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	{ 2₁₀₀ \| 0 }
3	x1,x2+1/2,-x3,x4,+1	{ m₀₀₁ \| 0 1/2 0 0 }
4	x1,-x2+1/2,x3,-x4,+1	{ m₀₁₀ \| 0 1/2 0 0 }
(1/2,1/2,1/2,0) + set click here to show and hide
5	x1+1/2,x2+1/2,x3+1/2,x4,+1	{ 1 \| 1/2 1/2 1/2 0 }
6	x1+1/2,-x2+1/2,-x3+1/2,-x4,+1	{ 2₁₀₀ \| 1/2 1/2 1/2 0 }
7	x1+1/2,x2,-x3+1/2,x4,+1	{ m₀₀₁ \| 1/2 0 1/2 0 }
8	x1+1/2,-x2,x3+1/2,-x4,+1	{ m₀₁₀ \| 1/2 0 1/2 0 }
(0,0,0,1/2)' + set click here to show and hide
9	x1,x2,x3,x4+1/2,-1	{ 1' \| 0 0 0 1/2 }
10	x1,-x2,-x3,-x4+1/2,-1	{ 2'₁₀₀ \| 0 0 0 1/2 }
11	x1,x2+1/2,-x3,x4+1/2,-1	{ m'₀₀₁ \| 0 1/2 0 1/2 }
12	x1,-x2+1/2,x3,-x4+1/2,-1	{ m'₀₁₀ \| 0 1/2 0 1/2 }
(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+1/2,-x4+1/2,-1	{ 2'₁₀₀ \| 1/2 1/2 1/2 1/2 }
15	x1+1/2,x2,-x3+1/2,x4+1/2,-1	{ m'₀₀₁ \| 1/2 0 1/2 1/2 }
16	x1+1/2,-x2,x3+1/2,-x4+1/2,-1	{ m'₀₁₀ \| 1/2 0 1/2 1/2 }

N	(x,y,z)	Seitz notation
1	x,y,z,+1	1
2	x,-y,-z,+1	2₁₀₀
3	x,y,-z,+1	m₀₀₁
4	x,-y,z,+1	m₀₁₀
1' + set click here to show and hide
5	x,y,z,-1	1'
6	x,-y,-z,-1	2'₁₀₀
7	x,y,-z,-1	m'₀₀₁
8	x,-y,z,-1	m'₀₁₀

Label	Atom type	x	y	z	Multiplicity
Li1	Li	0.25	0.25	0.75	4
V1	V	0	0.25	0.391(4)	4
O1	O	0	0.0155(4)	0.2742(5)	8
O2	O	0.2359(6)	0.25	-0.0012(2)	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
Cu1	M_xcos1	0	0	0.31	0.0	0.0	0	M_ysin1	M_zsin1	0.0	0.31	0.0

Atom	x	y	z
1	0.00000	0.00000	0.00000
2	0.00000	0.50000	0.00000
(1/2,1/2,1/2,0) + set click here to show and hide
3	0.50000	0.50000	0.50000
4	0.50000	0.00000	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	M_xcos1	0	0	0.31000	0.0	0.0	0	M_ysin1	M_zsin1	0.0	0.31000	0.0
2	-M_xcos1	0	0	-0.31000	0.0	0.0	0	-M_ysin1	M_zsin1	0.0	-0.31000	0.0
(1/2,1/2,1/2,0) + set click here to show and hide
3	M_xcos1	0	0	0.31000	0.0	0.0	0	M_ysin1	M_zsin1	0.0	0.31000	0.0
4	-M_xcos1	0	0	-0.31000	0.0	0.0	0	-M_ysin1	M_zsin1	0.0	-0.31000	0.0

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

Atom	x	y	z
1	0.00000	0.25000	0.39100
2	0.00000	0.75000	0.60900
(1/2,1/2,1/2,0) + set click here to show and hide
3	0.50000	0.75000	0.89100
4	0.50000	0.25000	0.10900

Atom	x	y	z
1	0.00000	0.01550	0.27420
2	0.00000	0.98450	0.72580
3	0.00000	0.51550	0.72580
4	0.00000	0.48450	0.27420
(1/2,1/2,1/2,0) + set click here to show and hide
5	0.50000	0.51550	0.77420
6	0.50000	0.48450	0.22580
7	0.50000	0.01550	0.22580
8	0.50000	0.98450	0.77420

Atom	x	y	z
1	0.23590	0.25000	0.99880
2	0.23590	0.75000	0.00120
(1/2,1/2,1/2,0) + set click here to show and hide
3	0.73590	0.75000	0.49880
4	0.73590	0.25000	0.50120

Reference: B. Gibson, R. Kremer, A. Prokofiev, W. Assmus and G. McIntyre, Physica B: Condensed Matter (2004) 350 E253-E256.
DOI: 10.1016/j.physb.2004.03.064
Atomic positions from: ICSD #261517

Parent space group (paramagnetic phase): Imma (#74)
Propagation vector: k1 (0.000000, 0.532000, 0.000000)

Transition Temperature: 2.1 K
Experiment Temperature: 1.6 K

Lattice parameters of the basic unit cell:
5.6477(9) 5.7864(9) 8.6940(13) 90 90 90
Transformation from parent structure: (a,b,c;0,0,0)
    [View matrix form]

Magnetic Superspace Group: I2mb1'(0β0)000s
    [View symmetry operations]

Magnetic Point Group: mm21' (7.2.21)
    [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

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     [Show all the atoms]

Average atomic positions of symmetry independent atoms

Label	Atom type	x	y	z	Multiplicity
Cu1	Cu	0	0	0	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
Cu1	M_xcos1	0	0	0.31	0.0	0.0	0	M_ysin1	M_zsin1	0.0	0.31	0.0

Atom	x	y	z
1	0.00000	0.00000	0.00000
2	0.00000	0.50000	0.00000
(1/2,1/2,1/2,0) + set click here to show and hide
3	0.50000	0.50000	0.50000
4	0.50000	0.00000	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	M_xcos1	0	0	0.31000	0.0	0.0	0	M_ysin1	M_zsin1	0.0	0.31000	0.0
2	-M_xcos1	0	0	-0.31000	0.0	0.0	0	-M_ysin1	M_zsin1	0.0	-0.31000	0.0
(1/2,1/2,1/2,0) + set click here to show and hide
3	M_xcos1	0	0	0.31000	0.0	0.0	0	M_ysin1	M_zsin1	0.0	0.31000	0.0
4	-M_xcos1	0	0	-0.31000	0.0	0.0	0	-M_ysin1	M_zsin1	0.0	-0.31000	0.0

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

Active Irreps:

label	dim. small irrep	dim. full irrep	action	number of modes
mDT1	1	2	primary	1
mDT4	1	2	primary	2

Comments:

Comments (symmetry):

1k incommensurate structure
Two irreps active. They superpose with a relative shift of pi/2
The plane of rotation of the spins along b is not symmetry forced to lie on the ab plane. The rotation plane is symmetry allowed to be oblique, but necessarily containing the a direction.
The circular form of the spin orbit is not symmetry dictated, and a more general elliptical form is allowed by the MSSG.
The magnetic order breaks the parent point group symmetry and the resulting point group symmetry is polar along a. Magnetic induced electric polarization along x is therefore expected, in agreement with experimental reports.
Multiferroic of type II
Domains related by the lost inversion have opposite chirality for the spin rotations. One has been chosen arbitrarily.

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

LiCuVO₄ (#1.1.45)

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

LiCuVO4 (#1.1.45)

LiCuVO₄ (#1.1.45)