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	{ 2₀₀₁ \| 0 0 1/2 0 }
3	-x1,x2+1/2,-x3+1/2,x4+1/2,+1	{ 2₀₁₀ \| 0 1/2 1/2 1/2 }
4	x1,-x2+1/2,-x3,-x4+1/2,+1	{ 2₁₀₀ \| 0 1/2 0 1/2 }
5	x1,x2,x3,x4+1/2,-1	{ 1' \| 0 0 0 1/2 }
6	-x1,-x2,x3+1/2,-x4+1/2,-1	{ 2'₀₀₁ \| 0 0 1/2 1/2 }
7	-x1,x2+1/2,-x3+1/2,x4,-1	{ 2'₀₁₀ \| 0 1/2 1/2 0 }
8	x1,-x2+1/2,-x3,-x4,-1	{ 2'₁₀₀ \| 0 1/2 0 0 }
9	x1,x2,x3,x4+1/2,-1	{ 1' \| 0 0 0 1/2 }
10	-x1,-x2,x3+1/2,-x4+1/2,-1	{ 2'₀₀₁ \| 0 0 1/2 1/2 }
11	-x1,x2+1/2,-x3+1/2,x4,-1	{ 2'₀₁₀ \| 0 1/2 1/2 0 }
12	x1,-x2+1/2,-x3,-x4,-1	{ 2'₁₀₀ \| 0 1/2 0 0 }
13	x1,x2,x3,x4,+1	{ 1 \| 0 }
14	-x1,-x2,x3+1/2,-x4,+1	{ 2₀₀₁ \| 0 0 1/2 0 }
15	-x1,x2+1/2,-x3+1/2,x4+1/2,+1	{ 2₀₁₀ \| 0 1/2 1/2 1/2 }
16	x1,-x2+1/2,-x3,-x4+1/2,+1	{ 2₁₀₀ \| 0 1/2 0 1/2 }

N	(x,y,z)	Seitz notation
1	x,y,z,+1	1
2	-x,-y,z,+1	2₀₀₁
3	-x,y,-z,+1	2₀₁₀
4	x,-y,-z,+1	2₁₀₀
1' + set click here to show and hide
5	x,y,z,-1	1'
6	-x,-y,z,-1	2'₀₀₁
7	-x,y,-z,-1	2'₀₁₀
8	x,-y,-z,-1	2'₁₀₀

Label	Atom type	x	y	z	Occupancy	Multiplicity
Bi1	Bi	0.9711(3)	-0.1301(2)	0.751(1)	1	4
Mn1_1	Mn	0.486	-0.160	-0.607	0.3	4
Mn1_2	Mn	-0.488	0.160	0.607	0.3	4
Mn2	Mn	0.000	0.000	0.500	0.4	4
O1_1	O	0.157(3)	0.439(3)	-0.6349(9)	1	4
O1_2	O	-0.162(3)	-0.441(3)	0.6386(9)	1	4
O2_1	O	0.672(2)	-0.408(2)	-0.5783(9)	1	4
O2_2	O	-0.660(2)	-0.593(2)	0.5746(9)	1	4
O3_1	O	0.787(3)	0.25	0.5	1	2
O3_2	O	âˆ’0.799(3)	0.75	0.5	1	1
O4	O	0.3444(6)	âˆ’0.3044(4)	0.753(1)	1	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_y_xc1	M_zcos1	3.25(2)	0.0	-1.94	M_xsin1	M_ysin1	M_zsin1	1.94(2)	0.0	3.25
Fe1_2	M_xcos1	m_y_xc1	M_zcos1	3.25	0.0	1.94	M_xsin1	M_ysin1	M_zsin1	-1.94	0.0	3.25
Fe2	m_y_xc1	m_y_xc1	M_zcos1	3.98(3)	0.0	0.0	M_ysin1	M_ysin1	M_zsin1	0.0	0.0	3.98

Atom	x	y	z
1	0.48600	0.84000	0.39300
2	0.51400	0.16000	0.89300
3	0.51400	0.34000	0.10700
4	0.48600	0.66000	0.60700

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_xcos1+M_ycos1	M_zcos1	3.25000	0.0	-1.94000	M_xsin1	M_ysin1	M_zsin1	1.94000	0.0	3.25000
2	-M_xcos1	-M_xcos1-M_ycos1	M_zcos1	-3.25000	0.0	-1.94000	M_xsin1	M_ysin1	-M_zsin1	1.94000	0.0	-3.25000
3	M_xcos1	-M_xcos1-M_ycos1	M_zcos1	3.25000	0.0	-1.94000	M_xsin1	-M_ysin1	M_zsin1	1.94000	0.0	3.25000
4	-M_xcos1	M_xcos1+M_ycos1	M_zcos1	-3.25000	0.0	-1.94000	M_xsin1	-M_ysin1	-M_zsin1	1.94000	0.0	-3.25000

