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,-x2,x3,-x4,+1	{ 2₀₀₁ \| 0 }
3	x1,-x2,x3,x4+1/2,+1	{ m₀₁₀ \| 0 0 0 1/2 }
4	-x1,x2,x3,-x4+1/2,+1	{ m₁₀₀ \| 0 0 0 1/2 }
(0,0,0,1/2)' + set click here to show and hide
5	x1,x2,x3,x4+1/2,-1	{ 1' \| 0 0 0 1/2 }
6	-x1,-x2,x3,-x4+1/2,-1	{ 2'₀₀₁ \| 0 0 0 1/2 }
7	x1,-x2,x3,x4,-1	{ m'₀₁₀ \| 0 }
8	-x1,x2,x3,-x4,-1	{ m'₁₀₀ \| 0 }
(1/2,1/2,0,0) + set click here to show and hide
9	x1+1/2,x2+1/2,x3,x4,+1	{ 1 \| 1/2 1/2 0 0 }
10	-x1+1/2,-x2+1/2,x3,-x4,+1	{ 2₀₀₁ \| 1/2 1/2 0 0 }
11	x1+1/2,-x2+1/2,x3,x4+1/2,+1	{ m₀₁₀ \| 1/2 1/2 0 1/2 }
12	-x1+1/2,x2+1/2,x3,-x4+1/2,+1	{ m₁₀₀ \| 1/2 1/2 0 1/2 }
(1/2,1/2,0,1/2)' + set click here to show and hide
13	x1+1/2,x2+1/2,x3,x4+1/2,-1	{ 1' \| 1/2 1/2 0 1/2 }
14	-x1+1/2,-x2+1/2,x3,-x4+1/2,-1	{ 2'₀₀₁ \| 1/2 1/2 0 1/2 }
15	x1+1/2,-x2+1/2,x3,x4,-1	{ m'₀₁₀ \| 1/2 1/2 0 0 }
16	-x1+1/2,x2+1/2,x3,-x4,-1	{ m'₁₀₀ \| 1/2 1/2 0 0 }

N	(x,y,z)	Seitz notation
1	x,y,z,+1	1
2	-x,-y,z,+1	2₀₀₁
3	x,-y,z,+1	m₀₁₀
4	-x,y,z,+1	m₁₀₀
1' + set click here to show and hide
5	x,y,z,-1	1'
6	-x,-y,z,-1	2'₀₀₁
7	x,-y,z,-1	m'₀₁₀
8	-x,y,z,-1	m'₁₀₀

Label	Atom type	x	y	z	Multiplicity
B1	B	0.00000	0.66667	0.50000	4

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
Cr1	0	0	M_zc1	0.0	0.0	0.5(2)	M_xs1	0	0	0.5(2)	0.0	0.0

Atom	x	y	z
1	0.00000	0.00000	0.00000
(0,0,0,1/2)' + set click here to show and hide
2	0.50000	0.50000	0.00000

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	0.50000	M_xcos1+M_ysin1	0	0	0.50000	0.0	0.0
(0,0,0,1/2)' + set click here to show and hide
2	0	0	M_zcos1	0.0	0.0	0.50000	M_xcos1+M_ysin1	0	0	0.50000	0.0	0.0

Atom	x	y	z
1	0.00000	0.66667	0.50000
(0,0,0,1/2)' + set click here to show and hide
2	0.00000	0.33333	0.50000
(1/2,1/2,0,0) + set click here to show and hide
3	0.50000	0.16667	0.50000
(1/2,1/2,0,1/2)' + set click here to show and hide
4	0.50000	0.83333	0.50000

Reference: S. Funahashi, Y. Hamaguchi, T. Tanaka, E. Bannai, Solid State Communieations (1977) 23 859 - 862
DOI: 10.1016/0038-1098(77)90969-3
Atomic positions from: same reference

Parent space group (paramagnetic phase): P6/mmm (#191)
Propagation vector: k1 (0.57000, 0.00000, 0.00000)

Transition Temperature: 84 K
Experiment Temperature: 14 K

Lattice parameters of the basic unit cell:
2.96900 5.14246 3.06600 90.00000 90.00000 90.00000
Transformation from parent structure: (a+b,-a+b,c;0,0,0)
    [View matrix form]

Magnetic Superspace Group: Cmm21'(0,0,g)0s0s
    [View symmetry operations]

Magnetic Point Group: mm21' (7.2.21)
    [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
Cr1	Cr	0.00000	0.00000	0.00000	2

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
Cr1	0	0	M_zc1	0.0	0.0	0.5(2)	M_xs1	0	0	0.5(2)	0.0	0.0

Atom	x	y	z
1	0.00000	0.00000	0.00000
(0,0,0,1/2)' + set click here to show and hide
2	0.50000	0.50000	0.00000

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	0.50000	M_xcos1+M_ysin1	0	0	0.50000	0.0	0.0
(0,0,0,1/2)' + set click here to show and hide
2	0	0	M_zcos1	0.0	0.0	0.50000	M_xcos1+M_ysin1	0	0	0.50000	0.0	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
mLD2	1	6	general	primary	1
mLD4	1	6	special	primary	1

Comments:

NSD
Position structure (including cell parameters) is not specified. Here a room temperature model retrieved from the ICSD is used.
The spin arrangement is described as cycloidal with spins rotating on the plane generated by [1,1,0]* and c* of the parent hexagonal setting, but at some points the text also states that the spins rotate on the a-c plane, which is contradictory. We have assumed the first statement, consistent with the propagation vector, is the correct one.
The spin arrangement breaks the inversion symmetry, the resulting MSSG being polar.
The description is done here using an orthorhombic basis, which is adapted to the orthorhombic MSSG of the structure.

Comments (symmetry):

1k incommensurate magnetic structure
Two irreps are involved in quadrature.

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

CrB₂ (#1.1.136)

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

CrB2 (#1.1.136)

CrB₂ (#1.1.136)