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	-x2+1/3,-x1+2/3,x3+1/6,-x4,+1	{ m₁₁₀ \| 1/3 2/3 1/6 0 }
(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	-x2+1/3,-x1+2/3,x3+1/6,-x4+1/2,-1	{ m'₁₁₀ \| 1/3 2/3 1/6 1/2 }
(1/3,2/3,2/3,0) + set click here to show and hide
5	x1+1/3,x2+2/3,x3+2/3,x4,+1	{ 1 \| 1/3 2/3 2/3 0 }
6	-x2+2/3,-x1+1/3,x3+5/6,-x4,+1	{ m₁₁₀ \| 2/3 1/3 5/6 0 }
(1/3,2/3,2/3,1/2)' + set click here to show and hide
7	x1+1/3,x2+2/3,x3+2/3,x4+1/2,-1	{ 1' \| 1/3 2/3 2/3 1/2 }
8	-x2+2/3,-x1+1/3,x3+5/6,-x4+1/2,-1	{ m'₁₁₀ \| 2/3 1/3 5/6 1/2 }
(2/3,1/3,1/3,0) + set click here to show and hide
9	x1+2/3,x2+1/3,x3+1/3,x4,+1	{ 1 \| 2/3 1/3 1/3 0 }
10	-x2,-x1,x3+1/2,-x4,+1	{ m₁₁₀ \| 0 0 1/2 0 }
(2/3,1/3,1/3,1/2)' + set click here to show and hide
11	x1+2/3,x2+1/3,x3+1/3,x4+1/2,-1	{ 1' \| 2/3 1/3 1/3 1/2 }
12	-x2,-x1,x3+1/2,-x4+1/2,-1	{ m'₁₁₀ \| 0 0 1/2 1/2 }

N	(x,y,z)	Seitz notation
1	x,y,z,+1	1
2	-y,-x,z,+1	m₁₁₀
1' + set click here to show and hide
3	x,y,z,-1	1'
4	-y,-x,z,-1	m'₁₁₀

Label	Atom type	x	y	z	Multiplicity
Bi1_1	Bi	0.00000	0.00000	0.7792	6
O1_1	O	0.44730	0.01980	0.7317	6
O1_2	O	0.98020	0.42750	0.7317	6
O1_3	O	0.57250	0.55270	0.7317	6

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	M_ycos1	M_zcos1	0.0	0.0	-4.0	M_xsin1	M_ysin1	M_zsin1	-4.0	-4.0	0.0

Atom	x	y	z
1	0.00000	0.00000	0.00000
(0,0,0,1/2)' + set click here to show and hide
2	0.33333	0.66667	0.16667
(1/3,2/3,2/3,0) + set click here to show and hide
3	0.33333	0.66667	0.66667
(1/3,2/3,2/3,1/2)' + set click here to show and hide
4	0.66667	0.33333	0.83333
(2/3,1/3,1/3,0) + set click here to show and hide
5	0.66667	0.33333	0.33333
(2/3,1/3,1/3,1/2)' + set click here to show and hide
6	0.00000	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	M_ycos1	M_zcos1	0.0	0.0	-4.00000	M_xsin1	M_ysin1	M_zsin1	-4.00000	-4.00000	0.0
(0,0,0,1/2)' + set click here to show and hide
2	M_ycos1	M_xcos1	-M_zcos1	0.0	0.0	4.00000	-M_ysin1	-M_xsin1	M_zsin1	4.00000	4.00000	0.0
(1/3,2/3,2/3,0) + set click here to show and hide
3	M_xcos1	M_ycos1	M_zcos1	0.0	0.0	-4.00000	M_xsin1	M_ysin1	M_zsin1	-4.00000	-4.00000	0.0
(1/3,2/3,2/3,1/2)' + set click here to show and hide
4	M_ycos1	M_xcos1	-M_zcos1	0.0	0.0	4.00000	-M_ysin1	-M_xsin1	M_zsin1	4.00000	4.00000	0.0
(2/3,1/3,1/3,0) + set click here to show and hide
5	M_xcos1	M_ycos1	M_zcos1	0.0	0.0	-4.00000	M_xsin1	M_ysin1	M_zsin1	-4.00000	-4.00000	0.0
(2/3,1/3,1/3,1/2)' + set click here to show and hide
6	M_ycos1	M_xcos1	-M_zcos1	0.0	0.0	4.00000	-M_ysin1	-M_xsin1	M_zsin1	4.00000	4.00000	0.0

Atom	x	y	z
1	0.00000	0.00000	0.77920
(0,0,0,1/2)' + set click here to show and hide
2	0.33333	0.66667	0.94587
(1/3,2/3,2/3,0) + set click here to show and hide
3	0.33333	0.66667	0.44587
(1/3,2/3,2/3,1/2)' + set click here to show and hide
4	0.66667	0.33333	0.61253
(2/3,1/3,1/3,0) + set click here to show and hide
5	0.66667	0.33333	0.11253
(2/3,1/3,1/3,1/2)' + set click here to show and hide
6	0.00000	0.00000	0.27920

