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	{ 2'₁₀₀ \| 0 0 0 1/2 }
3	-x1,x2,-x3,-x4,-1	{ 2'₀₁₀ \| 0 }
4	-x1,-x2,x3,x4+1/2,+1	{ 2₀₀₁ \| 0 0 0 1/2 }
5	-x2,-x1,-x3,-x4+1/4,-1	{ 2'_1-10 \| 0 0 0 1/4 }
6	-x2,x1,x3,x4+1/4,+1	{ 4⁺₀₀₁ \| 0 0 0 1/4 }
7	x2,-x1,x3,x4+3/4,+1	{ 4^-₀₀₁ \| 0 0 0 3/4 }
8	x2,x1,-x3,-x4+3/4,-1	{ 2'₁₁₀ \| 0 0 0 3/4 }
(1/2,1/2,1/2,0) + set click here to show and hide
9	x1+1/2,x2+1/2,x3+1/2,x4,+1	{ 1 \| 1/2 1/2 1/2 0 }
10	x1+1/2,-x2+1/2,-x3+1/2,-x4+1/2,-1	{ 2'₁₀₀ \| 1/2 1/2 1/2 1/2 }
11	-x1+1/2,x2+1/2,-x3+1/2,-x4,-1	{ 2'₀₁₀ \| 1/2 1/2 1/2 0 }
12	-x1+1/2,-x2+1/2,x3+1/2,x4+1/2,+1	{ 2₀₀₁ \| 1/2 1/2 1/2 1/2 }
13	-x2+1/2,-x1+1/2,-x3+1/2,-x4+1/4,-1	{ 2'_1-10 \| 1/2 1/2 1/2 1/4 }
14	-x2+1/2,x1+1/2,x3+1/2,x4+1/4,+1	{ 4⁺₀₀₁ \| 1/2 1/2 1/2 1/4 }
15	x2+1/2,-x1+1/2,x3+1/2,x4+3/4,+1	{ 4^-₀₀₁ \| 1/2 1/2 1/2 3/4 }
16	x2+1/2,x1+1/2,-x3+1/2,-x4+3/4,-1	{ 2'₁₁₀ \| 1/2 1/2 1/2 3/4 }

N	(x,y,z)	Seitz notation
1	x,y,z,+1	1
2	x,-y,-z,-1	2'₁₀₀
3	-x,y,-z,-1	2'₀₁₀
4	-x,-y,z,+1	2₀₀₁
5	-y,-x,-z,-1	2'_1-10
6	-y,x,z,+1	4⁺₀₀₁
7	y,-x,z,+1	4^-₀₀₁
8	y,x,-z,-1	2'₁₁₀

Label	Atom type	x	y	z	Multiplicity
Ge1	Ge	0.00000	0.00000	0.381(l)	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
Pr1	M_xcos1	0	0	0.0	0.0	0.0	0	M_xcos1	0	0.0	0.0	0.0
Mn1	M_xcos1	M_ycos1	0	0.0	2.40(10)	0.0	M_ycos1	M_xcos1	0	2.40(10)	0.0	0.0

Atom	x	y	z	Symmetry constraints on M	M_0x	M_0y	M_0z
1	0.00000	0.00000	0.00000	0,0,m_z	0.00000	0.00000	2.95000
(1/2,1/2,1/2,0) + set click here to show and hide
2	0.50000	0.50000	0.50000	0,0,m_z	0.00000	0.00000	2.95000

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	0	0.0	0.0	0.0	0	M_xcos1	0	0.0	0.0	0.0
(1/2,1/2,1/2,0) + set click here to show and hide
2	M_xcos1	0	0	0.0	0.0	0.0	0	M_xcos1	0	0.0	0.0	0.0

Atom	x	y	z	Symmetry constraints on M	M_0x	M_0y	M_0z
1	0.00000	0.50000	0.25000	0,0,m_z	0.00000	0.00000	1.48000
2	0.00000	0.50000	0.75000	0,0,m_z	0.00000	0.00000	1.48000
(1/2,1/2,1/2,0) + set click here to show and hide
3	0.50000	0.00000	0.75000	0,0,m_z	0.00000	0.00000	1.48000
4	0.50000	0.00000	0.25000	0,0,m_z	0.00000	0.00000	1.48000

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	0.0	2.40000	0.0	M_ycos1	M_xcos1	0	2.40000	0.0	0.0
2	M_xcos1	-M_ycos1	0	0.0	-2.40000	0.0	-M_ycos1	M_xcos1	0	-2.40000	0.0	0.0
(1/2,1/2,1/2,0) + set click here to show and hide
3	M_xcos1	M_ycos1	0	0.0	2.40000	0.0	M_ycos1	M_xcos1	0	2.40000	0.0	0.0
4	M_xcos1	-M_ycos1	0	0.0	-2.40000	0.0	-M_ycos1	M_xcos1	0	-2.40000	0.0	0.0

