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	{ 2₀₁₀ \| 1/2 1/2 1/2 1/2 }
4	x1+1/2,-x2+1/2,-x3,-x4+1/2,+1	{ 2₁₀₀ \| 1/2 1/2 0 1/2 }
5	-x1,-x2,-x3,-x4,+1	{ -1 \| 0 }
6	x1,x2,-x3+1/2,x4,+1	{ m₀₀₁ \| 0 0 1/2 0 }
7	x1+1/2,-x2+1/2,x3+1/2,-x4+1/2,+1	{ m₀₁₀ \| 1/2 1/2 1/2 1/2 }
8	-x1+1/2,x2+1/2,x3,x4+1/2,+1	{ m₁₀₀ \| 1/2 1/2 0 1/2 }
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+1/2,x2+1/2,-x3+1/2,x4,-1	{ 2'₀₁₀ \| 1/2 1/2 1/2 0 }
12	x1+1/2,-x2+1/2,-x3,-x4,-1	{ 2'₁₀₀ \| 1/2 1/2 0 0 }
13	-x1,-x2,-x3,-x4+1/2,-1	{ -1' \| 0 0 0 1/2 }
14	x1,x2,-x3+1/2,x4+1/2,-1	{ m'₀₀₁ \| 0 0 1/2 1/2 }
15	x1+1/2,-x2+1/2,x3+1/2,-x4,-1	{ m'₀₁₀ \| 1/2 1/2 1/2 0 }
16	-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	2₀₁₀
4	x,-y,-z,+1	2₁₀₀
5	-x,-y,-z,+1	-1
6	x,y,-z,+1	m₀₀₁
7	x,-y,z,+1	m₀₁₀
8	-x,y,z,+1	m₁₀₀
1' + set click here to show and hide
9	x,y,z,-1	1'
10	-x,-y,z,-1	2'₀₀₁
11	-x,y,-z,-1	2'₀₁₀
12	x,-y,-z,-1	2'₁₀₀
13	-x,-y,-z,-1	-1'
14	x,y,-z,-1	m'₀₀₁
15	x,-y,z,-1	m'₀₁₀
16	-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	8

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	0	0	M_zcos1	0.0	0.0	0.0(4)	0	0	M_zsin1	0.0	0.0	0.0
Mn1	M_xcos1	M_ycos1	M_zcos1	0.0(8)	2.90(5)	0.0(5)	0	0	0	0.0	0.0	0.0

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

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	0	0	M_zcos1	0.0	0.0	0.0	0	0	M_zsin1	0.0	0.0	0.0
2	0	0	M_zcos1	0.0	0.0	0.0	0	0	-M_zsin1	0.0	0.0	0.0
3	0	0	M_zcos1	0.0	0.0	0.0	0	0	M_zsin1	0.0	0.0	0.0
4	0	0	M_zcos1	0.0	0.0	0.0	0	0	-M_zsin1	0.0	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	2.90000	0.0	0	0	0	0.0	0.0	0.0
2	-M_xcos1	-M_ycos1	M_zcos1	0.0	-2.90000	0.0	0	0	0	0.0	0.0	0.0
3	M_xcos1	-M_ycos1	M_zcos1	0.0	-2.90000	0.0	0	0	0	0.0	0.0	0.0
4	-M_xcos1	M_ycos1	M_zcos1	0.0	2.90000	0.0	0	0	0	0.0	0.0	0.0

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

Atom	x	y	z
1	0.70400	0.33700	0.05600
2	0.29600	0.66300	0.55600
3	0.79600	0.83700	0.44400
4	0.20400	0.16300	0.94400
5	0.29600	0.66300	0.94400
6	0.70400	0.33700	0.44400
7	0.20400	0.16300	0.55600
8	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: 41 K
Experiment Temperature: 35 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: Pbnm1'(0,β,0)s00s
    [View symmetry operations]

Magnetic Point Group: mmm1' (8.2.25)
    [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	Multiplicity
Tb1	Tb3+	-0.028	0.072	0.25	4
Mn1	Mn3+	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	0	0	M_zcos1	0.0	0.0	0.0(4)	0	0	M_zsin1	0.0	0.0	0.0
Mn1	M_xcos1	M_ycos1	M_zcos1	0.0(8)	2.90(5)	0.0(5)	0	0	0	0.0	0.0	0.0

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

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	0	0	M_zcos1	0.0	0.0	0.0	0	0	M_zsin1	0.0	0.0	0.0
2	0	0	M_zcos1	0.0	0.0	0.0	0	0	-M_zsin1	0.0	0.0	0.0
3	0	0	M_zcos1	0.0	0.0	0.0	0	0	M_zsin1	0.0	0.0	0.0
4	0	0	M_zcos1	0.0	0.0	0.0	0	0	-M_zsin1	0.0	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	2.90000	0.0	0	0	0	0.0	0.0	0.0
2	-M_xcos1	-M_ycos1	M_zcos1	0.0	-2.90000	0.0	0	0	0	0.0	0.0	0.0
3	M_xcos1	-M_ycos1	M_zcos1	0.0	-2.90000	0.0	0	0	0	0.0	0.0	0.0
4	-M_xcos1	M_ycos1	M_zcos1	0.0	2.90000	0.0	0	0	0	0.0	0.0	0.0

[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

Comments:

Phase I. Below 28K a second phase (phase II) exists with a cycloidal spin arrangement.
NSD
Apparently Tb moment modulation (null value obtained) was assumed in phase with that of Mn. Symmetry allows however a phase shift.
Non-standard Pbnm setting of the parent structure wit space group N. 62

Comments (symmetry):

1k incommensurate magnetic structure
1-dim active small irrep (only 1 possible ss groups for this irrep)

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

TbMnO₃ (#1.1.6)

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

TbMnO3 (#1.1.6)

TbMnO₃ (#1.1.6)