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	√3M_xsin1	0	0	1.08000	0.0	0.0	M_xsin1	2M_xsin1	0	0.62300	1.24600	0.0
(2/3,1/3,1/3,0) + set click here to show and hide
2	√3M_xsin1	0	0	1.08000	0.0	0.0	M_xsin1	2M_xsin1	0	0.62300	1.24600	0.0
(1/3,2/3,2/3,0) + set click here to show and hide
3	√3M_xsin1	0	0	1.08000	0.0	0.0	M_xsin1	2M_xsin1	0	0.62300	1.24600	0.0

Atom	x	y	z
1	0.55050	0.00000	0.00000
2	0.00000	0.55050	0.00000
3	0.44950	0.44950	0.00000
(2/3,1/3,1/3,0) + set click here to show and hide
4	0.21717	0.33333	0.33333
5	0.66667	0.88383	0.33333
6	0.11617	0.78283	0.33333
(1/3,2/3,2/3,0) + set click here to show and hide
7	0.88383	0.66667	0.66667
8	0.33333	0.21717	0.66667
9	0.78283	0.11617	0.66667

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	M_xcos1	0	0	4.17000	0.0	0.0	M_xsin1	2M_xsin1	M_zsin1	2.41000	4.82000	0.0
2	√3M_xsin1	-1/2M_xcos1+√3/2M_xsin1	-√3/2M_zsin1	4.17424	0.00212	0.0	M_xsin1	√3/2M_xcos1+1/2M_xsin1	-1/2M_zsin1	2.41000	4.81633	0.0
3	1/2M_xcos1+√3/2M_xsin1	1/2M_xcos1-√3/2M_xsin1	√3/2M_zsin1	4.17212	-0.00212	0.0	√3/2M_xcos1-1/2M_xsin1	√3/2M_xcos1+1/2M_xsin1	-1/2M_zsin1	2.40633	4.81633	0.0
(2/3,1/3,1/3,0) + set click here to show and hide
4	M_xcos1	0	0	4.17000	0.0	0.0	M_xsin1	2M_xsin1	M_zsin1	2.41000	4.82000	0.0
5	√3M_xsin1	-1/2M_xcos1+√3/2M_xsin1	-√3/2M_zsin1	4.17424	0.00212	0.0	M_xsin1	√3/2M_xcos1+1/2M_xsin1	-1/2M_zsin1	2.41000	4.81633	0.0
6	1/2M_xcos1+√3/2M_xsin1	1/2M_xcos1-√3/2M_xsin1	√3/2M_zsin1	4.17212	-0.00212	0.0	√3/2M_xcos1-1/2M_xsin1	√3/2M_xcos1+1/2M_xsin1	-1/2M_zsin1	2.40633	4.81633	0.0
(1/3,2/3,2/3,0) + set click here to show and hide
7	M_xcos1	0	0	4.17000	0.0	0.0	M_xsin1	2M_xsin1	M_zsin1	2.41000	4.82000	0.0
8	√3M_xsin1	-1/2M_xcos1+√3/2M_xsin1	-√3/2M_zsin1	4.17424	0.00212	0.0	M_xsin1	√3/2M_xcos1+1/2M_xsin1	-1/2M_zsin1	2.41000	4.81633	0.0
9	1/2M_xcos1+√3/2M_xsin1	1/2M_xcos1-√3/2M_xsin1	√3/2M_zsin1	4.17212	-0.00212	0.0	√3/2M_xcos1-1/2M_xsin1	√3/2M_xcos1+1/2M_xsin1	-1/2M_zsin1	2.40633	4.81633	0.0

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

Atom	x	y	z
1	0.44680	0.00000	0.50000
2	0.00000	0.44680	0.50000
3	0.55320	0.55320	0.50000
(2/3,1/3,1/3,0) + set click here to show and hide
4	0.11347	0.33333	0.83333
5	0.66667	0.78013	0.83333
6	0.21987	0.88653	0.83333
(1/3,2/3,2/3,0) + set click here to show and hide
7	0.78013	0.66667	0.16667
8	0.33333	0.11347	0.16667
9	0.88653	0.21987	0.16667

