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,x3,3x3-x4,+1	{ m₁₁₀ \| 0 }
3	x1,x2,x3,x4+1/2,-1	{ 1' \| 0 0 0 1/2 }
4	-x2,-x1,x3,3x3-x4+1/2,-1	{ m'₁₁₀ \| 0 0 0 1/2 }
5	x1+2/3,x2+1/3,x3+1/3,x4,+1	{ 1 \| 2/3 1/3 1/3 0 }
6	-x2+2/3,-x1+1/3,x3+1/3,3x3-x4,+1	{ m₁₁₀ \| 2/3 1/3 1/3 0 }
7	x1+2/3,x2+1/3,x3+1/3,x4+1/2,-1	{ 1' \| 2/3 1/3 1/3 1/2 }
8	-x2+2/3,-x1+1/3,x3+1/3,3x3-x4+1/2,-1	{ m'₁₁₀ \| 2/3 1/3 1/3 1/2 }
(1/3,2/3,2/3,0) + set click here to show and hide
9	x1+1/3,x2+2/3,x3+2/3,x4,+1	{ 1 \| 1/3 2/3 2/3 0 }
10	-x2+1/3,-x1+2/3,x3+2/3,3x3-x4,+1	{ m₁₁₀ \| 1/3 2/3 2/3 0 }
11	x1+1/3,x2+2/3,x3+2/3,x4+1/2,-1	{ 1' \| 1/3 2/3 2/3 1/2 }
12	-x2+1/3,-x1+2/3,x3+2/3,3x3-x4+1/2,-1	{ m'₁₁₀ \| 1/3 2/3 2/3 1/2 }
13	x1,x2,x3,x4+1/2,-1	{ 1' \| 0 0 0 1/2 }
14	-x2,-x1,x3,3x3-x4+1/2,-1	{ m'₁₁₀ \| 0 0 0 1/2 }
15	x1,x2,x3,x4,+1	{ 1 \| 0 }
16	-x2,-x1,x3,3x3-x4,+1	{ m₁₁₀ \| 0 }
(2/3,1/3,1/3,1/2)' + set click here to show and hide
17	x1+2/3,x2+1/3,x3+1/3,x4+1/2,-1	{ 1' \| 2/3 1/3 1/3 1/2 }
18	-x2+2/3,-x1+1/3,x3+1/3,3x3-x4+1/2,-1	{ m'₁₁₀ \| 2/3 1/3 1/3 1/2 }
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+1/3,x3+1/3,3x3-x4,+1	{ m₁₁₀ \| 2/3 1/3 1/3 0 }
21	x1+1/3,x2+2/3,x3+2/3,x4+1/2,-1	{ 1' \| 1/3 2/3 2/3 1/2 }
22	-x2+1/3,-x1+2/3,x3+2/3,3x3-x4+1/2,-1	{ m'₁₁₀ \| 1/3 2/3 2/3 1/2 }
23	x1+1/3,x2+2/3,x3+2/3,x4,+1	{ 1 \| 1/3 2/3 2/3 0 }
24	-x2+1/3,-x1+2/3,x3+2/3,3x3-x4,+1	{ m₁₁₀ \| 1/3 2/3 2/3 0 }

N	(x,y,z)	Seitz notation
1	x,y,z,+1	1
2	-y,-x,z,+1	m₁₁₀
1' + set click here to show and hide
3	x,y,z,-1	1'
4	-y,-x,z,-1	m'₁₁₀

Label	Atom type	x	y	z	Multiplicity
Br1_1	Br	0	0	0.255	3
Br1_2	Br	0	0	-0.255	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_xcos1	0	2.00	2.00	0.0	M_xsin1	-M_xsin1	M_zsin1	-1.155	1.155	0.0

Atom	x	y	z
1	0.00000	0.00000	0.00000
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	M_xcos1	M_xcos1	0	2.00000	2.00000	0.0	M_xsin1	-M_xsin1	M_zsin1	-1.15500	1.15500	0.0
2	M_xcos1	M_xcos1	0	2.00000	2.00000	0.0	M_xsin1	-M_xsin1	M_zsin1	-1.15500	1.15500	0.0
(1/3,2/3,2/3,0) + set click here to show and hide
3	M_xcos1	M_xcos1	0	2.00000	2.00000	0.0	M_xsin1	-M_xsin1	M_zsin1	-1.15500	1.15500	0.0

Atom	x	y	z
1	0.00000	0.00000	0.25500
2	0.66667	0.33333	0.58833
(1/3,2/3,2/3,0) + set click here to show and hide
3	0.33333	0.66667	0.92167

Atom	x	y	z
1	0.00000	0.00000	0.74500
2	0.66667	0.33333	0.07833
(1/3,2/3,2/3,0) + set click here to show and hide
3	0.33333	0.66667	0.41167

Reference: A. Adam, D. Billerey, C. Terrier, R. Mainard, L. Regnault, J. Rossat-Mignod and P. Meriel, Solid State Communications (1980) 35 1-5.
DOI: 10.1016/0038-1098(80)90757-7
Atomic positions from: ICSD #22106

Parent space group (paramagnetic phase): R-3m (#166)
Propagation vector: k1 (0.027, 0.027, 1.500000)

Transition Temperature: 22.8 K
Experiment Temperature: 4.2 K

Lattice parameters of the basic unit cell:
3.723 3.723 18.34 90 90 120
Transformation from parent structure: (a,b,c;0,0,0)
    [View matrix form]

Magnetic Superspace Group: Rm1'(aag)0s
    [View symmetry operations]

Magnetic Point Group: m1' (4.2.10)
    [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	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_xcos1	0	2.00	2.00	0.0	M_xsin1	-M_xsin1	M_zsin1	-1.155	1.155	0.0

Atom	x	y	z
1	0.00000	0.00000	0.00000
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	M_xcos1	M_xcos1	0	2.00000	2.00000	0.0	M_xsin1	-M_xsin1	M_zsin1	-1.15500	1.15500	0.0
2	M_xcos1	M_xcos1	0	2.00000	2.00000	0.0	M_xsin1	-M_xsin1	M_zsin1	-1.15500	1.15500	0.0
(1/3,2/3,2/3,0) + set click here to show and hide
3	M_xcos1	M_xcos1	0	2.00000	2.00000	0.0	M_xsin1	-M_xsin1	M_zsin1	-1.15500	1.15500	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
mY1	1	6	general	primary	1
mY2	1	6	special	primary	2

Comments:

NSD and NPD
Between 52K and 22.8K a commensurate magnetic phase is reported (see entry # 1.248)
Ni moment: 2.00(15)
Moment components with non-significant digits to yield the reported moment modulus.

Comments (symmetry):

1k incommensurate magnetic structure
Two irreps are involved as primary. Their corresponding modulations are superposed in quadrature (pi/2 phase shifted).
The arbitrary phase of the global modulation is fixed by the simpler setting chosen for the MSSG and is different from the one chosen in the original reference.

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

NiBr₂ (#1.1.77)

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

NiBr2 (#1.1.77)

NiBr₂ (#1.1.77)