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+1/2,x4,+1	{ 2₀₁₀ \| 0 0 1/2 0 }
3	-x1,-x2,-x3+1/2,-x4+1/2,+1	{ -1 \| 0 0 1/2 1/2 }
4	x1,-x2,x3,-x4+1/2,+1	{ m₀₁₀ \| 0 0 0 1/2 }
(0,0,1/2,0)' + set click here to show and hide
5	x1,x2,x3+1/2,x4,-1	{ 1' \| 0 0 1/2 0 }
6	-x1,x2,-x3,x4,-1	{ 2'₀₁₀ \| 0 }
7	-x1,-x2,-x3,-x4+1/2,-1	{ -1' \| 0 0 0 1/2 }
8	x1,-x2,x3+1/2,-x4+1/2,-1	{ m'₀₁₀ \| 0 0 1/2 1/2 }
(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+1/2,x4,+1	{ 2₀₁₀ \| 1/2 1/2 1/2 0 }
11	-x1+1/2,-x2+1/2,-x3+1/2,-x4+1/2,+1	{ -1 \| 1/2 1/2 1/2 1/2 }
12	x1+1/2,-x2+1/2,x3,-x4+1/2,+1	{ m₀₁₀ \| 1/2 1/2 0 1/2 }
(1/2,1/2,1/2,0)' + set click here to show and hide
13	x1+1/2,x2+1/2,x3+1/2,x4,-1	{ 1' \| 1/2 1/2 1/2 0 }
14	-x1+1/2,x2+1/2,-x3,x4,-1	{ 2'₀₁₀ \| 1/2 1/2 0 0 }
15	-x1+1/2,-x2+1/2,-x3,-x4+1/2,-1	{ -1' \| 1/2 1/2 0 1/2 }
16	x1+1/2,-x2+1/2,x3+1/2,-x4+1/2,-1	{ m'₀₁₀ \| 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	2₀₁₀
3	-x,-y,-z,+1	-1
4	x,-y,z,+1	m₀₁₀
1' + set click here to show and hide
5	x,y,z,-1	1'
6	-x,y,-z,-1	2'₀₁₀
7	-x,-y,-z,-1	-1'
8	x,-y,z,-1	m'₀₁₀

Label	Atom type	x	z	Multiplicity
Cu1	Cu	0.32200	0.2575	8
Cu2	Cu	0.33800	0.078	8
Sn1	Sn	0.21600	0.364	8
Sn2	Sn	0.50700	0.1055	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
Er1	0	0	0	0.0	0.0	0.0	0	M_ys1	0	0.0	0.0	0.0
Er2	M_xc1	0	M_zc1	4.3(4)	0.0	9.6(2)	0	M_ys1	0	0.0	0.0	0.0

Atom	x	y	z	Symmetry constraints on M	M_0x	M_0y	M_0z
1	0.00000	0.00000	0.25000	0,m_y,0	0.00000	8.91000	0.00000
(0,0,1/2,0)' + set click here to show and hide
2	0.00000	0.00000	0.75000	0,-m_y,0	0.00000	-8.91000	0.00000
(1/2,1/2,0,0) + set click here to show and hide
3	0.50000	0.50000	0.25000	0,m_y,0	0.00000	8.91000	0.00000
(1/2,1/2,1/2,0)' + set click here to show and hide
4	0.50000	0.50000	0.75000	0,-m_y,0	0.00000	-8.91000	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	0	0.0	0.0	0.0	0	M_ycos1+M_ysin1	0	0.0	0.0	0.0
(0,0,1/2,0)' + set click here to show and hide
2	0	0	0	0.0	0.0	0.0	0	-M_ycos1-M_ysin1	0	0.0	0.0	0.0
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3	0	0	0	0.0	0.0	0.0	0	M_ycos1+M_ysin1	0	0.0	0.0	0.0
(1/2,1/2,1/2,0)' + set click here to show and hide
4	0	0	0	0.0	0.0	0.0	0	-M_ycos1-M_ysin1	0	0.0	0.0	0.0