Atom	x	y	z
1	0.85860	0.00000	0.50000
2	0.00000	0.85860	0.50000
3	0.14140	0.14140	0.50000
(2/3,1/3,1/3,0) + set click here to show and hide
4	0.52527	0.33333	0.83333
5	0.66667	0.19193	0.83333
6	0.80807	0.47473	0.83333
(1/3,2/3,2/3,0) + set click here to show and hide
7	0.19193	0.66667	0.16667
8	0.33333	0.52527	0.16667
9	0.47473	0.80807	0.16667

Atom	x	y	z
1	0.59030	0.00000	0.50000
2	0.00000	0.59030	0.50000
3	0.40970	0.40970	0.50000
(2/3,1/3,1/3,0) + set click here to show and hide
4	0.25697	0.33333	0.83333
5	0.66667	0.92363	0.83333
6	0.07637	0.74303	0.83333
(1/3,2/3,2/3,0) + set click here to show and hide
7	0.92363	0.66667	0.16667
8	0.33333	0.25697	0.16667
9	0.74303	0.07637	0.16667

Atom	x	y	z
1	0.45330	0.14480	0.51820
2	0.85520	0.30850	0.51820
3	0.69150	0.54670	0.51820
4	0.14480	0.45330	0.48180
5	0.30850	0.85520	0.48180
6	0.54670	0.69150	0.48180
(2/3,1/3,1/3,0) + set click here to show and hide
7	0.11997	0.47813	0.85153
8	0.52187	0.64183	0.85153
9	0.35817	0.88003	0.85153
10	0.81147	0.78663	0.81513
11	0.97517	0.18853	0.81513
12	0.21337	0.02483	0.81513
(1/3,2/3,2/3,0) + set click here to show and hide
13	0.78663	0.81147	0.18487
14	0.18853	0.97517	0.18487
15	0.02483	0.21337	0.18487
16	0.47813	0.11997	0.14847
17	0.64183	0.52187	0.14847
18	0.88003	0.35817	0.14847

Reference: M. Janoschek, P. Fischer, J. Schefer, B. Roessli, V. Pomjakushin, M. Meven, V. Petricek, G. Petrakovskii and L. Bezmaternikh, Physical Review B (2010) 81 094429.
DOI: 10.1103/physrevb.81.094429
Atomic positions from: same reference

Parent space group (paramagnetic phase): R32 (#155)
Propagation vector: k1 (0.000000, 0.000000, 1.502)

Transition Temperature: 13.5 K
Experiment Temperature: 5 K

Lattice parameters of the basic unit cell:
9.594 9.594 7.603 90 90 120
Transformation from parent structure: (a,b,c;0,0,0)
    [View matrix form]

Magnetic Superspace Group: R321'(00γ)t0s
    [View symmetry operations]

Magnetic Point Group: 321' (18.2.66)
    [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
Nd1	Nd	0	0	0	3
Fe1	Fe	0.5505(3)	0	0	9

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
Nd1	√3M_xsin1	0	0	1.08(9)	0.0	0.0	M_xsin1	2M_xsin1	0	0.623	1.246	0.0
Fe1	M_xcos1	0	0	4.17(4)	0.0	0.0	M_xsin1	2M_xsin1	M_zsin1	2.41	4.82	0.0

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

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	√3M_xsin1	0	0	1.08000	0.0	0.0	M_xsin1	2M_xsin1	0	0.62300	1.24600	0.0
(2/3,1/3,1/3,0) + set click here to show and hide
2	√3M_xsin1	0	0	1.08000	0.0	0.0	M_xsin1	2M_xsin1	0	0.62300	1.24600	0.0
(1/3,2/3,2/3,0) + set click here to show and hide
3	√3M_xsin1	0	0	1.08000	0.0	0.0	M_xsin1	2M_xsin1	0	0.62300	1.24600	0.0