Atom	x	y	z
1	0.44730	0.01980	0.73170
(0,0,0,1/2)' + set click here to show and hide
2	0.31353	0.21937	0.89837
(1/3,2/3,2/3,0) + set click here to show and hide
3	0.78063	0.68647	0.39837
(1/3,2/3,2/3,1/2)' + set click here to show and hide
4	0.64687	0.88603	0.56503
(2/3,1/3,1/3,0) + set click here to show and hide
5	0.11397	0.35313	0.06503
(2/3,1/3,1/3,1/2)' + set click here to show and hide
6	0.98020	0.55270	0.23170

Atom	x	y	z
1	0.98020	0.42750	0.73170
(0,0,0,1/2)' + set click here to show and hide
2	0.90583	0.68647	0.89837
(1/3,2/3,2/3,0) + set click here to show and hide
3	0.31353	0.09417	0.39837
(1/3,2/3,2/3,1/2)' + set click here to show and hide
4	0.23917	0.35313	0.56503
(2/3,1/3,1/3,0) + set click here to show and hide
5	0.64687	0.76083	0.06503
(2/3,1/3,1/3,1/2)' + set click here to show and hide
6	0.57250	0.01980	0.23170

Atom	x	y	z
1	0.57250	0.55270	0.73170
(0,0,0,1/2)' + set click here to show and hide
2	0.78063	0.09417	0.89837
(1/3,2/3,2/3,0) + set click here to show and hide
3	0.90583	0.21937	0.39837
(1/3,2/3,2/3,1/2)' + set click here to show and hide
4	0.11397	0.76083	0.56503
(2/3,1/3,1/3,0) + set click here to show and hide
5	0.23917	0.88603	0.06503
(2/3,1/3,1/3,1/2)' + set click here to show and hide
6	0.44730	0.42750	0.23170

Reference: I Sosnowska, T P Neumaier, E Steichele, J. Phys. C: Solid State Phys. (1982) 15 4835 - 4846
DOI: 10.1088/0022-3719/15/23/020
Atomic positions from: ICSD #75324

Parent space group (paramagnetic phase): R3c (#161)
Propagation vector: k1 (0.0045, 0.0045, 0.00000)

Transition Temperature: 643 K
Experiment Temperature: 293 K

Lattice parameters of the basic unit cell:
5.57750 5.57750 13.86160 90.00000 90.00000 120.00000
Transformation from parent structure: (a,b,c;0,0,0)
    [View matrix form]

Magnetic Superspace Group: Cc1'(0,0,g)0s
    [View symmetry operations]

Magnetic Point Group: m1' (4.2.10)
    [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	0.00000	0.0000	6

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	M_ycos1	M_zcos1	0.0	0.0	-4.0	M_xsin1	M_ysin1	M_zsin1	-4.0	-4.0	0.0

Atom	x	y	z
1	0.00000	0.00000	0.00000
(0,0,0,1/2)' + set click here to show and hide
2	0.33333	0.66667	0.16667
(1/3,2/3,2/3,0) + set click here to show and hide
3	0.33333	0.66667	0.66667
(1/3,2/3,2/3,1/2)' + set click here to show and hide
4	0.66667	0.33333	0.83333
(2/3,1/3,1/3,0) + set click here to show and hide
5	0.66667	0.33333	0.33333
(2/3,1/3,1/3,1/2)' + set click here to show and hide
6	0.00000	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	M_ycos1	M_zcos1	0.0	0.0	-4.00000	M_xsin1	M_ysin1	M_zsin1	-4.00000	-4.00000	0.0
(0,0,0,1/2)' + set click here to show and hide
2	M_ycos1	M_xcos1	-M_zcos1	0.0	0.0	4.00000	-M_ysin1	-M_xsin1	M_zsin1	4.00000	4.00000	0.0
(1/3,2/3,2/3,0) + set click here to show and hide
3	M_xcos1	M_ycos1	M_zcos1	0.0	0.0	-4.00000	M_xsin1	M_ysin1	M_zsin1	-4.00000	-4.00000	0.0
(1/3,2/3,2/3,1/2)' + set click here to show and hide
4	M_ycos1	M_xcos1	-M_zcos1	0.0	0.0	4.00000	-M_ysin1	-M_xsin1	M_zsin1	4.00000	4.00000	0.0
(2/3,1/3,1/3,0) + set click here to show and hide
5	M_xcos1	M_ycos1	M_zcos1	0.0	0.0	-4.00000	M_xsin1	M_ysin1	M_zsin1	-4.00000	-4.00000	0.0
(2/3,1/3,1/3,1/2)' + set click here to show and hide
6	M_ycos1	M_xcos1	-M_zcos1	0.0	0.0	4.00000	-M_ysin1	-M_xsin1	M_zsin1	4.00000	4.00000	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	6	general	primary	6

Comments:

NPD
Position structure from a different paper
Moment magnitude was not adjusted. It was assumed 4 muB
Very long period modulation

Comments (symmetry):

1k incommensurate magnetic structur
2-dim extended (k,-k) small irrep as primary.
The irrep star has three (k,-k) pairs. Possible multi-k modulations involving more than one pair were not considered.
Polar on the plane perpendicular to the propagation vector

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

BiFeO₃ (#1.1.110)

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

BiFeO3 (#1.1.110)

BiFeO₃ (#1.1.110)