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 }
(2/3,1/3,1/3,0) + set click here to show and hide
2	x1+2/3,x2+1/3,x3+1/3,x4,+1	{ 1 \| 2/3 1/3 1/3 0 }
(1/3,2/3,2/3,0) + set click here to show and hide
3	x1+1/3,x2+2/3,x3+2/3,x4,+1	{ 1 \| 1/3 2/3 2/3 0 }
(0,0,0,1/2)' + set click here to show and hide
4	x1,x2,x3,x4+1/2,-1	{ 1' \| 0 0 0 1/2 }
(2/3,1/3,1/3,1/2)' + set click here to show and hide
5	x1+2/3,x2+1/3,x3+1/3,x4+1/2,-1	{ 1' \| 2/3 1/3 1/3 1/2 }
(1/3,2/3,2/3,1/2)' + set click here to show and hide
6	x1+1/3,x2+2/3,x3+2/3,x4+1/2,-1	{ 1' \| 1/3 2/3 2/3 1/2 }

N	(x,y,z)	Seitz notation
1	x,y,z,+1	1
1' + set click here to show and hide
2	x,y,z,-1	1'

Label	Atom type	x	y	z	Multiplicity
Sc1	Sc	0	0	0.1874(6)	3
Sb1	Sb	0	0	0.6770(5)	3
O1	O	0.3164(8)	0.0147(7)	0.0749(6)	3
O2	O	-0.0147(7)	0.3017(11)	0.0749(6)	3
O3	O	-0.3017(11)	-0.3164(8)	0.0749(6)	3
O4	O	0.3324(7)	0.3692(8)	0.25	3
O5	O	-0.3692(8)	-0.0368(11)	0.25	3
O6	O	0.0368(11)	-0.3324(7)	0.25	3

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
Ni1	M_xcos1	M_ycos1	M_zcos1	0.0	0.0	-1.87	M_xsin1	M_ysini	M_zsin1	1.87(5)	0.0	0.0
Ni2	M_xcos1	M_ycos1	M_zcos1	0.0	0.0	1.87	M_xsin1	M_ysini	M_zsin1	-1.87	0.0	0.0

Atom	x	y	z
1	0.00000	0.00000	0.98230
(2/3,1/3,1/3,0) + set click here to show and hide
2	0.66667	0.33333	0.31563
(1/3,2/3,2/3,0) + set click here to show and hide
3	0.33333	0.66667	0.64897

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	M_ycos1	M_zcos1	0.0	0.0	-1.87000	M_xsin1	M_ycos1+M_ysin1	M_zsin1	1.87000	0.0	0.0
(2/3,1/3,1/3,0) + set click here to show and hide
2	M_xcos1	M_ycos1	M_zcos1	0.0	0.0	-1.87000	M_xsin1	M_ycos1+M_ysin1	M_zsin1	1.87000	0.0	0.0
(1/3,2/3,2/3,0) + set click here to show and hide
3	M_xcos1	M_ycos1	M_zcos1	0.0	0.0	-1.87000	M_xsin1	M_ycos1+M_ysin1	M_zsin1	1.87000	0.0	0.0

Atom	x	y	z
1	0.00000	0.00000	0.47830
(2/3,1/3,1/3,0) + set click here to show and hide
2	0.66667	0.33333	0.81163
(1/3,2/3,2/3,0) + set click here to show and hide
3	0.33333	0.66667	0.14497

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	M_ycos1	M_zcos1	0.0	0.0	1.87000	M_xsin1	M_ycos1+M_ysin1	M_zsin1	-1.87000	0.0	0.0
(2/3,1/3,1/3,0) + set click here to show and hide
2	M_xcos1	M_ycos1	M_zcos1	0.0	0.0	1.87000	M_xsin1	M_ycos1+M_ysin1	M_zsin1	-1.87000	0.0	0.0
(1/3,2/3,2/3,0) + set click here to show and hide
3	M_xcos1	M_ycos1	M_zcos1	0.0	0.0	1.87000	M_xsin1	M_ycos1+M_ysin1	M_zsin1	-1.87000	0.0	0.0

Atom	x	y	z
1	0.00000	0.00000	0.18740
(2/3,1/3,1/3,0) + set click here to show and hide
2	0.66667	0.33333	0.52073
(1/3,2/3,2/3,0) + set click here to show and hide
3	0.33333	0.66667	0.85407

Atom	x	y	z
1	0.00000	0.00000	0.67700
(2/3,1/3,1/3,0) + set click here to show and hide
2	0.66667	0.33333	0.01033
(1/3,2/3,2/3,0) + set click here to show and hide
3	0.33333	0.66667	0.34367

Atom	x	y	z
1	0.31640	0.01470	0.07490
(2/3,1/3,1/3,0) + set click here to show and hide
2	0.98307	0.34803	0.40823
(1/3,2/3,2/3,0) + set click here to show and hide
3	0.64973	0.68137	0.74157

Atom	x	y	z
1	0.98530	0.30170	0.07490
(2/3,1/3,1/3,0) + set click here to show and hide
2	0.65197	0.63503	0.40823
(1/3,2/3,2/3,0) + set click here to show and hide
3	0.31863	0.96837	0.74157

