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+1/2,-x2,x3+1/2,-x4,+1	{ 2₀₀₁ \| 1/2 0 1/2 0 }
3	-x1,x2+1/2,-x3,x4,+1	{ 2₀₁₀ \| 0 1/2 0 0 }
4	x1+1/2,-x2+1/2,-x3+1/2,-x4,+1	{ 2₁₀₀ \| 1/2 1/2 1/2 0 }
5	-x1,-x2,-x3,-x4,+1	{ -1 \| 0 }
6	x1+1/2,x2,-x3+1/2,x4,+1	{ m₀₀₁ \| 1/2 0 1/2 0 }
7	x1,-x2+1/2,x3,-x4,+1	{ m₀₁₀ \| 0 1/2 0 0 }
8	-x1+1/2,x2+1/2,x3+1/2,x4,+1	{ m₁₀₀ \| 1/2 1/2 1/2 0 }
(0,0,0,1/2)' + set click here to show and hide
9	x1,x2,x3,x4+1/2,-1	{ 1' \| 0 0 0 1/2 }
10	-x1+1/2,-x2,x3+1/2,-x4+1/2,-1	{ 2'₀₀₁ \| 1/2 0 1/2 1/2 }
11	-x1,x2+1/2,-x3,x4+1/2,-1	{ 2'₀₁₀ \| 0 1/2 0 1/2 }
12	x1+1/2,-x2+1/2,-x3+1/2,-x4+1/2,-1	{ 2'₁₀₀ \| 1/2 1/2 1/2 1/2 }
13	-x1,-x2,-x3,-x4+1/2,-1	{ -1' \| 0 0 0 1/2 }
14	x1+1/2,x2,-x3+1/2,x4+1/2,-1	{ m'₀₀₁ \| 1/2 0 1/2 1/2 }
15	x1,-x2+1/2,x3,-x4+1/2,-1	{ m'₀₁₀ \| 0 1/2 0 1/2 }
16	-x1+1/2,x2+1/2,x3+1/2,x4+1/2,-1	{ m'₁₀₀ \| 1/2 1/2 1/2 1/2 }

N	(x,y,z)	Seitz notation
1	x,y,z,+1	1
2	-x,-y,z,+1	2₀₀₁
3	-x,y,-z,+1	2₀₁₀
4	x,-y,-z,+1	2₁₀₀
5	-x,-y,-z,+1	-1
6	x,y,-z,+1	m₀₀₁
7	x,-y,z,+1	m₀₁₀
8	-x,y,z,+1	m₁₀₀
1' + set click here to show and hide
9	x,y,z,-1	1'
10	-x,-y,z,-1	2'₀₀₁
11	-x,y,-z,-1	2'₀₁₀
12	x,-y,-z,-1	2'₁₀₀
13	-x,-y,-z,-1	-1'
14	x,y,-z,-1	m'₀₀₁
15	x,-y,z,-1	m'₀₁₀
16	-x,y,z,-1	m'₁₀₀

Label	Atom type	x	y	z	Multiplicity
Cs1	Cs	0.134	0.25	0.1031	4
Cs2	Cs	-0.0567	0.75	0.3252	4
Cl1	Cl	0.3433	0.25	0.5739	4
Cl2	Cl	0.005	0.25	0.382	4
Cl3	Cl	0.2936	-0.0119	0.355	8

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
Cu1	0	M_ycos1	0	0.0	-0.78(2)	0.0	M_xsin1	0	M_zsin1	-0.24(2)	0.0	0.84(4)

Atom	x	y	z
1	0.23020	0.25000	0.41820
2	0.26980	0.75000	0.91820
3	0.76980	0.75000	0.58180
4	0.73020	0.25000	0.08180

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	M_ycos1	0	0.0	-0.78000	0.0	M_xsin1	0	M_zsin1	-0.24000	0.0	0.84000
2	0	-M_ycos1	0	0.0	0.78000	0.0	M_xsin1	0	-M_zsin1	-0.24000	0.0	-0.84000
3	0	M_ycos1	0	0.0	-0.78000	0.0	-M_xsin1	0	-M_zsin1	0.24000	0.0	-0.84000
4	0	-M_ycos1	0	0.0	0.78000	0.0	-M_xsin1	0	M_zsin1	0.24000	0.0	0.84000