Atom	x	y	z	Symmetry constraints on M	M_0x	M_0y	M_0z
1	0.13000	0.00000	0.05950	0,m_y,0	0.00000	0.00000	0.00000
2	0.87000	0.00000	0.44050	0,m_y,0	0.00000	0.00000	0.00000
(0,0,1/2,0)' + set click here to show and hide
3	0.13000	0.00000	0.55950	0,-m_y,0	0.00000	0.00000	0.00000
4	0.87000	0.00000	0.94050	0,-m_y,0	0.00000	0.00000	0.00000
(1/2,1/2,0,0) + set click here to show and hide
5	0.63000	0.50000	0.05950	0,m_y,0	0.00000	0.00000	0.00000
6	0.37000	0.50000	0.44050	0,m_y,0	0.00000	0.00000	0.00000
(1/2,1/2,1/2,0)' + set click here to show and hide
7	0.63000	0.50000	0.55950	0,-m_y,0	0.00000	0.00000	0.00000
8	0.37000	0.50000	0.94050	0,-m_y,0	0.00000	0.00000	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	M_xcos1	0	M_zcos1	4.30000	0.0	9.60000	0	M_ycos1+M_ysin1	0	0.0	0.0	0.0
2	-M_xcos1	0	-M_zcos1	-4.30000	0.0	-9.60000	0	M_ycos1+M_ysin1	0	0.0	0.0	0.0
(0,0,1/2,0)' + set click here to show and hide
3	-M_xcos1	0	-M_zcos1	-4.30000	0.0	-9.60000	0	-M_ycos1-M_ysin1	0	0.0	0.0	0.0
4	M_xcos1	0	M_zcos1	4.30000	0.0	9.60000	0	-M_ycos1-M_ysin1	0	0.0	0.0	0.0
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5	M_xcos1	0	M_zcos1	4.30000	0.0	9.60000	0	M_ycos1+M_ysin1	0	0.0	0.0	0.0
6	-M_xcos1	0	-M_zcos1	-4.30000	0.0	-9.60000	0	M_ycos1+M_ysin1	0	0.0	0.0	0.0
(1/2,1/2,1/2,0)' + set click here to show and hide
7	-M_xcos1	0	-M_zcos1	-4.30000	0.0	-9.60000	0	-M_ycos1-M_ysin1	0	0.0	0.0	0.0
8	M_xcos1	0	M_zcos1	4.30000	0.0	9.60000	0	-M_ycos1-M_ysin1	0	0.0	0.0	0.0

Atom	x	y	z
1	0.32200	0.00000	0.25750
2	0.67800	0.00000	0.24250
(0,0,1/2,0)' + set click here to show and hide
3	0.32200	0.00000	0.75750
4	0.67800	0.00000	0.74250
(1/2,1/2,0,0) + set click here to show and hide
5	0.82200	0.50000	0.25750
6	0.17800	0.50000	0.24250
(1/2,1/2,1/2,0)' + set click here to show and hide
7	0.82200	0.50000	0.75750
8	0.17800	0.50000	0.74250

Atom	x	y	z
1	0.33800	0.00000	0.07800
2	0.66200	0.00000	0.42200
(0,0,1/2,0)' + set click here to show and hide
3	0.33800	0.00000	0.57800
4	0.66200	0.00000	0.92200
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5	0.83800	0.50000	0.07800
6	0.16200	0.50000	0.42200
(1/2,1/2,1/2,0)' + set click here to show and hide
7	0.83800	0.50000	0.57800
8	0.16200	0.50000	0.92200

Atom	x	y	z
1	0.21600	0.00000	0.36400
2	0.78400	0.00000	0.13600
(0,0,1/2,0)' + set click here to show and hide
3	0.21600	0.00000	0.86400
4	0.78400	0.00000	0.63600
(1/2,1/2,0,0) + set click here to show and hide
5	0.71600	0.50000	0.36400
6	0.28400	0.50000	0.13600
(1/2,1/2,1/2,0)' + set click here to show and hide
7	0.71600	0.50000	0.86400
8	0.28400	0.50000	0.63600

Atom	x	y	z
1	0.50700	0.00000	0.10550
2	0.49300	0.00000	0.39450
(0,0,1/2,0)' + set click here to show and hide
3	0.50700	0.00000	0.60550
4	0.49300	0.00000	0.89450
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5	0.00700	0.50000	0.10550
6	0.99300	0.50000	0.39450
(1/2,1/2,1/2,0)' + set click here to show and hide
7	0.00700	0.50000	0.60550
8	0.99300	0.50000	0.89450

Reference: S. Baran, A. Deptuch, B. Penc, A. Hoser, A. Szytula, Acta Cryst. B (2021) 77 219 - 224
DOI: 10.1107/S205252062100127X
Atomic positions from: same reference

Parent space group (paramagnetic phase): C2/m (#12)
Propagation vector: k1 (0.00000, 0.5333(1), 0.00000)

Transition Temperature: 2 K
Experiment Temperature: 1.4 K

Lattice parameters of the basic unit cell:
16.08310 4.38870 13.74640 90.00000 115.75400 90.00000
Transformation from parent structure: (a,b,2c;0,0,0)
    [View matrix form]

Magnetic Superspace Group: C2/m1'_c(0,b,0)s00
    [View symmetry operations]

Magnetic Point Group: 2/m1' (5.2.13)
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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

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Average atomic positions and magnetic moments of symmetry independent atoms

Label	Atom type	x	y	z	Multiplicity	Symmetry constraints on M	M_0x	M_0y	M_0z	\|M\|
Er1	Er	0.00000	0.00000	0.25000	4	0,M_y,0	0.0	8.91(8)	0.0	8.91
Er2	Er	0.13000	0.00000	0.0595	8	0,M_y,0	0.0	0.0	0.0	0.00

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
Er1	0	0	0	0.0	0.0	0.0	0	M_ys1	0	0.0	0.0	0.0
Er2	M_xc1	0	M_zc1	4.3(4)	0.0	9.6(2)	0	M_ys1	0	0.0	0.0	0.0

