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+1/2,-1	{ m'₁₀₀ \| 0 0 0 1/2 }
4	x1,x2,-x3+1/2,x4+1/2,-1	{ m'₀₀₁ \| 0 0 1/2 1/2 }
(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	{ 2₀₁₀ \| 1/2 1/2 1/2 0 }
7	-x1+1/2,x2+1/2,x3,-x4+1/2,-1	{ m'₁₀₀ \| 1/2 1/2 0 1/2 }
8	x1+1/2,x2+1/2,-x3+1/2,x4+1/2,-1	{ m'₀₀₁ \| 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	2₀₁₀
3	-x,y,z,-1	m'₁₀₀
4	x,y,-z,-1	m'₀₀₁

Label	Atom type	x	y	z	Multiplicity
S1_1	S	0.00000	0.36100	0.25000	2
S1_2	S	0.00000	0.63900	0.75000	2
O1_1	O	0.00000	0.25500	0.07100	4
O1_2	O	0.00000	0.74500	-0.07100	4
O2_1	O	0.73000	-0.04100	0.25000	4
O2_2	O	0.73000	0.04100	0.75000	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	M_xcos1	0	0	4.70	0.0	0.0	0	M_ysin1	M_zsin1	0.0	4.70	0.0

Atom	x	y	z	Symmetry constraints on M	M_0x	M_0y	M_0z
1	0.00000	0.00000	0.00000	0,m_y,m_z	0.00000	0.00000	1.00000
2	0.00000	0.00000	0.50000	0,m_y,-m_z	0.00000	0.00000	-1.00000
(1/2,1/2,0,0) + set click here to show and hide
3	0.50000	0.50000	0.00000	0,m_y,m_z	0.00000	0.00000	1.00000
4	0.50000	0.50000	0.50000	0,m_y,-m_z	0.00000	0.00000	-1.00000

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	M_xcos1	0	0	4.70000	0.0	0.0	0	M_ysin1	M_zsin1	0.0	4.70000	0.0
2	-M_xcos1	0	0	-4.70000	0.0	0.0	0	-M_ysin1	M_zsin1	0.0	-4.70000	0.0
(1/2,1/2,0,0) + set click here to show and hide
3	M_xcos1	0	0	4.70000	0.0	0.0	0	M_ysin1	M_zsin1	0.0	4.70000	0.0
4	-M_xcos1	0	0	-4.70000	0.0	0.0	0	-M_ysin1	M_zsin1	0.0	-4.70000	0.0

Atom	x	y	z
1	0.00000	0.36100	0.25000
(1/2,1/2,0,0) + set click here to show and hide
2	0.50000	0.86100	0.25000

Atom	x	y	z
1	0.00000	0.63900	0.75000
(1/2,1/2,0,0) + set click here to show and hide
2	0.50000	0.13900	0.75000

Atom	x	y	z
1	0.00000	0.25500	0.07100
2	0.00000	0.25500	0.42900
(1/2,1/2,0,0) + set click here to show and hide
3	0.50000	0.75500	0.07100
4	0.50000	0.75500	0.42900

Atom	x	y	z
1	0.00000	0.74500	0.92900
2	0.00000	0.74500	0.57100
(1/2,1/2,0,0) + set click here to show and hide
3	0.50000	0.24500	0.92900
4	0.50000	0.24500	0.57100

Atom	x	y	z
1	0.73000	0.95900	0.25000
2	0.27000	0.95900	0.25000
(1/2,1/2,0,0) + set click here to show and hide
3	0.23000	0.45900	0.25000
4	0.77000	0.45900	0.25000

Atom	x	y	z
1	0.73000	0.04100	0.75000
2	0.27000	0.04100	0.75000
(1/2,1/2,0,0) + set click here to show and hide
3	0.23000	0.54100	0.75000
4	0.77000	0.54100	0.75000

Reference: G. Will, B. C. Frazer, G. Shirane, D. E. Cox, P. J. Brown, Physical Review (1965) 140 A2139 - A2142
DOI: 10.1103/PhysRev.140.A2139
Atomic positions from: same reference

Parent space group (paramagnetic phase): Cmcm (#63)
Propagation vector: k1 (0.1667, 0.0, 0.0)

Transition Temperature: 7.2 K
Experiment Temperature: 4.2 K

Lattice parameters of the basic unit cell:
5.26000 8.04200 6.84700 90.00000 90.00000 90.00000
Transformation from parent structure: (a,b,c;0,0,0)
    [View matrix form]

Magnetic Superspace Group: Cm'2m'(0,0,g)00s
    [View symmetry operations]

Magnetic Point Group: m'm'2 (7.4.23)
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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 and magnetic moments of symmetry independent atoms

Label	Atom type	x	y	z	Multiplicity	Symmetry constraints on M	M_0x	M_0y	M_0z	\|M\|
Mn1	Mn	0.00000	0.00000	0.00000	4	0,m_y,m_z	0.0	0.0	1.00	1.00

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	M_xcos1	0	0	4.70	0.0	0.0	0	M_ysin1	M_zsin1	0.0	4.70	0.0

Atom	x	y	z	Symmetry constraints on M	M_0x	M_0y	M_0z
1	0.00000	0.00000	0.00000	0,m_y,m_z	0.00000	0.00000	1.00000
2	0.00000	0.00000	0.50000	0,m_y,-m_z	0.00000	0.00000	-1.00000
(1/2,1/2,0,0) + set click here to show and hide
3	0.50000	0.50000	0.00000	0,m_y,m_z	0.00000	0.00000	1.00000
4	0.50000	0.50000	0.50000	0,m_y,-m_z	0.00000	0.00000	-1.00000

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	M_xcos1	0	0	4.70000	0.0	0.0	0	M_ysin1	M_zsin1	0.0	4.70000	0.0
2	-M_xcos1	0	0	-4.70000	0.0	0.0	0	-M_ysin1	M_zsin1	0.0	-4.70000	0.0
(1/2,1/2,0,0) + set click here to show and hide
3	M_xcos1	0	0	4.70000	0.0	0.0	0	M_ysin1	M_zsin1	0.0	4.70000	0.0
4	-M_xcos1	0	0	-4.70000	0.0	0.0	0	-M_ysin1	M_zsin1	0.0	-4.70000	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
mGM4+	1	1		primary	2
mSM1	1	2	general	primary	1
mSM4	1	2	special	primary	2

Comments:

NPD
moment magnitude:4.8
cone half-angle: 78 degrees
k vector approximately (1/6,0,0)

Comments (symmetry):

incommensurate magnetic structure
Simple spin conical modulation, which however from the viewpoint of symmetry and Landau theory requires the superposition of three order parameters transforming according to three different irreps, one with k=0 and two with the incommensurate wave vector. These latter being pi/2 phase shifted with their modulations in quadrature.
The transition temperature is taken from Legrand et al. (Journal of Magnetism and Magnetic Materials 15-18 (1980) 529), where three phase transitions are observed, corresponding to the three distinct irrep orderings, as expected from the Landau theory perspective.
Polar along b. Possible multiferroicity of type II (magnetically induced spontaneous polarization along b)

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

MnSO₄ (#1.1.105)

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

MnSO4 (#1.1.105)

MnSO₄ (#1.1.105)