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+1/2,-x2,x3+1/2,-x4+1/2,+1	{ 2₀₀₁ \| 1/2 0 1/2 1/2 }
3	-x1,x2+1/2,-x3+1/2,x4+1/2,+1	{ 2₀₁₀ \| 0 1/2 1/2 1/2 }
4	x1+1/2,-x2+1/2,-x3,-x4,+1	{ 2₁₀₀ \| 1/2 1/2 0 0 }
(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+1/2,-x2,x3+1/2,-x4,-1	{ 2'₀₀₁ \| 1/2 0 1/2 0 }
7	-x1,x2+1/2,-x3+1/2,x4,-1	{ 2'₀₁₀ \| 0 1/2 1/2 0 }
8	x1+1/2,-x2+1/2,-x3,-x4+1/2,-1	{ 2'₁₀₀ \| 1/2 1/2 0 1/2 }

N	(x,y,z)	Seitz notation
1	x,y,z,+1	1
2	-x,-y,z,+1	2₀₀₁
3	-x,y,-z,+1	2₀₁₀
4	x,-y,-z,+1	2₁₀₀
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	2'₀₁₀
8	x,-y,-z,-1	2'₁₀₀

Label	Atom type	x	y	z	Multiplicity
Ge1	Ge	0.1567	0.1567	0.1567	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
Mn1	M_xc1	M_yc1	M_zc1	0.814	0.0	0.0	M_xs1	M_ys1	M_zs1	0.0	0.0	-0.814

Atom	x	y	z
1	0.86160	0.86160	0.86160
2	0.63840	0.13840	0.36160
3	0.13840	0.36160	0.63840
4	0.36160	0.63840	0.13840

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	M_zcos1	0.81400	0.0	0.0	M_xcos1+M_ysin1	M_ycos1+M_ysin1	M_zcos1+M_ysin1	0.0	0.0	-0.81400
2	M_xcos1	M_ycos1	-M_zcos1	0.81400	0.0	0.0	-M_xcos1-M_ysin1	-M_ycos1-M_ysin1	M_zcos1+M_ysin1	0.0	0.0	-0.81400
3	M_xcos1	-M_ycos1	M_zcos1	0.81400	0.0	0.0	M_xcos1+M_ysin1	-M_ycos1-M_ysin1	M_zcos1+M_ysin1	0.0	0.0	-0.81400
4	M_xcos1	-M_ycos1	-M_zcos1	0.81400	0.0	0.0	-M_xcos1-M_ysin1	M_ycos1+M_ysin1	M_zcos1+M_ysin1	0.0	0.0	-0.81400

Atom	x	y	z
1	0.15670	0.15670	0.15670
2	0.34330	0.84330	0.65670
3	0.84330	0.65670	0.34330
4	0.65670	0.34330	0.84330

Reference: V. Pomjakushin, I. Plokhikh, J.S. White, Y. Fujishiro, N. Kanazawa, Y. Tokura, E. Pomjakushina, Physical (2023) 107 024410
DOI: 10.1103/PhysRevB.107.024410
Atomic positions from: same reference

Parent space group (paramagnetic phase): P2₁3 (#198)
Propagation vector: k1 (0.000000, 0.16498, 0.000000)

Transition Temperature: 170K K
Experiment Temperature: 2K K

Lattice parameters of the basic unit cell:
4.78049 4.78049 4.78049 90.0000 90.0000 90.0000
Transformation from parent structure: (a,b,c;0,0,0)
    [View matrix form]

Magnetic Superspace Group: P212121.1'(0b0)0s0s
    [View symmetry operations]

Magnetic Point Group: 222.1' (6.2.18)
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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 of symmetry independent atoms

Label	Atom type	x	y	z	Multiplicity
Mn1	Mn	0.8616	0.8616	0.8616	4

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
Mn1	M_xc1	M_yc1	M_zc1	0.814	0.0	0.0	M_xs1	M_ys1	M_zs1	0.0	0.0	-0.814

Atom	x	y	z
1	0.86160	0.86160	0.86160
2	0.63840	0.13840	0.36160
3	0.13840	0.36160	0.63840
4	0.36160	0.63840	0.13840

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	M_zcos1	0.81400	0.0	0.0	M_xcos1+M_ysin1	M_ycos1+M_ysin1	M_zcos1+M_ysin1	0.0	0.0	-0.81400
2	M_xcos1	M_ycos1	-M_zcos1	0.81400	0.0	0.0	-M_xcos1-M_ysin1	-M_ycos1-M_ysin1	M_zcos1+M_ysin1	0.0	0.0	-0.81400
3	M_xcos1	-M_ycos1	M_zcos1	0.81400	0.0	0.0	M_xcos1+M_ysin1	-M_ycos1-M_ysin1	M_zcos1+M_ysin1	0.0	0.0	-0.81400
4	M_xcos1	-M_ycos1	-M_zcos1	0.81400	0.0	0.0	-M_xcos1-M_ysin1	M_ycos1+M_ysin1	M_zcos1+M_ysin1	0.0	0.0	-0.81400

[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
mDT2	1	6	special	primary	6

Comments:

NPD
A difference curve 2K-300K was used

Comments (symmetry):

1k incommensurate magnetic structure
The star of the active irrep has 6 vectors. This is the model of maximal symmetry considering a 1k arrangement according to the (k,-k) extended small irrep.
2k and 3k models involving the other k-vectors of the irrep star were also refined as possible alternative models (see corresponding entries)
An observed small orthorhombic distortion in the space group P2_12_12_1 of the nuclear structure, with respect to the parent cubic structure is disregarded and not included in this model.

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

MnGe (#1.1.150)