Atom	x	y	z	Symmetry constraints on M	M_0x	M_0y	M_0z
1	0.00000	0.00000	0.25000	0,m_y,0	0.00000	8.91000	0.00000
(0,0,1/2,0)' + set click here to show and hide
2	0.00000	0.00000	0.75000	0,-m_y,0	0.00000	-8.91000	0.00000
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3	0.50000	0.50000	0.25000	0,m_y,0	0.00000	8.91000	0.00000
(1/2,1/2,1/2,0)' + set click here to show and hide
4	0.50000	0.50000	0.75000	0,-m_y,0	0.00000	-8.91000	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	0	0.0	0.0	0.0	0	M_ycos1+M_ysin1	0	0.0	0.0	0.0
(0,0,1/2,0)' + set click here to show and hide
2	0	0	0	0.0	0.0	0.0	0	-M_ycos1-M_ysin1	0	0.0	0.0	0.0
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3	0	0	0	0.0	0.0	0.0	0	M_ycos1+M_ysin1	0	0.0	0.0	0.0
(1/2,1/2,1/2,0)' + set click here to show and hide
4	0	0	0	0.0	0.0	0.0	0	-M_ycos1-M_ysin1	0	0.0	0.0	0.0

Atom	x	y	z	Symmetry constraints on M	M_0x	M_0y	M_0z
1	0.13000	0.00000	0.05950	0,m_y,0	0.00000	0.00000	0.00000
2	0.87000	0.00000	0.44050	0,m_y,0	0.00000	0.00000	0.00000
(0,0,1/2,0)' + set click here to show and hide
3	0.13000	0.00000	0.55950	0,-m_y,0	0.00000	0.00000	0.00000
4	0.87000	0.00000	0.94050	0,-m_y,0	0.00000	0.00000	0.00000
(1/2,1/2,0,0) + set click here to show and hide
5	0.63000	0.50000	0.05950	0,m_y,0	0.00000	0.00000	0.00000
6	0.37000	0.50000	0.44050	0,m_y,0	0.00000	0.00000	0.00000
(1/2,1/2,1/2,0)' + set click here to show and hide
7	0.63000	0.50000	0.55950	0,-m_y,0	0.00000	0.00000	0.00000
8	0.37000	0.50000	0.94050	0,-m_y,0	0.00000	0.00000	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	M_xcos1	0	M_zcos1	4.30000	0.0	9.60000	0	M_ycos1+M_ysin1	0	0.0	0.0	0.0
2	-M_xcos1	0	-M_zcos1	-4.30000	0.0	-9.60000	0	M_ycos1+M_ysin1	0	0.0	0.0	0.0
(0,0,1/2,0)' + set click here to show and hide
3	-M_xcos1	0	-M_zcos1	-4.30000	0.0	-9.60000	0	-M_ycos1-M_ysin1	0	0.0	0.0	0.0
4	M_xcos1	0	M_zcos1	4.30000	0.0	9.60000	0	-M_ycos1-M_ysin1	0	0.0	0.0	0.0
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5	M_xcos1	0	M_zcos1	4.30000	0.0	9.60000	0	M_ycos1+M_ysin1	0	0.0	0.0	0.0
6	-M_xcos1	0	-M_zcos1	-4.30000	0.0	-9.60000	0	M_ycos1+M_ysin1	0	0.0	0.0	0.0
(1/2,1/2,1/2,0)' + set click here to show and hide
7	-M_xcos1	0	-M_zcos1	-4.30000	0.0	-9.60000	0	-M_ycos1-M_ysin1	0	0.0	0.0	0.0
8	M_xcos1	0	M_zcos1	4.30000	0.0	9.60000	0	-M_ycos1-M_ysin1	0	0.0	0.0	0.0

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Active Irreps:

label	dim. small irrep	dim. full irrep	direction	action	number of modes
mA2-	1	1		primary	2
mU2	1	2	general	primary	4

Comments:

NPD
Above 2K, up to 6K, another phase with only Er1 ordered with the same spin arrangement as here (see entry #0.651)
This corrects a previous model proposed by the same group (Wawrzynska et al, J._Phys. _Condens._Matter (2003) 15,5279; DOI:10.1088/0953-8984/15/30/310).
The incommensurate propagation assigned in the paper is here substituted for the simpler equivalent vector: (0, 0.5333,1/2)
The basic unit cell used here is (a,b,2c). With respect to this unit cell the incommensurate wave vector becomes (0,0.5333,0), while the effect of the 1/2 component is taken care by the superspace symmetry associated with the modulation.

Comments (symmetry):

2k magnetic structure, one incommensurate and one commensurate
k-maximal magnetic symmetry
Two irreps, one with commensurate wave vector (0,0,1/2) and another with incommensurate one, are involved as primary. One for the ordering of Er1, and the incommensurate one for Er2.

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

Er₃Cu₄Sn₄ (#1.1.120)

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

Er3Cu4Sn4 (#1.1.120)

Er₃Cu₄Sn₄ (#1.1.120)