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,-x4+1/2,+1	{ 2₀₁₀ \| 0 1/2 0 1/2 }
4	x1+1/2,-x2+1/2,-x3+1/2,-x4,+1	{ 2₁₀₀ \| 1/2 1/2 1/2 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,-x4,-1	{ 2'₀₁₀ \| 0 1/2 0 0 }
8	x1+1/2,-x2+1/2,-x3+1/2,-x4+1/2,-1	{ 2'₁₀₀ \| 1/2 1/2 1/2 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
As1	As	0.2011(10)	0.25	0.5802(12)	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
Cr1	M_xcos1	M_ycos1	M_zcos1	0.99	1.42	0.0	M_xsin1	M_ysin1	M_zsin1	-1.42	0.99	0.0

Atom	x	y	z
1	0.00680	0.25000	0.20340
2	0.49320	0.75000	0.70340
3	0.99320	0.75000	0.79660
4	0.50680	0.25000	0.29660

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	0.99000	1.42000	0.0	M_xsin1	M_ysin1	M_zsin1	-1.42000	0.99000	0.0
2	M_xcos1	M_ycos1	-M_zcos1	0.99000	1.42000	0.0	M_xsin1	M_ysin1	-M_zsin1	-1.42000	0.99000	0.0
3	M_xcos1	-M_ycos1	M_zcos1	0.99000	-1.42000	0.0	-M_xsin1	M_ysin1	-M_zsin1	1.42000	0.99000	0.0
4	M_xcos1	-M_ycos1	-M_zcos1	0.99000	-1.42000	0.0	-M_xsin1	M_ysin1	M_zsin1	1.42000	0.99000	0.0

Atom	x	y	z
1	0.20110	0.25000	0.58020
2	0.29890	0.75000	0.08020
3	0.79890	0.75000	0.41980
4	0.70110	0.25000	0.91980

Reference: L. Keller, J.S. White, M. Frontzek, P. Babkevich, M.A. Susner, Z.C. Sims, A.S. Sefat, H.M. Ronnow and C. Ruegg, Physical Review B (2015) 91 020409.
DOI: 10.1103/physrevb.91.020409
Atomic positions from: same reference

Parent space group (paramagnetic phase): Pnma (#62)
Propagation vector: k1 (0.000000, 0.000000, 0.356200)

Transition Temperature: 265 K
Experiment Temperature: 1.5 K

Lattice parameters of the basic unit cell:
5.65 3.47 6.203 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
Cr1	Cr	0.0068(12)	0.25	0.2034(10)	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
Cr1	M_xcos1	M_ycos1	M_zcos1	0.99	1.42	0.0	M_xsin1	M_ysin1	M_zsin1	-1.42	0.99	0.0

Atom	x	y	z
1	0.00680	0.25000	0.20340
2	0.49320	0.75000	0.70340
3	0.99320	0.75000	0.79660
4	0.50680	0.25000	0.29660

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	0.99000	1.42000	0.0	M_xsin1	M_ysin1	M_zsin1	-1.42000	0.99000	0.0
2	M_xcos1	M_ycos1	-M_zcos1	0.99000	1.42000	0.0	M_xsin1	M_ysin1	-M_zsin1	-1.42000	0.99000	0.0
3	M_xcos1	-M_ycos1	M_zcos1	0.99000	-1.42000	0.0	-M_xsin1	M_ysin1	-M_zsin1	1.42000	0.99000	0.0
4	M_xcos1	-M_ycos1	-M_zcos1	0.99000	-1.42000	0.0	-M_xsin1	M_ysin1	M_zsin1	1.42000	0.99000	0.0

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Active Irreps:

label	dim. small irrep	dim. full irrep	direction	action	number of modes
mLD3	1	2	special	primary	4
mLD4	1	2	special	primary	2

Comments:

NPD
Model originally reported in Selte et al., Acta Chemica Scandinavica 25 (1971) 1703.
In the figure the modulation phase has been shifted to coincide with the choice done in the reference.

Comments (symmetry):

1k magnetic structure
Two irreps are combined in quadrature (origin shift pi/2 between the two irrep modulations).
Cr1 lies in a general position of the MSSG (mirror plane my is broken), and therefore its modulation has no symmetry-restriction.
The model constrains the modulation to be an helical modulation on the ab plane (2 free parameters). A general spin model complying with the same magnetic symmetry allows 6 free parameters.
The spin modulation breaks the inversion center but the resulting point group 2221' remains non-polar.

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

CrAs (#1.1.24)