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+1/2,+1	{ 2₀₁₀ \| 0 0 1/2 1/2 }
(0,0,0,1/2)' + set click here to show and hide
3	x1,x2,x3,x4+1/2,-1	{ 1' \| 0 0 0 1/2 }
4	-x1,x2,-x3+1/2,-x4,-1	{ 2'₀₁₀ \| 0 0 1/2 0 }
(1/2,1/2,0,0) + set click here to show and hide
5	x1+1/2,x2+1/2,x3,x4,+1	{ 1 \| 1/2 1/2 0 0 }
6	-x1+1/2,x2+1/2,-x3+1/2,-x4+1/2,+1	{ 2₀₁₀ \| 1/2 1/2 1/2 1/2 }
(1/2,1/2,0,1/2)' + set click here to show and hide
7	x1+1/2,x2+1/2,x3,x4+1/2,-1	{ 1' \| 1/2 1/2 0 1/2 }
8	-x1+1/2,x2+1/2,-x3+1/2,-x4,-1	{ 2'₀₁₀ \| 1/2 1/2 1/2 0 }

N	(x,y,z)	Seitz notation
1	x,y,z,+1	1
2	-x,y,-z,+1	2₀₁₀
1' + set click here to show and hide
3	x,y,z,-1	1'
4	-x,y,-z,-1	2'₀₁₀

Label	Atom type	x	y	z	Multiplicity
W1_1	W	0.74703	0.59137	0.24675	4
W1_2	W	0.75297	-0.09137	0.75325	4
Li1_1	Li	0.00000	0.84600	0.25000	2
Li1_2	Li	0.00000	0.15400	0.75000	2
O1_1	O	0.86380	0.55980	-0.07550	4
O1_2	O	0.63620	-0.05980	0.07550	4
O2_1	O	0.88010	0.68220	0.41150	4
O2_2	O	0.61990	0.81780	0.58850	4
O3_1	O	0.35620	0.54970	-0.05630	4
O3_2	O	0.14380	-0.04970	0.05630	4
O4_1	O	0.37750	0.69510	0.39330	4
O4_2	O	0.12250	0.80490	0.60670	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
Fe1_1	M_xcos1	0	M_zsin1	5.05(19)	0.0	2.93(27)	0	M_ysin1	0	0.0	4.21(24)	0.0
Fe1_2	M_xcos1	0	M_zcos1	5.05(19)	0.0	2.93(27)	0	M_ysin1	0	0.0	4.21(24)	0.0

Atom	x	y	z
1	0.00000	0.33474	0.25000
(0,0,0,1/2)' + set click here to show and hide
2	0.50000	0.83474	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	M_xcos1	0	M_zsin1	5.05000	0.0	2.93000	0	M_ysin1	0	0.0	4.21000	0.0
(0,0,0,1/2)' + set click here to show and hide
2	M_xcos1	0	M_zsin1	5.05000	0.0	2.93000	0	M_ysin1	0	0.0	4.21000	0.0

Atom	x	y	z
1	0.00000	0.66526	0.75000
(0,0,0,1/2)' + set click here to show and hide
2	0.50000	0.16526	0.75000

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	0	M_zcos1	5.05000	0.0	2.93000	0	M_ysin1	0	0.0	4.21000	0.0
(0,0,0,1/2)' + set click here to show and hide
2	M_xcos1	0	M_zcos1	5.05000	0.0	2.93000	0	M_ysin1	0	0.0	4.21000	0.0

Atom	x	y	z
1	0.74703	0.59137	0.24675
(0,0,0,1/2)' + set click here to show and hide
2	0.25297	0.59137	0.25325
(1/2,1/2,0,0) + set click here to show and hide
3	0.24703	0.09137	0.24675
(1/2,1/2,0,1/2)' + set click here to show and hide
4	0.75297	0.09137	0.25325

Atom	x	y	z
1	0.75297	0.90863	0.75325
(0,0,0,1/2)' + set click here to show and hide
2	0.24703	0.90863	0.74675
(1/2,1/2,0,0) + set click here to show and hide
3	0.25297	0.40863	0.75325
(1/2,1/2,0,1/2)' + set click here to show and hide
4	0.74703	0.40863	0.74675

Atom	x	y	z
1	0.00000	0.84600	0.25000
(0,0,0,1/2)' + set click here to show and hide
2	0.50000	0.34600	0.25000

Atom	x	y	z
1	0.00000	0.15400	0.75000
(0,0,0,1/2)' + set click here to show and hide
2	0.50000	0.65400	0.75000

Atom	x	y	z
1	0.86380	0.55980	0.92450
(0,0,0,1/2)' + set click here to show and hide
2	0.13620	0.55980	0.57550
(1/2,1/2,0,0) + set click here to show and hide
3	0.36380	0.05980	0.92450
(1/2,1/2,0,1/2)' + set click here to show and hide
4	0.63620	0.05980	0.57550

Atom	x	y	z
1	0.63620	0.94020	0.07550
(0,0,0,1/2)' + set click here to show and hide
2	0.36380	0.94020	0.42450
(1/2,1/2,0,0) + set click here to show and hide
3	0.13620	0.44020	0.07550
(1/2,1/2,0,1/2)' + set click here to show and hide
4	0.86380	0.44020	0.42450

