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

N	(x,y,z)	Seitz notation
1	x,y,z,+1	1
2	-x,-y,z,+1	2₀₀₁
3	-x,-y,-z,+1	-1
4	x,y,-z,+1	m₀₀₁
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	-1'
8	x,y,-z,-1	m'₀₀₁

Label	Atom type	x	y	Multiplicity
Al1	Al	-0.08065	-0.08065	4
Al2	Al	0.30641	0.30641	4
Ge1	Ge	0.22367	0.22367	4
Pt1	Pt	0.00000	0.00000	2

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
Ce1	M_xc1	M_yc1	0	3.678	-3.871	0.0	0	0	0	0.0	0.0	0.0

Atom	x	y	z
1	0.00000	0.50000	0.50000
(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	M_xcos1	M_ycos1	0	3.67800	-3.87100	0.0	0	0	0	0.0	0.0	0.0
(0,0,0,1/2)' + set click here to show and hide
2	M_xcos1	M_ycos1	0	3.67800	-3.87100	0.0	0	0	0	0.0	0.0	0.0

Atom	x	y	z
1	0.91935	0.91935	0.00000
(0,0,0,1/2)' + set click here to show and hide
2	0.08065	0.08065	0.00000
(1/2,0,1/2,0) + set click here to show and hide
3	0.41935	0.91935	0.50000
(1/2,0,1/2,1/2)' + set click here to show and hide
4	0.58065	0.08065	0.50000

Atom	x	y	z
1	0.30641	0.30641	0.00000
(0,0,0,1/2)' + set click here to show and hide
2	0.69359	0.69359	0.00000
(1/2,0,1/2,0) + set click here to show and hide
3	0.80641	0.30641	0.50000
(1/2,0,1/2,1/2)' + set click here to show and hide
4	0.19359	0.69359	0.50000

Atom	x	y	z
1	0.22367	0.22367	0.00000
(0,0,0,1/2)' + set click here to show and hide
2	0.77633	0.77633	0.00000
(1/2,0,1/2,0) + set click here to show and hide
3	0.72367	0.22367	0.50000
(1/2,0,1/2,1/2)' + set click here to show and hide
4	0.27633	0.77633	0.50000

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	0.00000	0.50000

Reference: S. Shin, V. Pomjakushin, L. Keller, P.F.S. Rosa, U. Stuhr, C. Niedermayer, R. Sibille, S. Toth, J. Kim, H. Jang, S.-K. Son, H.-O. Lee, T. Shang, M. Medarde, E.D. Bauer, M. Kenzelmann, T. Park, PHYSICAL REVIEW B (2020) 101 224421
DOI: 10.1103/PhysRevB.101.224421
Atomic positions from: same reference

Parent space group (paramagnetic phase): R-3m (#166)
Propagation vector: k1 (0.86667, -0.95667, 0.00000)

Transition Temperature: 2.3 K
Experiment Temperature: 0.07 K

Lattice parameters of the basic unit cell:
21.26216 10.83481 4.18243 90.00000 90.00000 19.39862
Transformation from parent structure: (-1/3a+1/3b-2/3c,1/3a-1/3b-1/3c,-a-b;0,0,0)
    [View matrix form]

Magnetic Superspace Group: B2/m.1'(a,b,0)0ss
    [View symmetry operations]

Magnetic Point Group: 2/m.1' (5.2.13)
    [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
Ce1	Ce	0.00000	0.50000	0.50000	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
Ce1	M_xc1	M_yc1	0	3.678	-3.871	0.0	0	0	0	0.0	0.0	0.0

Atom	x	y	z
1	0.00000	0.50000	0.50000
(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	M_xcos1	M_ycos1	0	3.67800	-3.87100	0.0	0	0	0	0.0	0.0	0.0
(0,0,0,1/2)' + set click here to show and hide
2	M_xcos1	M_ycos1	0	3.67800	-3.87100	0.0	0	0	0	0.0	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
mC2	1	6	general	primary	2

Comments:

NPD
In the published paper, MSSG was not used. The magnetic structure was described with the k-vector [1.39, 0, 0.09], corresponding to the C-point of the Brillouin Zone (BZ), and basis vectors were defined in the parent crystal metrics. The k-vector was adjusted to the standard ISODISTORT arm [-1.39, 1.39, 0.09] with the appropriate changes to the basis vectors (by 3+ 0,0,z). The structure was then converted to MSSG B2/m.1â€™(a,b,0)0ss, with the basis transformation {(-1/3,1/3,-2/3), (1/3,-1/3,-1/3), (-1,-1,0)}.
The basic unit cell in the standard setting of the MSSG used here is very different from the parent unit cell, with a very small monoclinic angle.

Comments (symmetry):

1k incommensurate magnetic structure
k-maximal magnetic symmetry
2-dim extended small irrep extended for (k,-k). The relevant irrep is 6-dim with 6 k-vectors in the irrep star.

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