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,x4+1/2,+1	{ 2₁₁₀ \| 0 0 0 1/2 }
(2/3,1/3,1/3,0) + set click here to show and hide
3	x1+2/3,x2+1/3,x3+1/3,x4,+1	{ 1 \| 2/3 1/3 1/3 0 }
4	x2+2/3,x1+1/3,-x3+1/3,x4+1/2,+1	{ 2₁₁₀ \| 2/3 1/3 1/3 1/2 }
(1/3,2/3,2/3,0) + set click here to show and hide
5	x1+1/3,x2+2/3,x3+2/3,x4,+1	{ 1 \| 1/3 2/3 2/3 0 }
6	x2+1/3,x1+2/3,-x3+2/3,x4+1/2,+1	{ 2₁₁₀ \| 1/3 2/3 2/3 1/2 }
(0,0,0,1/2)' + set click here to show and hide
7	x1,x2,x3,x4+1/2,-1	{ 1' \| 0 0 0 1/2 }
8	x2,x1,-x3,x4,-1	{ 2'₁₁₀ \| 0 }
(2/3,1/3,1/3,1/2)' + set click here to show and hide
9	x1+2/3,x2+1/3,x3+1/3,x4+1/2,-1	{ 1' \| 2/3 1/3 1/3 1/2 }
10	x2+2/3,x1+1/3,-x3+1/3,x4,-1	{ 2'₁₁₀ \| 2/3 1/3 1/3 0 }
(1/3,2/3,2/3,1/2)' + set click here to show and hide
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,x4,-1	{ 2'₁₁₀ \| 1/3 2/3 2/3 0 }

N	(x,y,z)	Seitz notation
1	x,y,z,+1	1
2	y,x,-z,+1	2₁₁₀
1' + set click here to show and hide
3	x,y,z,-1	1'
4	y,x,-z,-1	2'₁₁₀

Label	Atom type	x	y	z	Multiplicity
Cu1	Cu	0	0	0	3
O1	O	0	0	0.10792	6

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	M_xcos1	-M_xcos1	M_zcos1	1.56	-1.56	0.0	M_xsin1	-M_xsin1	M_zsin1	0.0	0.0	2.8(2)

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	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	M_zcos1	1.56000	-1.56000	0.0	M_xsin1	-M_xsin1	M_zsin1	0.0	0.0	2.80000
(2/3,1/3,1/3,0) + set click here to show and hide
2	M_xcos1	-M_xcos1	M_zcos1	1.56000	-1.56000	0.0	M_xsin1	-M_xsin1	M_zsin1	0.0	0.0	2.80000
(1/3,2/3,2/3,0) + set click here to show and hide
3	M_xcos1	-M_xcos1	M_zcos1	1.56000	-1.56000	0.0	M_xsin1	-M_xsin1	M_zsin1	0.0	0.0	2.80000

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	x	y	z
1	0.00000	0.00000	0.10792
2	0.00000	0.00000	0.89208
(2/3,1/3,1/3,0) + set click here to show and hide
3	0.66667	0.33333	0.44125
4	0.66667	0.33333	0.22541
(1/3,2/3,2/3,0) + set click here to show and hide
5	0.33333	0.66667	0.77459
6	0.33333	0.66667	0.55875

Reference: M. Frontzek, G. Ehlers, A. Podlesnyak, H. Cao, M. Matsuda, O. Zaharko, N. Aliouane, S. Barilo and S.V. Shiryaev, Journal of Physics: Condensed Matter (2011) 24 016004.
DOI: 10.1088/0953-8984/24/1/016004
Atomic positions from: ICSD #402290

Parent space group (paramagnetic phase): R-3m (#166)
Propagation vector: k1 (0.329800, 0.329800, 0.000000)

Transition Temperature: 23.6 K
Experiment Temperature: 5 K

Lattice parameters of the basic unit cell:
2.9734 2.9734 17.100 90 90 120
Transformation from parent structure: (a,b,c;0,0,0)
    [View matrix form]

Magnetic Superspace Group: X21'(a,a,0)ss
    [View symmetry operations]

Magnetic Point Group: 21' (3.2.7)
    [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	0	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
Cr1	M_xcos1	-M_xcos1	M_zcos1	1.56	-1.56	0.0	M_xsin1	-M_xsin1	M_zsin1	0.0	0.0	2.8(2)

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	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	M_zcos1	1.56000	-1.56000	0.0	M_xsin1	-M_xsin1	M_zsin1	0.0	0.0	2.80000
(2/3,1/3,1/3,0) + set click here to show and hide
2	M_xcos1	-M_xcos1	M_zcos1	1.56000	-1.56000	0.0	M_xsin1	-M_xsin1	M_zsin1	0.0	0.0	2.80000
(1/3,2/3,2/3,0) + set click here to show and hide
3	M_xcos1	-M_xcos1	M_zcos1	1.56000	-1.56000	0.0	M_xsin1	-M_xsin1	M_zsin1	0.0	0.0	2.80000

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

Active Irreps:

label	dim. small irrep	dim. full irrep	action	number of modes
mSM2	1	2	primary	2
mSM2	1	2	primary	2

Comments:

NSD
Position structure from a room temperature determination taken from icsd
Modulus magnetic moment in the direction

Comments (symmetry):

1k incommensurate magnetic structure
Simple spin spiral modulation, which however from the viewpoint of symmetry and Landau theory requires the superposition of two order parameters transforming according to the same irrep but shifted by pi/2 (i.e. two modulations with the same irrep, but being phase shifted the resulting superposed modulation does not transform according to this irrep).

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

CuCrO₂ (#1.1.72)

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

CuCrO2 (#1.1.72)

CuCrO₂ (#1.1.72)