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+1/2,-x4,+1	{ 2₀₁₀ \| 0 0 1/2 0 }
3	x1,x2,-x3,x4,+1	{ m₀₀₁ \| 0 }
4	-x1,x2,x3+1/2,-x4,+1	{ m₁₀₀ \| 0 0 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,x2,-x3+1/2,-x4+1/2,-1	{ 2'₀₁₀ \| 0 0 1/2 1/2 }
7	x1,x2,-x3,x4+1/2,-1	{ m'₀₀₁ \| 0 0 0 1/2 }
8	-x1,x2,x3+1/2,-x4+1/2,-1	{ m'₁₀₀ \| 0 0 1/2 1/2 }
(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,-x4,+1	{ 2₀₁₀ \| 1/2 1/2 0 0 }
11	x1+1/2,x2+1/2,-x3+1/2,x4,+1	{ m₀₀₁ \| 1/2 1/2 1/2 0 }
12	-x1+1/2,x2+1/2,x3,-x4,+1	{ m₁₀₀ \| 1/2 1/2 0 0 }
(1/2,1/2,1/2,1/2)' + set click here to show and hide
13	x1+1/2,x2+1/2,x3+1/2,x4+1/2,-1	{ 1' \| 1/2 1/2 1/2 1/2 }
14	-x1+1/2,x2+1/2,-x3,-x4+1/2,-1	{ 2'₀₁₀ \| 1/2 1/2 0 1/2 }
15	x1+1/2,x2+1/2,-x3+1/2,x4+1/2,-1	{ m'₀₀₁ \| 1/2 1/2 1/2 1/2 }
16	-x1+1/2,x2+1/2,x3,-x4+1/2,-1	{ m'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	2₀₁₀
3	x,y,-z,+1	m₀₀₁
4	-x,y,z,+1	m₁₀₀
1' + set click here to show and hide
5	x,y,z,-1	1'
6	-x,y,-z,-1	2'₀₁₀
7	x,y,-z,-1	m'₀₀₁
8	-x,y,z,-1	m'₁₀₀

Label	Atom type	x	y	Multiplicity
K1_1	K	0.34500	0.14780	4
K1_2	K	0.84500	0.35220	4
S1_1	S	0.19530	0.89650	4
S1_2	S	0.69530	0.60350	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_1	0	M_ycos1	0	0.0	2.279	0.0	M_xsin1	0	M_zsin1	2.279	0.0	0.0

Atom	x	y	z
1	0.00000	0.00000	0.25000
(0,0,0,1/2)' + set click here to show and hide
2	0.00000	0.00000	0.75000
(1/2,1/2,1/2,0) + set click here to show and hide
3	0.50000	0.50000	0.75000
(1/2,1/2,1/2,1/2)' + set click here to show and hide
4	0.50000	0.50000	0.25000

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	2.27900	0.0	M_xsin1	0	M_zsin1	2.27900	0.0	0.0
(0,0,0,1/2)' + set click here to show and hide
2	0	-M_ycos1	0	0.0	-2.27900	0.0	-M_xsin1	0	M_zsin1	-2.27900	0.0	0.0
(1/2,1/2,1/2,0) + set click here to show and hide
3	0	M_ycos1	0	0.0	2.27900	0.0	M_xsin1	0	M_zsin1	2.27900	0.0	0.0
(1/2,1/2,1/2,1/2)' + set click here to show and hide
4	0	-M_ycos1	0	0.0	-2.27900	0.0	-M_xsin1	0	M_zsin1	-2.27900	0.0	0.0

Atom	x	y	z
1	0.34500	0.14780	0.00000
(0,0,0,1/2)' + set click here to show and hide
2	0.65500	0.14780	0.50000
(1/2,1/2,1/2,0) + set click here to show and hide
3	0.84500	0.64780	0.50000
(1/2,1/2,1/2,1/2)' + set click here to show and hide
4	0.15500	0.64780	0.00000

Atom	x	y	z
1	0.84500	0.35220	0.00000
(0,0,0,1/2)' + set click here to show and hide
2	0.15500	0.35220	0.50000
(1/2,1/2,1/2,0) + set click here to show and hide
3	0.34500	0.85220	0.50000
(1/2,1/2,1/2,1/2)' + set click here to show and hide
4	0.65500	0.85220	0.00000

