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,-x4,+1	{ 2₀₁₀ \| 0 }
(0,1/2,0,1/2) + set click here to show and hide
3	x1,x2+1/2,x3,x4+1/2,+1	{ 1 \| 0 1/2 0 1/2 }
4	-x1,x2+1/2,-x3,-x4+1/2,+1	{ 2₀₁₀ \| 0 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,x2,-x3,-x4+1/2,-1	{ 2'₀₁₀ \| 0 0 0 1/2 }
(0,1/2,0,0)' + set click here to show and hide
7	x1,x2+1/2,x3,x4,-1	{ 1' \| 0 1/2 0 0 }
8	-x1,x2+1/2,-x3,-x4,-1	{ 2'₀₁₀ \| 0 1/2 0 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	0.4097	0	2
W1_2	W	0	0.08885	0.5	2
O1_1	O	-0.252	-0.1899	-0.1566	4
O1_2	O	-0.2522	-0.3153	0.3692	4
O2_1	O	-0.2207	0.05105	-0.1815	4
O2_2	O	-0.2009	-0.05125	0.2978	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_yc1	0	0.0	3.6	0.0	M_xs1	0	M_zs1	3.3	0.0	2.2
Mn1_2	0	M_yc1	0	0.0	-2.4	0.0	M_xs1	0	M_zs1	-2.8	0.0	-1.6

Atom	x	y	z
1	0.50000	0.15970	0.00000
(0,1/2,0,1/2) + set click here to show and hide
2	0.50000	0.65970	0.00000

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	3.60000	0.0	M_xcos1+M_ysin1	0	M_zcos1+M_ysin1	3.30000	0.0	2.20000
(0,1/2,0,1/2) + set click here to show and hide
2	0	-M_ycos1	0	0.0	-3.60000	0.0	-M_xcos1-M_ysin1	0	-M_zcos1-M_ysin1	-3.30000	0.0	-2.20000

Atom	x	y	z
1	0.50000	0.34355	0.50000
(0,1/2,0,1/2) + set click here to show and hide
2	0.50000	0.84355	0.50000

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	-2.40000	0.0	M_xcos1+M_ysin1	0	M_zcos1+M_ysin1	-2.80000	0.0	-1.60000
(0,1/2,0,1/2) + set click here to show and hide
2	0	-M_ycos1	0	0.0	2.40000	0.0	-M_xcos1-M_ysin1	0	-M_zcos1-M_ysin1	2.80000	0.0	1.60000

Atom	x	y	z
1	0.00000	0.40970	0.00000
(0,1/2,0,1/2) + set click here to show and hide
2	0.00000	0.90970	0.00000

Atom	x	y	z
1	0.00000	0.08885	0.50000
(0,1/2,0,1/2) + set click here to show and hide
2	0.00000	0.58885	0.50000

Atom	x	y	z
1	0.74800	0.81010	0.84340
2	0.25200	0.81010	0.15660
(0,1/2,0,1/2) + set click here to show and hide
3	0.74800	0.31010	0.84340
4	0.25200	0.31010	0.15660

Atom	x	y	z
1	0.74780	0.68470	0.36920
2	0.25220	0.68470	0.63080
(0,1/2,0,1/2) + set click here to show and hide
3	0.74780	0.18470	0.36920
4	0.25220	0.18470	0.63080

Atom	x	y	z
1	0.77930	0.05105	0.81850
2	0.22070	0.05105	0.18150
(0,1/2,0,1/2) + set click here to show and hide
3	0.77930	0.55105	0.81850
4	0.22070	0.55105	0.18150

Atom	x	y	z
1	0.79910	0.94875	0.29780
2	0.20090	0.94875	0.70220
(0,1/2,0,1/2) + set click here to show and hide
3	0.79910	0.44875	0.29780
4	0.20090	0.44875	0.70220

Reference: S.-H. Park, D. Behal and B. Pedersen, Physica B: Condensed Matter (2018) 551 118-121.
DOI: 10.1016/j.physb.2017.11.034
Atomic positions from: same reference

Parent space group (paramagnetic phase): P2 (#3)
Propagation vector: k1 (-0.2152, 0.000000, 0.455800)

Transition Temperature: 12.5 K
Experiment Temperature: 10 K

Lattice parameters of the basic unit cell:
4.808(1) 11.484(2) 4.979(1) 90 91.03 90
Transformation from parent structure: (a,2b,c;0,0,0)
    [View matrix form]

Magnetic Superspace Group: X21'(a0g)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
Mn1_1	Mn	0.5	0.1597	0	2
Mn1_2	Mn	0.5	0.34355	0.5	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
Mn1_1	0	M_yc1	0	0.0	3.6	0.0	M_xs1	0	M_zs1	3.3	0.0	2.2
Mn1_2	0	M_yc1	0	0.0	-2.4	0.0	M_xs1	0	M_zs1	-2.8	0.0	-1.6

Atom	x	y	z
1	0.50000	0.15970	0.00000
(0,1/2,0,1/2) + set click here to show and hide
2	0.50000	0.65970	0.00000

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	3.60000	0.0	M_xcos1+M_ysin1	0	M_zcos1+M_ysin1	3.30000	0.0	2.20000
(0,1/2,0,1/2) + set click here to show and hide
2	0	-M_ycos1	0	0.0	-3.60000	0.0	-M_xcos1-M_ysin1	0	-M_zcos1-M_ysin1	-3.30000	0.0	-2.20000

Atom	x	y	z
1	0.50000	0.34355	0.50000
(0,1/2,0,1/2) + set click here to show and hide
2	0.50000	0.84355	0.50000

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	-2.40000	0.0	M_xcos1+M_ysin1	0	M_zcos1+M_ysin1	-2.80000	0.0	-1.60000
(0,1/2,0,1/2) + set click here to show and hide
2	0	-M_ycos1	0	0.0	2.40000	0.0	-M_xcos1-M_ysin1	0	-M_zcos1-M_ysin1	2.80000	0.0	1.60000

[Show all magnetic atoms in unit cell and their moment relations]

Active Irreps:

label	dim. small irrep	dim. full irrep	direction	action
mG1	1	2	general	primary

Comments:

Phase AF2
Phase AF3 between 13.5K and 12.5K
Phase AF1 below 6.5K
Multiferroic. Electric polarization along b
This model considers a basic average structure with space group P2, with the polarity already present in the parent paramagnetic structure.

Comments (symmetry):

1k incommensurate magnetic structure
With respect to the parent unit cell, the propagation vector is of type (a,1/2,g). The used basic structure is doubled along y, in order to simplify the description, with a wave vector of type (a,0,g) and a centering (0,1/2,0,1/2).
A single irrep exists for the assumed parent space group, which results in a single possible MSSG.
See #1.1.11 for a different model of this structure with its symmetry given by the same MSSG. The choice of origin is different in the two models (origin shift (0 0 1/4) ).

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

MnWO₄ (#1.1.95)

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

MnWO4 (#1.1.95)

MnWO₄ (#1.1.95)