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+1/2,-x2+1/2,x3+1/2,-x4+1/2,+1	{ m₀₁₀ \| 1/2 1/2 1/2 1/2 }
4	-x1+1/2,x2+1/2,x3,x4+1/2,+1	{ m₁₀₀ \| 1/2 1/2 0 1/2 }
(0,0,0,1/2)' + set click here to show and hide
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+1/2,-x2+1/2,x3+1/2,-x4,-1	{ m'₀₁₀ \| 1/2 1/2 1/2 0 }
8	-x1+1/2,x2+1/2,x3,x4,-1	{ m'₁₀₀ \| 1/2 1/2 0 0 }

N	(x,y,z)	Seitz notation
1	x,y,z,+1	1
2	-x,-y,z,+1	2₀₀₁
3	x,-y,z,+1	m₀₁₀
4	-x,y,z,+1	m₁₀₀
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	m'₀₁₀
8	-x,y,z,-1	m'₁₀₀

Label	Atom type	x	y	z	Multiplicity
O1	O	0.097	0.46	0.25	4
O2	O	-0.296	0.337	0.056	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
Tb1	M_xcos1	M_ycos1	M_zcos1	0.0	0.0	0.0(3)	M_xsin1	M_ysin1	M_zsin1	0.3(2)	0.0(4)	0.0
Mn1	M_xcos1	M_ycos1	M_zcos1	0.0(5)	4.7(3)	0.3(4)	M_xsin1	M_ysin1	M_zsin1	0.0(2)	0.0(4)	3.0(3)

Atom	x	y	z
1	0.97200	0.07200	0.25000
2	0.02800	0.92800	0.75000
3	0.47200	0.42800	0.75000
4	0.52800	0.57200	0.25000

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	0.0	M_xsin1	M_ysin1	M_zsin1	0.30000	0.0	0.0
2	-M_xcos1	-M_ycos1	M_zcos1	0.0	0.0	0.0	M_xsin1	M_ysin1	-M_zsin1	0.30000	0.0	0.0
3	M_xcos1	-M_ycos1	M_zcos1	0.0	0.0	0.0	-M_xsin1	M_ysin1	-M_zsin1	-0.30000	0.0	0.0
4	-M_xcos1	M_ycos1	M_zcos1	0.0	0.0	0.0	-M_xsin1	M_ysin1	M_zsin1	-0.30000	0.0	0.0

Atom	x	y	z
1	0.50000	0.00000	0.00000
2	0.50000	0.00000	0.50000
3	0.00000	0.50000	0.50000
4	0.00000	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	M_ycos1	M_zcos1	0.0	4.70000	0.30000	M_xsin1	M_ysin1	M_zsin1	0.0	0.0	3.00000
2	-M_xcos1	-M_ycos1	M_zcos1	0.0	-4.70000	0.30000	M_xsin1	M_ysin1	-M_zsin1	0.0	0.0	-3.00000
3	M_xcos1	-M_ycos1	M_zcos1	0.0	-4.70000	0.30000	-M_xsin1	M_ysin1	-M_zsin1	0.0	0.0	-3.00000
4	-M_xcos1	M_ycos1	M_zcos1	0.0	4.70000	0.30000	-M_xsin1	M_ysin1	M_zsin1	0.0	0.0	3.00000

Atom	x	y	z
1	0.09700	0.46000	0.25000
2	0.90300	0.54000	0.75000
3	0.59700	0.04000	0.75000
4	0.40300	0.96000	0.25000

Atom	x	y	z
1	0.70400	0.33700	0.05600
2	0.29600	0.66300	0.55600
3	0.20400	0.16300	0.55600
4	0.79600	0.83700	0.05600

Reference: M. Kenzelmann, A.B. Harris, S. Jonas, C. Broholm, J. Schefer, S.B. Kim, C.L. Zhang, S.-W. Cheong, O.P. Vajk and J.W. Lynn, Physical Review Letters (2005) 95 087206.
DOI: 10.1103/physrevlett.95.087206
Atomic positions from: ICSD #15720

