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	{ 2'₀₁₀ \| 0 0 0 1/2 }
3	-x1,x2,x3,x4+1/2,+1	{ m₁₀₀ \| 0 0 0 1/2 }
4	x1,x2,-x3,-x4,-1	{ m'₀₀₁ \| 0 }
(1/2,1/2,1/2,0) + set click here to show and hide
5	x1+1/2,x2+1/2,x3+1/2,x4,+1	{ 1 \| 1/2 1/2 1/2 0 }
6	-x1+1/2,x2+1/2,-x3+1/2,-x4+1/2,-1	{ 2'₀₁₀ \| 1/2 1/2 1/2 1/2 }
7	-x1+1/2,x2+1/2,x3+1/2,x4+1/2,+1	{ m₁₀₀ \| 1/2 1/2 1/2 1/2 }
8	x1+1/2,x2+1/2,-x3+1/2,-x4,-1	{ m'₀₀₁ \| 1/2 1/2 1/2 0 }

N	(x,y,z)	Seitz notation
1	x,y,z,+1	1
2	-x,y,-z,-1	2'₀₁₀
3	-x,y,z,+1	m₁₀₀
4	x,y,-z,-1	m'₀₀₁

Label	Atom type	x	y	z	Multiplicity
Ge1	Ge	0.00000	0.00000	0.386(1)	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
Nd1	0	M_yc1	0	0.0	0.0	0.0	0	0	M_zs1	0.0	0.0	0.0
Mn1	0	M_yc1	M_zc1	0.0	0.0	-2.26(9)	0	M_ys1	M_zs1	0.0	-2.26(9)	0.0

Atom	x	y	z	Symmetry constraints on M	M_0x	M_0y	M_0z
1	0.00000	0.00000	0.00000	m_x,0,0	-2.35000	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	m_x,0,0	-2.35000	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	0	M_ycos1	0	0.0	0.0	0.0	0	0	M_zcos1+M_ysin1	0.0	0.0	0.0
(1/2,1/2,1/2,0) + set click here to show and hide
2	0	M_ycos1	0	0.0	0.0	0.0	0	0	M_zcos1+M_ysin1	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	m_x,0,0	-1.52000	0.00000	0.00000
2	0.00000	0.50000	0.75000	m_x,0,0	-1.52000	0.00000	0.00000
(1/2,1/2,1/2,0) + set click here to show and hide
3	0.50000	0.00000	0.75000	m_x,0,0	-1.52000	0.00000	0.00000
4	0.50000	0.00000	0.25000	m_x,0,0	-1.52000	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	0	M_ycos1	M_zcos1	0.0	0.0	-2.26000	0	M_ycos1+M_ysin1	M_zcos1+M_ysin1	0.0	-2.26000	0.0
2	0	M_ycos1	-M_zcos1	0.0	0.0	2.26000	0	-M_ycos1-M_ysin1	M_zcos1+M_ysin1	0.0	2.26000	0.0
(1/2,1/2,1/2,0) + set click here to show and hide
3	0	M_ycos1	M_zcos1	0.0	0.0	-2.26000	0	M_ycos1+M_ysin1	M_zcos1+M_ysin1	0.0	-2.26000	0.0
4	0	M_ycos1	-M_zcos1	0.0	0.0	2.26000	0	-M_ycos1-M_ysin1	M_zcos1+M_ysin1	0.0	2.26000	0.0

Atom	x	y	z
1	0.00000	0.00000	0.38600
2	0.00000	0.00000	0.61400
(1/2,1/2,1/2,0) + set click here to show and hide
3	0.50000	0.50000	0.88600
4	0.50000	0.50000	0.11400

Reference: R. Welter, G. Venturini, E. Ressouche, B. Malaman, Journal of AlAys and Compounds (1995) 218 204 - 215
DOI: 10.1016/0925-8388(94)01378-0
Atomic positions from: ICSD #106911

Parent space group (paramagnetic phase): I4/mmm (#139)
Propagation vector: k1 (0.00000, 0.00000, 0.227(1))

Transition Temperature: 100 K
Experiment Temperature: 2 K

Lattice parameters of the basic unit cell:
4.103(1) 4.103(1) 10.901(4) 90.00000 90.00000 90.00000
Transformation from parent structure: (a,b,c;0,0,0)
    [View matrix form]

Magnetic Superspace Group: Im2'm'(0,0,g)s00
    [View symmetry operations]

Magnetic Point Group: m'm2' (7.3.22)
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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\|
Nd1	Nd	0.00000	0.00000	0.00000	2	m_x,0,0	-2.35(24)	0.0	0.0	2.35
Mn1	Mn	0.00000	0.50000	0.25000	4	m_x,0,0	-1.52(24)	0.0	0.0	1.52

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
Nd1	0	M_yc1	0	0.0	0.0	0.0	0	0	M_zs1	0.0	0.0	0.0
Mn1	0	M_yc1	M_zc1	0.0	0.0	-2.26(9)	0	M_ys1	M_zs1	0.0	-2.26(9)	0.0

Atom	x	y	z	Symmetry constraints on M	M_0x	M_0y	M_0z
1	0.00000	0.00000	0.00000	m_x,0,0	-2.35000	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	m_x,0,0	-2.35000	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	0	M_ycos1	0	0.0	0.0	0.0	0	0	M_zcos1+M_ysin1	0.0	0.0	0.0
(1/2,1/2,1/2,0) + set click here to show and hide
2	0	M_ycos1	0	0.0	0.0	0.0	0	0	M_zcos1+M_ysin1	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	m_x,0,0	-1.52000	0.00000	0.00000
2	0.00000	0.50000	0.75000	m_x,0,0	-1.52000	0.00000	0.00000
(1/2,1/2,1/2,0) + set click here to show and hide
3	0.50000	0.00000	0.75000	m_x,0,0	-1.52000	0.00000	0.00000
4	0.50000	0.00000	0.25000	m_x,0,0	-1.52000	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	0	M_ycos1	M_zcos1	0.0	0.0	-2.26000	0	M_ycos1+M_ysin1	M_zcos1+M_ysin1	0.0	-2.26000	0.0
2	0	M_ycos1	-M_zcos1	0.0	0.0	2.26000	0	-M_ycos1-M_ysin1	M_zcos1+M_ysin1	0.0	2.26000	0.0
(1/2,1/2,1/2,0) + set click here to show and hide
3	0	M_ycos1	M_zcos1	0.0	0.0	-2.26000	0	M_ycos1+M_ysin1	M_zcos1+M_ysin1	0.0	-2.26000	0.0
4	0	M_ycos1	-M_zcos1	0.0	0.0	2.26000	0	-M_ycos1-M_ysin1	M_zcos1+M_ysin1	0.0	2.26000	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
mGM5+	2	2	special	primary	2
mLD4	1	2	general	primary	2
mLD5	2	4	special	primary	3
mLD3	1	2	special	secondary	1

Comments:

NPD
FM along a
Polar along b
Figure in the paper is inconsistent with the propagation vector being reported. The propagation vector is assumed correct.
Three different phases reported as temperature is decreased. This is the one at the lowest temperature, where Nd moments become ordered.

Comments (symmetry):

1k incommensurate structure
Three irreps as primary: three order parameters in the sense of Landau theory are involved.

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

NdMn₂Ge₂ (#1.1.123)

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

NdMn2Ge2 (#1.1.123)

NdMn₂Ge₂ (#1.1.123)