Atom	x	y	z
1	0.13400	0.25000	0.10310
2	0.36600	0.75000	0.60310
3	0.86600	0.75000	0.89690
4	0.63400	0.25000	0.39690

Atom	x	y	z
1	0.94330	0.75000	0.32520
2	0.55670	0.25000	0.82520
3	0.05670	0.25000	0.67480
4	0.44330	0.75000	0.17480

Atom	x	y	z
1	0.34330	0.25000	0.57390
2	0.15670	0.75000	0.07390
3	0.65670	0.75000	0.42610
4	0.84330	0.25000	0.92610

Atom	x	y	z
1	0.00500	0.25000	0.38200
2	0.49500	0.75000	0.88200
3	0.99500	0.75000	0.61800
4	0.50500	0.25000	0.11800

Atom	x	y	z
1	0.29360	0.98810	0.35500
2	0.20640	0.01190	0.85500
3	0.70640	0.48810	0.64500
4	0.79360	0.51190	0.14500
5	0.70640	0.01190	0.64500
6	0.79360	0.98810	0.14500
7	0.29360	0.51190	0.35500
8	0.20640	0.48810	0.85500

Reference: R. Coldea, D.A. Tennant, R.A. Cowley, D.F. McMorrow, B. Dorner and Z. Tylczynski, Journal of Physics: Condensed Matter (1996) 8 7473-7491.
DOI: 10.1088/0953-8984/8/40/012
Atomic positions from: ICSD #66311

Parent space group (paramagnetic phase): Pnma (#62)
Propagation vector: k1 (0.000000, 0.472000, 0.000000)

Transition Temperature: 0.62 K
Experiment Temperature: 0.3 K

Lattice parameters of the basic unit cell:
9.769(3) 7.607(3) 12.381(3) 90 90 90
Transformation from parent structure: (a,b,c;0,0,0)
    [View matrix form]

Magnetic Superspace Group: Pnma1'(0β0)000s
    [View symmetry operations]

Magnetic Point Group: mmm1' (8.2.25)
    [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
Cu1	Cu	0.2302	0.25	0.4182	4

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
Cu1	0	M_ycos1	0	0.0	-0.78(2)	0.0	M_xsin1	0	M_zsin1	-0.24(2)	0.0	0.84(4)

Atom	x	y	z
1	0.23020	0.25000	0.41820
2	0.26980	0.75000	0.91820
3	0.76980	0.75000	0.58180
4	0.73020	0.25000	0.08180

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	M_ycos1	0	0.0	-0.78000	0.0	M_xsin1	0	M_zsin1	-0.24000	0.0	0.84000
2	0	-M_ycos1	0	0.0	0.78000	0.0	M_xsin1	0	-M_zsin1	-0.24000	0.0	-0.84000
3	0	M_ycos1	0	0.0	-0.78000	0.0	-M_xsin1	0	-M_zsin1	0.24000	0.0	-0.84000
4	0	-M_ycos1	0	0.0	0.78000	0.0	-M_xsin1	0	M_zsin1	0.24000	0.0	0.84000

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

Active Irreps:

label	dim. small irrep	dim. full irrep	action	number of modes
mDT1	1	2	primary	3

Comments:

NSD
The component Mycos1 is given here opposite sign to the one in the reference, as it fits much better intensities listed in the article. This means opposite chirality to the cycloidal chains.
A solution that fits data equally well is obtained by switching Mxsin1 and Mycos1.

Comments (symmetry):

1k incommensurate magnetic structure
active small irrep 1-dim: one to one correspondence between superspace group and primary irrep.

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

Cs₂CuCl₄ (#1.1.1)

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

Cs2CuCl4 (#1.1.1)

Cs₂CuCl₄ (#1.1.1)