Atom	x	y	z
1	0.19530	0.89650	0.00000
(0,0,0,1/2)' + set click here to show and hide
2	0.80470	0.89650	0.50000
(1/2,1/2,1/2,0) + set click here to show and hide
3	0.69530	0.39650	0.50000
(1/2,1/2,1/2,1/2)' + set click here to show and hide
4	0.30470	0.39650	0.00000

Atom	x	y	z
1	0.69530	0.60350	0.00000
(0,0,0,1/2)' + set click here to show and hide
2	0.30470	0.60350	0.50000
(1/2,1/2,1/2,0) + set click here to show and hide
3	0.19530	0.10350	0.50000
(1/2,1/2,1/2,1/2)' + set click here to show and hide
4	0.80470	0.10350	0.00000

Reference: A. Bhutani, P. Behera, R.D. McAuliffe, H. Cao, A. Huq, M.J. Kirkham, C.R. dela Cruz, T. Woods and D.P. Shoemaker, Physical Review Materials (2019) 3 064404.
DOI: 10.1103/physrevmaterials.3.064404
Atomic positions from: same reference

Parent space group (paramagnetic phase): Ibam (#72)
Propagation vector: k1 (0.42000, 0.00000, 0.00000)

Transition Temperature: 17 K
Experiment Temperature: 4 K

Lattice parameters of the basic unit cell:
6.93200 12.63600 6.17900 90.00000 90.00000 90.00000
Transformation from parent structure: (a,b,c;0,0,0)
    [View matrix form]

Magnetic Superspace Group: Ic2m1'(a,0,0)000s
    [View symmetry operations]

Magnetic Point Group: m2m1' ()
    [View symmetry operations]
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

     [Show only magnetic atoms]
     [Show all the atoms]

Average atomic positions of symmetry independent atoms

Label	Atom type	x	y	z	Multiplicity
Mn1_1	Mn	0.00000	0.00000	0.25000	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_1	0	M_ycos1	0	0.0	2.279	0.0	M_xsin1	0	M_zsin1	2.279	0.0	0.0

Atom	x	y	z
1	0.00000	0.00000	0.25000
(0,0,0,1/2)' + set click here to show and hide
2	0.00000	0.00000	0.75000
(1/2,1/2,1/2,0) + set click here to show and hide
3	0.50000	0.50000	0.75000
(1/2,1/2,1/2,1/2)' + set click here to show and hide
4	0.50000	0.50000	0.25000

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	2.27900	0.0	M_xsin1	0	M_zsin1	2.27900	0.0	0.0
(0,0,0,1/2)' + set click here to show and hide
2	0	-M_ycos1	0	0.0	-2.27900	0.0	-M_xsin1	0	M_zsin1	-2.27900	0.0	0.0
(1/2,1/2,1/2,0) + set click here to show and hide
3	0	M_ycos1	0	0.0	2.27900	0.0	M_xsin1	0	M_zsin1	2.27900	0.0	0.0
(1/2,1/2,1/2,1/2)' + set click here to show and hide
4	0	-M_ycos1	0	0.0	-2.27900	0.0	-M_xsin1	0	M_zsin1	-2.27900	0.0	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
mSM1	1	2		primary	1
mSM4	1	2	special	primary	2

Comments:

NSD and NPD
The propagation vector is changed to a simpler one but equivalent to the one reported in the original reference.

Comments (symmetry):

1k incommensurate magnetic structure
Two modulations corresponding to two different irreps are combined in quadrature. Two primary irreps are involved and therefore two order parameters can be defined with respect to the paramagnetic phase.
The spin modulation breaks the parent centrosymmetry
Polar structure along b
The magnetic superspace group describing the symmetry of the reported spin modulation allows three free parameters: they allow an elliptical form of the spin rotation and the rotation plane to be oblique with respect to the modulation direction.

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

K₂MnS₂ (#1.1.64)

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

K2MnS2 (#1.1.64)

K₂MnS₂ (#1.1.64)