Atom	x	y	z
1	0.51200	0.16000	0.60700
2	0.48800	0.84000	0.10700
3	0.48800	0.66000	0.89300
4	0.51200	0.34000	0.39300

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_xcos1+M_ycos1	M_zcos1	3.25000	0.0	1.94000	M_xsin1	M_ysin1	M_zsin1	-1.94000	0.0	3.25000
2	-M_xcos1	-M_xcos1-M_ycos1	M_zcos1	-3.25000	0.0	1.94000	M_xsin1	M_ysin1	-M_zsin1	-1.94000	0.0	-3.25000
3	M_xcos1	-M_xcos1-M_ycos1	M_zcos1	3.25000	0.0	1.94000	M_xsin1	-M_ysin1	M_zsin1	-1.94000	0.0	3.25000
4	-M_xcos1	M_xcos1+M_ycos1	M_zcos1	-3.25000	0.0	1.94000	M_xsin1	-M_ysin1	-M_zsin1	-1.94000	0.0	-3.25000

Atom	y	z
1	0.00000	0.50000
2	0.00000	0.00000
3	0.50000	0.00000
4	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+M_ycos1	M_xcos1+M_ycos1	M_zcos1	3.98000	0.0	0.0	M_ysin1	M_ysin1	M_zsin1	0.0	0.0	3.98000
2	-M_xcos1-M_ycos1	-M_xcos1-M_ycos1	M_zcos1	-3.98000	0.0	0.0	M_ysin1	M_ysin1	-M_zsin1	0.0	0.0	-3.98000
3	M_xcos1+M_ycos1	-M_xcos1-M_ycos1	M_zcos1	3.98000	0.0	0.0	M_ysin1	-M_ysin1	M_zsin1	0.0	0.0	3.98000
4	-M_xcos1-M_ycos1	M_xcos1+M_ycos1	M_zcos1	-3.98000	0.0	0.0	M_ysin1	-M_ysin1	-M_zsin1	0.0	0.0	-3.98000

Atom	x	y	z
1	0.97110	0.86990	0.75100
2	0.02890	0.13010	0.25100
3	0.02890	0.36990	0.74900
4	0.97110	0.63010	0.24900

Atom	x	y	z
1	0.48600	0.84000	0.39300
2	0.51400	0.16000	0.89300
3	0.51400	0.34000	0.10700
4	0.48600	0.66000	0.60700

Atom	x	y	z
1	0.51200	0.16000	0.60700
2	0.48800	0.84000	0.10700
3	0.48800	0.66000	0.89300
4	0.51200	0.34000	0.39300

Atom	y	z
1	0.00000	0.50000
2	0.00000	0.00000
3	0.50000	0.00000
4	0.50000	0.50000

Atom	x	y	z
1	0.15700	0.43900	0.36510
2	0.84300	0.56100	0.86510
3	0.84300	0.93900	0.13490
4	0.15700	0.06100	0.63490

Atom	x	y	z
1	0.83800	0.55900	0.63860
2	0.16200	0.44100	0.13860
3	0.16200	0.05900	0.86140
4	0.83800	0.94100	0.36140

Atom	x	y	z
1	0.67200	0.59200	0.42170
2	0.32800	0.40800	0.92170
3	0.32800	0.09200	0.07830
4	0.67200	0.90800	0.57830

Atom	x	y	z
1	0.34000	0.40700	0.57460
2	0.66000	0.59300	0.07460
3	0.66000	0.90700	0.92540
4	0.34000	0.09300	0.42540

Atom	x	y	z
1	0.78700	0.25000	0.50000
2	0.21300	0.75000	0.00000

Atom	x	y	z
1

Atom	x	y	z
1

Reference: A.M. Abakumov, A.A. Tsirlin, J.M. Perez-Mato, V. PetriÄek, H. Rosner, T. Yang and M. Greenblatt, Physical Review B (2011) 83 214402.
DOI: 10.1103/physrevb.83.214402
Atomic positions from: same reference

Parent space group (paramagnetic phase): Pbcm (#57)
Propagation vector: k1 (0.000000, 0.13801(8), 0.000000)

Transition Temperature: 220 K
Experiment Temperature: 7 K

Lattice parameters of the basic unit cell:
5.02305(7) 7.06232(9) 12.6424(2) 90 90 90
Transformation from parent structure: (a,b,c;0,0,0)
    [View matrix form]