Atom	x	y	z
1	0.69830	0.68360	0.07490
(2/3,1/3,1/3,0) + set click here to show and hide
2	0.36497	0.01693	0.40823
(1/3,2/3,2/3,0) + set click here to show and hide
3	0.03163	0.35027	0.74157

Atom	x	y	z
1	0.33240	0.36920	0.25000
(2/3,1/3,1/3,0) + set click here to show and hide
2	0.99907	0.70253	0.58333
(1/3,2/3,2/3,0) + set click here to show and hide
3	0.66573	0.03587	0.91667

Atom	x	y	z
1	0.63080	0.96320	0.25000
(2/3,1/3,1/3,0) + set click here to show and hide
2	0.29747	0.29653	0.58333
(1/3,2/3,2/3,0) + set click here to show and hide
3	0.96413	0.62987	0.91667

Atom	x	y	z
1	0.03680	0.66760	0.25000
(2/3,1/3,1/3,0) + set click here to show and hide
2	0.70347	0.00093	0.58333
(1/3,2/3,2/3,0) + set click here to show and hide
3	0.37013	0.33427	0.91667

Reference: S.A. Ivanov, R. Mathieu, P. Nordblad, R. Tellgren, C. Ritter, E. Politova, G. Kaleva, A. Mosunov, S. Stefanovich and M. Weil, Chemistry of Materials (2013) 25 935-945.
DOI: 10.1021/cm304095s
Atomic positions from: ICSD #237879

Parent space group (paramagnetic phase): (#146)
Propagation vector: k1 (0.000000, 0.036000, 0.000000)

Transition Temperature: 60 K
Experiment Temperature: 1.7 K

Lattice parameters of the basic unit cell:
5.1614(3) 5.1614(3) 14.0025(6) 90 90 120
Transformation from parent structure: (a,b,c;0,0,0)
    [View matrix form]

Magnetic Superspace Group: P11'(αβγ)0s
    [View symmetry operations]

Magnetic Point Group: 11' (1.2.2)
    [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
Ni1	Ni	0	0	-0.0177(8)	3
Ni2	Ni	0	0	0.4783(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
Ni1	M_xcos1	M_ycos1	M_zcos1	0.0	0.0	-1.87	M_xsin1	M_ysini	M_zsin1	1.87(5)	0.0	0.0
Ni2	M_xcos1	M_ycos1	M_zcos1	0.0	0.0	1.87	M_xsin1	M_ysini	M_zsin1	-1.87	0.0	0.0

Atom	x	y	z
1	0.00000	0.00000	0.98230
(2/3,1/3,1/3,0) + set click here to show and hide
2	0.66667	0.33333	0.31563
(1/3,2/3,2/3,0) + set click here to show and hide
3	0.33333	0.66667	0.64897

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	M_ycos1	M_zcos1	0.0	0.0	-1.87000	M_xsin1	M_ycos1+M_ysin1	M_zsin1	1.87000	0.0	0.0
(2/3,1/3,1/3,0) + set click here to show and hide
2	M_xcos1	M_ycos1	M_zcos1	0.0	0.0	-1.87000	M_xsin1	M_ycos1+M_ysin1	M_zsin1	1.87000	0.0	0.0
(1/3,2/3,2/3,0) + set click here to show and hide
3	M_xcos1	M_ycos1	M_zcos1	0.0	0.0	-1.87000	M_xsin1	M_ycos1+M_ysin1	M_zsin1	1.87000	0.0	0.0

Atom	x	y	z
1	0.00000	0.00000	0.47830
(2/3,1/3,1/3,0) + set click here to show and hide
2	0.66667	0.33333	0.81163
(1/3,2/3,2/3,0) + set click here to show and hide
3	0.33333	0.66667	0.14497

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	M_ycos1	M_zcos1	0.0	0.0	1.87000	M_xsin1	M_ycos1+M_ysin1	M_zsin1	-1.87000	0.0	0.0
(2/3,1/3,1/3,0) + set click here to show and hide
2	M_xcos1	M_ycos1	M_zcos1	0.0	0.0	1.87000	M_xsin1	M_ycos1+M_ysin1	M_zsin1	-1.87000	0.0	0.0
(1/3,2/3,2/3,0) + set click here to show and hide
3	M_xcos1	M_ycos1	M_zcos1	0.0	0.0	1.87000	M_xsin1	M_ycos1+M_ysin1	M_zsin1	-1.87000	0.0	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
mGP1GP1	1	2	primary	11

Comments:

NPD
The global origin of the modulation is not fixed by the MSSG and one spin modulation phase can be chosen arbitrarily.
A completely different model with cycloidal modulations, the spin rotating on the plane yz, instead of on the plane xz could equally fit the data. The spin modulations have no symmetry constraints.
It seems that the phase shift between the modulations of Ni1 and Ni2 did not influence much the fit, and the antiphase relation between the modulations of Ni1 and Ni2 was assumed.

Comments (symmetry):

1k incommensurate magnetic structure
The wave vector has no symmetry, and there is only a single possible trivial irrep

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

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

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