Atom	x	y	z
1

Reference: R. Welter, G. Venturini, E. Ressouche, B. Malaman, Journal of Alloys and Compounds (1995) 218 204 - 215
DOI: 10.1016/0925-8388(94)01378-0
Atomic positions from: ICSD #106914

Parent space group (paramagnetic phase): I4/mmm (#139)
Propagation vector: k1 (0.00000, 0.00000, 0.268(1))

Transition Temperature: 280 K
Experiment Temperature: 2 K

Lattice parameters of the basic unit cell:
4.113(1) 4.113(1) 10.896(4) 90.00000 90.00000 90.00000
Transformation from parent structure: (a,b,c;0,0,0)
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Magnetic Superspace Group: I42'2'(0,0,g)q00
    [View symmetry operations]

Magnetic Point Group: 42'2' (12.4.43)
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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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     [Show all the atoms]

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\|
Pr1	Pr	0.00000	0.00000	0.00000	2	0,0,m_z	0.0	0.0	2.95(20)	2.95
Mn1	Mn	0.00000	0.50000	0.25000	4	0,0,m_z	0.0	0.0	1.48(25)	1.48

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
Pr1	M_xcos1	0	0	0.0	0.0	0.0	0	M_xcos1	0	0.0	0.0	0.0
Mn1	M_xcos1	M_ycos1	0	0.0	2.40(10)	0.0	M_ycos1	M_xcos1	0	2.40(10)	0.0	0.0

Atom	x	y	z	Symmetry constraints on M	M_0x	M_0y	M_0z
1	0.00000	0.00000	0.00000	0,0,m_z	0.00000	0.00000	2.95000
(1/2,1/2,1/2,0) + set click here to show and hide
2	0.50000	0.50000	0.50000	0,0,m_z	0.00000	0.00000	2.95000

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	0	0.0	0.0	0.0	0	M_xcos1	0	0.0	0.0	0.0
(1/2,1/2,1/2,0) + set click here to show and hide
2	M_xcos1	0	0	0.0	0.0	0.0	0	M_xcos1	0	0.0	0.0	0.0

Atom	x	y	z	Symmetry constraints on M	M_0x	M_0y	M_0z
1	0.00000	0.50000	0.25000	0,0,m_z	0.00000	0.00000	1.48000
2	0.00000	0.50000	0.75000	0,0,m_z	0.00000	0.00000	1.48000
(1/2,1/2,1/2,0) + set click here to show and hide
3	0.50000	0.00000	0.75000	0,0,m_z	0.00000	0.00000	1.48000
4	0.50000	0.00000	0.25000	0,0,m_z	0.00000	0.00000	1.48000

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	0.0	2.40000	0.0	M_ycos1	M_xcos1	0	2.40000	0.0	0.0
2	M_xcos1	-M_ycos1	0	0.0	-2.40000	0.0	-M_ycos1	M_xcos1	0	-2.40000	0.0	0.0
(1/2,1/2,1/2,0) + set click here to show and hide
3	M_xcos1	M_ycos1	0	0.0	2.40000	0.0	M_ycos1	M_xcos1	0	2.40000	0.0	0.0
4	M_xcos1	-M_ycos1	0	0.0	-2.40000	0.0	-M_ycos1	M_xcos1	0	-2.40000	0.0	0.0

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Active Irreps:

label	dim. small irrep	dim. full irrep	direction	action	number of modes
mGM3+	1	1		primary	1
mLD5	2	4	special	primary	2

Comments:

NPD
Conical modulation
Mn Moment magnitude: 2.8
A similar model at 142K with smaller moment of Pr (1.0(3)) is also given in the same reference.
The rotation of the spins in consecutive Mn layers related by the lattice translation (1/2,1/2,1/2) shown in the figure of the article is not consistent with the propagation vector. The propagation vector has been assumed correct.
The MSSG used in the description here fixes the phase origin of the modulation, in a value that is different from the one used in the graphical representation in the paper. Apply a phase shift of apprx. -0.33 to obtain a graphical representation with approximately the same phase choice.

Comments (symmetry):

1k incommensurate magnetic structure
k-maximal magnetic symmetry
Two irreps as primary: two order parameters in the sense of Landau theory are present

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

PrMn₂Ge₂ (#1.1.124)

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

PrMn2Ge2 (#1.1.124)

PrMn₂Ge₂ (#1.1.124)