Magnetic Superspace Group: P22_12_11'(0b0)0s0s
    [View symmetry operations]

Magnetic Point Group: 2221' (6.2.18)
    [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	Occupancy	Multiplicity
Fe1_1	Fe	0.486(3)	-0.160(2)	-0.607(1)	0.7	4
Fe1_2	Fe	-0.488(3)	0.160(3)	0.607(1)	0.7	4
Fe2	Fe	0.000(6)	0.000(6)	0.500(2)	0.6	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
Fe1_1	M_xcos1	m_y_xc1	M_zcos1	3.25(2)	0.0	-1.94	M_xsin1	M_ysin1	M_zsin1	1.94(2)	0.0	3.25
Fe1_2	M_xcos1	m_y_xc1	M_zcos1	3.25	0.0	1.94	M_xsin1	M_ysin1	M_zsin1	-1.94	0.0	3.25
Fe2	m_y_xc1	m_y_xc1	M_zcos1	3.98(3)	0.0	0.0	M_ysin1	M_ysin1	M_zsin1	0.0	0.0	3.98

Atom	x	y	z
1	0.48600	0.84000	0.39300
2	0.51400	0.16000	0.89300
3	0.51400	0.34000	0.10700
4	0.48600	0.66000	0.60700

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_xcos1+M_ycos1	M_zcos1	3.25000	0.0	-1.94000	M_xsin1	M_ysin1	M_zsin1	1.94000	0.0	3.25000
2	-M_xcos1	-M_xcos1-M_ycos1	M_zcos1	-3.25000	0.0	-1.94000	M_xsin1	M_ysin1	-M_zsin1	1.94000	0.0	-3.25000
3	M_xcos1	-M_xcos1-M_ycos1	M_zcos1	3.25000	0.0	-1.94000	M_xsin1	-M_ysin1	M_zsin1	1.94000	0.0	3.25000
4	-M_xcos1	M_xcos1+M_ycos1	M_zcos1	-3.25000	0.0	-1.94000	M_xsin1	-M_ysin1	-M_zsin1	1.94000	0.0	-3.25000

Atom	x	y	z
1	0.51200	0.16000	0.60700
2	0.48800	0.84000	0.10700
3	0.48800	0.66000	0.89300
4	0.51200	0.34000	0.39300

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_xcos1+M_ycos1	M_zcos1	3.25000	0.0	1.94000	M_xsin1	M_ysin1	M_zsin1	-1.94000	0.0	3.25000
2	-M_xcos1	-M_xcos1-M_ycos1	M_zcos1	-3.25000	0.0	1.94000	M_xsin1	M_ysin1	-M_zsin1	-1.94000	0.0	-3.25000
3	M_xcos1	-M_xcos1-M_ycos1	M_zcos1	3.25000	0.0	1.94000	M_xsin1	-M_ysin1	M_zsin1	-1.94000	0.0	3.25000
4	-M_xcos1	M_xcos1+M_ycos1	M_zcos1	-3.25000	0.0	1.94000	M_xsin1	-M_ysin1	-M_zsin1	-1.94000	0.0	-3.25000

Atom	y	z
1	0.00000	0.50000
2	0.00000	0.00000
3	0.50000	0.00000
4	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+M_ycos1	M_xcos1+M_ycos1	M_zcos1	3.98000	0.0	0.0	M_ysin1	M_ysin1	M_zsin1	0.0	0.0	3.98000
2	-M_xcos1-M_ycos1	-M_xcos1-M_ycos1	M_zcos1	-3.98000	0.0	0.0	M_ysin1	M_ysin1	-M_zsin1	0.0	0.0	-3.98000
3	M_xcos1+M_ycos1	-M_xcos1-M_ycos1	M_zcos1	3.98000	0.0	0.0	M_ysin1	-M_ysin1	M_zsin1	0.0	0.0	3.98000
4	-M_xcos1-M_ycos1	M_xcos1+M_ycos1	M_zcos1	-3.98000	0.0	0.0	M_ysin1	-M_ysin1	-M_zsin1	0.0	0.0	-3.98000

[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
mDT3	1	2		primary	9
mDT4	1	2	special	primary	9

Comments:

NPD
Values of the moment modulations and the propagation vector are also reported for other higher temperatures
Spiral modulation not symmetry-forced by the MSSG
For simplicity, the moment is here only associated to the Fe in the shared Fe/Mn sites.

Comments (symmetry):

1k incommensurate structure
Two modulations corresponding to two different irreps, shifted by pi/2, are superposed
The structure point group is non-polar, not allowing ferroelectricity.

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