Atom	x	y	z
1	0.55050	0.00000	0.00000
2	0.00000	0.55050	0.00000
3	0.44950	0.44950	0.00000
(2/3,1/3,1/3,0) + set click here to show and hide
4	0.21717	0.33333	0.33333
5	0.66667	0.88383	0.33333
6	0.11617	0.78283	0.33333
(1/3,2/3,2/3,0) + set click here to show and hide
7	0.88383	0.66667	0.66667
8	0.33333	0.21717	0.66667
9	0.78283	0.11617	0.66667

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	M_xcos1	0	0	4.17000	0.0	0.0	M_xsin1	2M_xsin1	M_zsin1	2.41000	4.82000	0.0
2	√3M_xsin1	-1/2M_xcos1+√3/2M_xsin1	-√3/2M_zsin1	4.17424	0.00212	0.0	M_xsin1	√3/2M_xcos1+1/2M_xsin1	-1/2M_zsin1	2.41000	4.81633	0.0
3	1/2M_xcos1+√3/2M_xsin1	1/2M_xcos1-√3/2M_xsin1	√3/2M_zsin1	4.17212	-0.00212	0.0	√3/2M_xcos1-1/2M_xsin1	√3/2M_xcos1+1/2M_xsin1	-1/2M_zsin1	2.40633	4.81633	0.0
(2/3,1/3,1/3,0) + set click here to show and hide
4	M_xcos1	0	0	4.17000	0.0	0.0	M_xsin1	2M_xsin1	M_zsin1	2.41000	4.82000	0.0
5	√3M_xsin1	-1/2M_xcos1+√3/2M_xsin1	-√3/2M_zsin1	4.17424	0.00212	0.0	M_xsin1	√3/2M_xcos1+1/2M_xsin1	-1/2M_zsin1	2.41000	4.81633	0.0
6	1/2M_xcos1+√3/2M_xsin1	1/2M_xcos1-√3/2M_xsin1	√3/2M_zsin1	4.17212	-0.00212	0.0	√3/2M_xcos1-1/2M_xsin1	√3/2M_xcos1+1/2M_xsin1	-1/2M_zsin1	2.40633	4.81633	0.0
(1/3,2/3,2/3,0) + set click here to show and hide
7	M_xcos1	0	0	4.17000	0.0	0.0	M_xsin1	2M_xsin1	M_zsin1	2.41000	4.82000	0.0
8	√3M_xsin1	-1/2M_xcos1+√3/2M_xsin1	-√3/2M_zsin1	4.17424	0.00212	0.0	M_xsin1	√3/2M_xcos1+1/2M_xsin1	-1/2M_zsin1	2.41000	4.81633	0.0
9	1/2M_xcos1+√3/2M_xsin1	1/2M_xcos1-√3/2M_xsin1	√3/2M_zsin1	4.17212	-0.00212	0.0	√3/2M_xcos1-1/2M_xsin1	√3/2M_xcos1+1/2M_xsin1	-1/2M_zsin1	2.40633	4.81633	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
mLD3	1	2	primary	4

Comments:

NSD
Commensurate AFM phase between 30K and 13.5K (see entry 1.7)
From the many models reported in the reference, this is the one refined with JANA2006 under maximal symmetry.
very small incommensurability

Comments (symmetry):

1k magnetic structure
k-maximal magnetic symmetry
non-polar symmetry. No twinning except trivial one.
Nd1 circular spin helix and the sign of its helicity is symmetry dictated.
MSSG only forces a elliptical spin helix for Fe1 with elliptical axes long (1,0,0) and (1,2,0). The sign of Fe1 spin helicity is not forced by symmetry.
2-dim active irrep, which means a one to one correspondence with the MSSG, but less free parameters than in the representation approach, due to the inclusion of the symmetry properties for operations changing k into -k.
Helices of the other Fe atoms in the basic unit cell are related by the three-fold rotation operations.
The MSSG allows a z component of the Fe1 spin modulation (non-observed). But to comply with the MSSG it should be in phase with the spin component along (1,2,0), i.e. it should be null when the Fe1 spin points along (1,0,0).
MSSG setting used has a 1/3 origin shift along x4 with respect to the default setting in JANA2006.

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

NdFe₃B₄O₁₂ (#1.1.18)

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

NdFe3B4O12 (#1.1.18)

NdFe₃B₄O₁₂ (#1.1.18)