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

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	0.845(6)	0.843(7)	0.842(6)	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_xcos1	M_ycos1	M_zcos1	0.0	2.3(5)	0.0	M_xsin1	M_ysin1	M_zsin1	-2.3	0.0	0.0

Atom	x	y	z
1	0.14200	0.13100	0.13600
2	0.35800	0.86900	0.63600
3	0.85800	0.63100	0.36400
4	0.64200	0.36900	0.86400

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	0.0	2.30000	0.0	M_xsin1	M_ysin1	M_zsin1	-2.30000	0.0	0.0
2	M_xcos1	M_ycos1	-M_zcos1	0.0	2.30000	0.0	M_xsin1	M_ysin1	-M_zsin1	-2.30000	0.0	0.0
3	-M_xcos1	M_ycos1	-M_zcos1	0.0	2.30000	0.0	M_xsin1	-M_ysin1	M_zsin1	-2.30000	0.0	0.0
4	-M_xcos1	M_ycos1	M_zcos1	0.0	2.30000	0.0	M_xsin1	-M_ysin1	-M_zsin1	-2.30000	0.0	0.0

Atom	x	y	z
1	0.84500	0.84300	0.84200
2	0.65500	0.15700	0.34200
3	0.15500	0.34300	0.65800
4	0.34500	0.65700	0.15800

Reference: O.L. Makarova, A.V. Tsvyashchenko, G. Andre, F. Porcher, L.N. Fomicheva, N. Rey and I. Mirebeau, Physical Review B (2012) 85 205205.
DOI: 10.1103/physrevb.85.205205
Atomic positions from: ICSD #187195

Parent space group (paramagnetic phase): P2₁3 (#198)
Propagation vector: k1 (0.000000, 0.000000, 0.167(4))

Transition Temperature: 170 K
Experiment Temperature: 2 K

Lattice parameters of the basic unit cell:
4.781(3) 4.781(3) 4.794(1) 90 90 90
Transformation from parent structure: (a,b,c;0,0,0)
    [View matrix form]

Magnetic Superspace Group: P2121211'(00γ)00ss
    [View symmetry operations]

Magnetic Point Group: 2221' (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	0.142(12)	0.131(16)	0.136(11)	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_xcos1	M_ycos1	M_zcos1	0.0	2.3(5)	0.0	M_xsin1	M_ysin1	M_zsin1	-2.3	0.0	0.0

Atom	x	y	z
1	0.14200	0.13100	0.13600
2	0.35800	0.86900	0.63600
3	0.85800	0.63100	0.36400
4	0.64200	0.36900	0.86400

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	0.0	2.30000	0.0	M_xsin1	M_ysin1	M_zsin1	-2.30000	0.0	0.0
2	M_xcos1	M_ycos1	-M_zcos1	0.0	2.30000	0.0	M_xsin1	M_ysin1	-M_zsin1	-2.30000	0.0	0.0
3	-M_xcos1	M_ycos1	-M_zcos1	0.0	2.30000	0.0	M_xsin1	-M_ysin1	M_zsin1	-2.30000	0.0	0.0
4	-M_xcos1	M_ycos1	M_zcos1	0.0	2.30000	0.0	M_xsin1	-M_ysin1	-M_zsin1	-2.30000	0.0	0.0

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Active Irreps:

label	dim. small irrep	dim. full irrep	action	number of modes
mDT2	1	6	primary	6

Comments:

NPD
Helical structure
Wave vector parameter g varies from 0.107 to 0.167 between TN and 30K.
The magnetic ordering breaks the symmetry from cubic to orthorhombic.
Symmetry reduction of the average structure to P212121, as expected from the MSSG.
Mn in general position of the MSSG with no constraint on its spin modulation.
Assumed helical model is not symmetry forced. Very poor fit.

Comments (symmetry):

1k magnetic structure
k-maximal magnetic symmetry (2 possible)
one to one correspondence between MSSG and active irrep
Absolute chirality of the spin helix is not given. One helix sense has been chosen arbitrarily.

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

MnGe (#1.1.14)