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	{ 2_1-10 \| 0 0 0 1/2 }
(1/2,1/2,1/2,0) + set click here to show and hide
3	x1+1/2,x2+1/2,x3+1/2,x4,+1	{ 1 \| 1/2 1/2 1/2 0 }
4	-x2+1/2,-x1+1/2,-x3+1/2,-x4+1/2,+1	{ 2_1-10 \| 1/2 1/2 1/2 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	-x2,-x1,-x3,-x4,-1	{ 2'_1-10 \| 0 }
(1/2,1/2,1/2,1/2)' + set click here to show and hide
7	x1+1/2,x2+1/2,x3+1/2,x4+1/2,-1	{ 1' \| 1/2 1/2 1/2 1/2 }
8	-x2+1/2,-x1+1/2,-x3+1/2,-x4,-1	{ 2'_1-10 \| 1/2 1/2 1/2 0 }

N	(x,y,z)	Seitz notation
1	x,y,z,+1	1
2	-y,-x,-z,+1	2_1-10
1' + set click here to show and hide
3	x,y,z,-1	1'
4	-y,-x,-z,-1	2'_1-10

Label	Atom type	y	z	Multiplicity
Cu1_1	Cu	0.5	0.25	2
Cu1_2	Cu	-0.5	-0.25	2
Ge1	Ge	0	0.385	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
Ce1	M_xcos1	M_xcos1	M_zcos1	0.25	0.25	-0.65	M_xsin1	-M_xsin1	0	0.52	-0.52	0.0

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

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	0.25000	0.25000	-0.65000	M_xsin1	-M_xsin1	0	0.52000	-0.52000	0.0
(1/2,1/2,1/2,0) + set click here to show and hide
2	M_xcos1	M_xcos1	M_zcos1	0.25000	0.25000	-0.65000	M_xsin1	-M_xsin1	0	0.52000	-0.52000	0.0

Atom	x	y	z
1	0.00000	0.50000	0.25000
(1/2,1/2,1/2,0) + set click here to show and hide
2	0.50000	0.00000	0.75000

Atom	x	y	z
1	0.00000	0.50000	0.75000
(1/2,1/2,1/2,0) + set click here to show and hide
2	0.50000	0.00000	0.25000

Atom	x	y	z
1	0.00000	0.00000	0.38500
2	0.00000	0.00000	0.61500
(1/2,1/2,1/2,0) + set click here to show and hide
3	0.50000	0.50000	0.88500
4	0.50000	0.50000	0.11500

Reference: G. Knopp, A. Loidl, K. Knorr, L. Pawlak, M. Duczmal, R. Caspary, U. Gottwick, H. Spille, F. Steglich and A.P. Murani, Zeitschrift fï¿½r Physik B Condensed Matter (1989) 77 95-104.
DOI: 10.1007/bf01313625
Atomic positions from: ICSD #52848

Parent space group (paramagnetic phase): (#139)
Propagation vector: k1 (0.280000, 0.280000, 0.540000)

Transition Temperature: 4.1 K
Experiment Temperature: 1.5 K

Lattice parameters of the basic unit cell:
4.158 4.158 10.227 90 90 90
Transformation from parent structure: (a,b,c;0,0,0)
    [View matrix form]

Magnetic Superspace Group: I21'(a,a,g)0s
    [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

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Average atomic positions of symmetry independent atoms

Label	Atom type	x	y	z	Multiplicity
Ce1	Ce	0	0	0	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_xcos1	M_xcos1	M_zcos1	0.25	0.25	-0.65	M_xsin1	-M_xsin1	0	0.52	-0.52	0.0

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

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	0.25000	0.25000	-0.65000	M_xsin1	-M_xsin1	0	0.52000	-0.52000	0.0
(1/2,1/2,1/2,0) + set click here to show and hide
2	M_xcos1	M_xcos1	M_zcos1	0.25000	0.25000	-0.65000	M_xsin1	-M_xsin1	0	0.52000	-0.52000	0.0

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

Active Irreps:

label	dim. small irrep	dim. full irrep	action	number of modes
mA1	1	8	primary	1
mA2	1	8	primary	2

Comments:

NPD
The model is a circular spin spiral with the plane of the spin rotation perpendicular to the propagation vector
The spin modulation components are here only approximate to reproduce the spin modulus, and also the perpendicularity of the spiral plane with respect to the propagation vector, which is not forced by symmetry.

Comments (symmetry):

1k incommensurate magnetic structure
The two possible irreps are involved with a pi/2 shift
The 2-fold symmetry of the structure is along the (1,-1,0) direction.
The MSSG only forces that the plane of the spin rotation includes the (1,-1,0) direction, and allows ellipcity of the spin rotation.

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

CeCu₂Ge₂ (#1.1.55)

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

CeCu2Ge2 (#1.1.55)

CeCu₂Ge₂ (#1.1.55)