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+1/2,+1	{ 2₀₁₀ \| 0 0 0 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,x4,-1	{ 2'₀₁₀ \| 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,x4+1/2,+1	{ 2₀₁₀ \| 1/2 1/2 0 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,x4,-1	{ 2'₀₁₀ \| 1/2 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	z	Multiplicity
Bi1	Bi	0.21400	0.36400	4
Bi2	Bi	0.35300	0.13800	4
Se1	Se	0.66000	0.04200	4
Se2	Se	0.01100	0.17200	4
Se3	Se	0.60200	0.44200	4
Se4	Se	0.82000	0.31400	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	M_zcos1	3.83	0.0	1.67	M_xsin1	0	M_zsin1	0.0	0.0	-3.45(14)
Mn2	M_xcos1	0	M_zcos1	3.83	0.0	1.67	M_xsin1	0	M_zsin1	0.0	0.0	-3.45(14)

Atom	x	y	z
1	0.00000	0.00000	0.50000
(0,0,0,1/2)' + set click here to show and hide
2	0.50000	0.50000	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	M_zcos1	3.83000	0.0	1.67000	M_xsin1	0	M_zsin1	0.0	0.0	-3.45000
(0,0,0,1/2)' + set click here to show and hide
2	M_xcos1	0	M_zcos1	3.83000	0.0	1.67000	M_xsin1	0	M_zsin1	0.0	0.0	-3.45000

Atom	x	y	z
1	0.00000	0.00000	0.00000
(0,0,0,1/2)' + set click here to show and hide
2	0.50000	0.50000	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	M_xcos1	0	M_zcos1	3.83000	0.0	1.67000	M_xsin1	0	M_zsin1	0.0	0.0	-3.45000
(0,0,0,1/2)' + set click here to show and hide
2	M_xcos1	0	M_zcos1	3.83000	0.0	1.67000	M_xsin1	0	M_zsin1	0.0	0.0	-3.45000

Atom	x	y	z
1	0.21400	0.00000	0.36400
(0,0,0,1/2)' + set click here to show and hide
2	0.78600	0.00000	0.63600
(1/2,1/2,0,0) + set click here to show and hide
3	0.71400	0.50000	0.36400
(1/2,1/2,0,1/2)' + set click here to show and hide
4	0.28600	0.50000	0.63600

Atom	x	y	z
1	0.35300	0.00000	0.13800
(0,0,0,1/2)' + set click here to show and hide
2	0.64700	0.00000	0.86200
(1/2,1/2,0,0) + set click here to show and hide
3	0.85300	0.50000	0.13800
(1/2,1/2,0,1/2)' + set click here to show and hide
4	0.14700	0.50000	0.86200

Atom	x	y	z
1	0.66000	0.00000	0.04200
(0,0,0,1/2)' + set click here to show and hide
2	0.34000	0.00000	0.95800
(1/2,1/2,0,0) + set click here to show and hide
3	0.16000	0.50000	0.04200
(1/2,1/2,0,1/2)' + set click here to show and hide
4	0.84000	0.50000	0.95800

Atom	x	y	z
1	0.01100	0.00000	0.17200
(0,0,0,1/2)' + set click here to show and hide
2	0.98900	0.00000	0.82800
(1/2,1/2,0,0) + set click here to show and hide
3	0.51100	0.50000	0.17200
(1/2,1/2,0,1/2)' + set click here to show and hide
4	0.48900	0.50000	0.82800

Atom	x	y	z
1	0.60200	0.00000	0.44200
(0,0,0,1/2)' + set click here to show and hide
2	0.39800	0.00000	0.55800
(1/2,1/2,0,0) + set click here to show and hide
3	0.10200	0.50000	0.44200
(1/2,1/2,0,1/2)' + set click here to show and hide
4	0.89800	0.50000	0.55800

Atom	x	y	z
1	0.82000	0.00000	0.31400
(0,0,0,1/2)' + set click here to show and hide
2	0.18000	0.00000	0.68600
(1/2,1/2,0,0) + set click here to show and hide
3	0.32000	0.50000	0.31400
(1/2,1/2,0,1/2)' + set click here to show and hide
4	0.68000	0.50000	0.68600

Reference: J. K. Clark, C. Pak, H. Cao, M. Shatruk, Crystals (2021) 11 242
DOI: 10.3390/cryst11030242
Atomic positions from: ICSD #603311

Parent space group (paramagnetic phase): C2/m (#12)
Propagation vector: k1 (0.00000, 0.35600, 0.00000)

Transition Temperature: 15 K
Experiment Temperature: 4.2 K

Lattice parameters of the basic unit cell:
13.35700 4.07300 15.30100 90.00000 115.89000 90.00000
Transformation from parent structure: (a,b,c;0,0,0)
    [View matrix form]

Magnetic Superspace Group: C21'(0,b,0)ss
    [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	Mn	0.00000	0.00000	0.50000	2
Mn2	Mn	0.00000	0.00000	0.00000	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	M_xcos1	0	M_zcos1	3.83	0.0	1.67	M_xsin1	0	M_zsin1	0.0	0.0	-3.45(14)
Mn2	M_xcos1	0	M_zcos1	3.83	0.0	1.67	M_xsin1	0	M_zsin1	0.0	0.0	-3.45(14)

Atom	x	y	z
1	0.00000	0.00000	0.50000
(0,0,0,1/2)' + set click here to show and hide
2	0.50000	0.50000	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	M_zcos1	3.83000	0.0	1.67000	M_xsin1	0	M_zsin1	0.0	0.0	-3.45000
(0,0,0,1/2)' + set click here to show and hide
2	M_xcos1	0	M_zcos1	3.83000	0.0	1.67000	M_xsin1	0	M_zsin1	0.0	0.0	-3.45000

Atom	x	y	z
1	0.00000	0.00000	0.00000
(0,0,0,1/2)' + set click here to show and hide
2	0.50000	0.50000	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	M_xcos1	0	M_zcos1	3.83000	0.0	1.67000	M_xsin1	0	M_zsin1	0.0	0.0	-3.45000
(0,0,0,1/2)' + set click here to show and hide
2	M_xcos1	0	M_zcos1	3.83000	0.0	1.67000	M_xsin1	0	M_zsin1	0.0	0.0	-3.45000

[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
mLD2	1	2	general	primary	2
mLD2	1	2	general	primary	2

Comments:

NSD
The two independent Mn sites have been constrained, beyond the symmetry requirements, to have equal spin modulations and to be in phase.
Position structure is not provided. Here a model at room temperature retrieved from the ICSD database is used.

Comments (symmetry):

1k incommensurate magnetic structure
The helicoidal arrangement of this model requires the superposition of two modulations according to the same irrep mLD2, but phase shifted, which decreases the symmetry of the resulting MSSG. In the sense of Landau theory, two order parameters are present. The circular rotation of the moments assumed in the refined model requires a shift in quadrature of the two modulations, but this shift value is not symmetry protected, and more general modulations are possible under the same MSSG.
The modulation breaks the inversion symmetry and the structure is polar along b
The MSSG does not contain any operation transforming k into -k, and therefore the origin along x4 is fixed by the arbitrary choice of the initial phase of one of the spin modulations.

Bilbao Crystallographic Server
http://www.cryst.ehu.es

For comments, please mail to
cryst@wm.lc.ehu.es

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

MnBi₂Se₄ (#1.1.138)

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

MnBi2Se4 (#1.1.138)

MnBi₂Se₄ (#1.1.138)