Parent space group (paramagnetic phase): Pbnm (#62) (non-standard)
Transformation to a standard setting: (b,c,a;0,0,0)
    [View matrix form]
Propagation vector: k1 (0.000000, 0.27, 0.000000)

Transition Temperature: 28 K
Experiment Temperature: 4 K

Lattice parameters of the basic unit cell:
5.297 5.831 7.403 90 90 90
Transformation from parent structure: (a,b,c;0,0,0)
    [View matrix form]

Magnetic Superspace Group: Pbn211'(0b0)s00s
    [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

     [Show only magnetic atoms]
     [Show all the atoms]

Average atomic positions of symmetry independent atoms

Label	Atom type	x	y	z	Multiplicity
Tb1	Tb	-0.028	0.072	0.25	4
Mn1	Mn	0.5	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
Tb1	M_xcos1	M_ycos1	M_zcos1	0.0	0.0	0.0(3)	M_xsin1	M_ysin1	M_zsin1	0.3(2)	0.0(4)	0.0
Mn1	M_xcos1	M_ycos1	M_zcos1	0.0(5)	4.7(3)	0.3(4)	M_xsin1	M_ysin1	M_zsin1	0.0(2)	0.0(4)	3.0(3)

Atom	x	y	z
1	0.97200	0.07200	0.25000
2	0.02800	0.92800	0.75000
3	0.47200	0.42800	0.75000
4	0.52800	0.57200	0.25000

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	0.0	M_xsin1	M_ysin1	M_zsin1	0.30000	0.0	0.0
2	-M_xcos1	-M_ycos1	M_zcos1	0.0	0.0	0.0	M_xsin1	M_ysin1	-M_zsin1	0.30000	0.0	0.0
3	M_xcos1	-M_ycos1	M_zcos1	0.0	0.0	0.0	-M_xsin1	M_ysin1	-M_zsin1	-0.30000	0.0	0.0
4	-M_xcos1	M_ycos1	M_zcos1	0.0	0.0	0.0	-M_xsin1	M_ysin1	M_zsin1	-0.30000	0.0	0.0

Atom	x	y	z
1	0.50000	0.00000	0.00000
2	0.50000	0.00000	0.50000
3	0.00000	0.50000	0.50000
4	0.00000	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	M_ycos1	M_zcos1	0.0	4.70000	0.30000	M_xsin1	M_ysin1	M_zsin1	0.0	0.0	3.00000
2	-M_xcos1	-M_ycos1	M_zcos1	0.0	-4.70000	0.30000	M_xsin1	M_ysin1	-M_zsin1	0.0	0.0	-3.00000
3	M_xcos1	-M_ycos1	M_zcos1	0.0	-4.70000	0.30000	-M_xsin1	M_ysin1	-M_zsin1	0.0	0.0	-3.00000
4	-M_xcos1	M_ycos1	M_zcos1	0.0	4.70000	0.30000	-M_xsin1	M_ysin1	M_zsin1	0.0	0.0	3.00000

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

Active Irreps:

label	dim. small irrep	dim. full irrep	action	number of modes
mDT3	1	2	primary	5
mDT2	1	2	primary	7

Comments:

NSD
Phase II under a field of 4T along a. Similar to the structure at zero field
Both Mn and Tb occupy general positions and have no restrictions on their moment modulations.
Non-standard Pbnm setting of the parent structure wit space group N. 62.

Comments (symmetry):

1k incommensurate magnetic structure
Two irreps active. Both having a 1-dim small irrep.
mDT_i are the irrep labels in the standard Pnma setting
Elliptical cycloidal spin modulation.
Multiferroic of type II. Magnetic ordering breaks the symmetry into a polar group.

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

TbMnO₃ (#1.1.8)

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

TbMnO3 (#1.1.8)

TbMnO₃ (#1.1.8)