Atom	x	y	z
1	0.88010	0.68220	0.41150
(0,0,0,1/2)' + set click here to show and hide
2	0.11990	0.68220	0.08850
(1/2,1/2,0,0) + set click here to show and hide
3	0.38010	0.18220	0.41150
(1/2,1/2,0,1/2)' + set click here to show and hide
4	0.61990	0.18220	0.08850

Atom	x	y	z
1	0.61990	0.81780	0.58850
(0,0,0,1/2)' + set click here to show and hide
2	0.38010	0.81780	0.91150
(1/2,1/2,0,0) + set click here to show and hide
3	0.11990	0.31780	0.58850
(1/2,1/2,0,1/2)' + set click here to show and hide
4	0.88010	0.31780	0.91150

Atom	x	y	z
1	0.35620	0.54970	0.94370
(0,0,0,1/2)' + set click here to show and hide
2	0.64380	0.54970	0.55630
(1/2,1/2,0,0) + set click here to show and hide
3	0.85620	0.04970	0.94370
(1/2,1/2,0,1/2)' + set click here to show and hide
4	0.14380	0.04970	0.55630

Atom	x	y	z
1	0.14380	0.95030	0.05630
(0,0,0,1/2)' + set click here to show and hide
2	0.85620	0.95030	0.44370
(1/2,1/2,0,0) + set click here to show and hide
3	0.64380	0.45030	0.05630
(1/2,1/2,0,1/2)' + set click here to show and hide
4	0.35620	0.45030	0.44370

Atom	x	y	z
1	0.37750	0.69510	0.39330
(0,0,0,1/2)' + set click here to show and hide
2	0.62250	0.69510	0.10670
(1/2,1/2,0,0) + set click here to show and hide
3	0.87750	0.19510	0.39330
(1/2,1/2,0,1/2)' + set click here to show and hide
4	0.12250	0.19510	0.10670

Atom	x	y	z
1	0.12250	0.80490	0.60670
(0,0,0,1/2)' + set click here to show and hide
2	0.87750	0.80490	0.89330
(1/2,1/2,0,0) + set click here to show and hide
3	0.62250	0.30490	0.60670
(1/2,1/2,0,1/2)' + set click here to show and hide
4	0.37750	0.30490	0.89330

Reference: S. Biesenkamp, D. Gorkov, D. Bruning, A. Bertin, T. Frohlich, X. Fabreges, A. Gukasov, M. Meven, P. Becker, L. Bohaty, T. Lorenz, M. Braden, PHYSICAL REVIEW B (2021) 103 134412
DOI: 10.1103/PhysRevB.103.134412
Atomic positions from: same reference

Parent space group (paramagnetic phase): C2/c (#15)
Propagation vector: k1 (0.91000, 0.00000, 0.30000)

Transition Temperature: 19 K
Experiment Temperature: 3 K

Lattice parameters of the basic unit cell:
9.26480 11.38580 4.89180 90.00000 90.40000 90.00000
Transformation from parent structure: (a,b,c;0,0,0)
    [View matrix form]

Magnetic Superspace Group: C21'(a,0,g)0s
    [View symmetry operations]

Magnetic Point Group: 21' (3.2.7)
    [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
Fe1_1	Fe	0.00000	0.33474	0.25000	2
Fe1_2	Fe	0.00000	0.66526	0.75000	2

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
Fe1_1	M_xcos1	0	M_zsin1	5.05(19)	0.0	2.93(27)	0	M_ysin1	0	0.0	4.21(24)	0.0
Fe1_2	M_xcos1	0	M_zcos1	5.05(19)	0.0	2.93(27)	0	M_ysin1	0	0.0	4.21(24)	0.0

Atom	x	y	z
1	0.00000	0.33474	0.25000
(0,0,0,1/2)' + set click here to show and hide
2	0.50000	0.83474	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	M_xcos1	0	M_zsin1	5.05000	0.0	2.93000	0	M_ysin1	0	0.0	4.21000	0.0
(0,0,0,1/2)' + set click here to show and hide
2	M_xcos1	0	M_zsin1	5.05000	0.0	2.93000	0	M_ysin1	0	0.0	4.21000	0.0

Atom	x	y	z
1	0.00000	0.66526	0.75000
(0,0,0,1/2)' + set click here to show and hide
2	0.50000	0.16526	0.75000

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	0	M_zcos1	5.05000	0.0	2.93000	0	M_ysin1	0	0.0	4.21000	0.0
(0,0,0,1/2)' + set click here to show and hide
2	M_xcos1	0	M_zcos1	5.05000	0.0	2.93000	0	M_ysin1	0	0.0	4.21000	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
mB2	1	2	general	primary	3
mB1	1	2	special	primary	3

Comments:

NSD
Position structure from a determination at 37K
Betweem 22.2K and 19K another incommensurate phase with higher centrosymmetric symmetry exists (see #1.1.128)
Polar along b. Type II multiferroic.

Comments (symmetry):

1k incommensurate magnetic structure
Two irreps as primary. One for the mx and mz components, and the other one for the my components. The MSSG (and the combination of the two irreps) allows a much general spin modulation with 6 free parameters instead of 3.
The two irrep modulations combine in quadrature.

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

LiFe(WO₄)₂ (#1.1.129)

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

LiFe(WO4)2 (#1.1.129)

LiFe(WO₄)₂ (#1.1.129)