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+1/4,x2+1/2,-x3,-x4+1/2,+1	{ 2₀₁₀ \| 1/4 1/2 0 1/2 }
3	-x1+1/4,x2+1/2,x3,x4,+1	{ m₁₀₀ \| 1/4 1/2 0 0 }
4	x1,x2,-x3,-x4+1/2,+1	{ m₀₀₁ \| 0 0 0 1/2 }
(1/2,0,0,1/2) + set click here to show and hide
5	x1+1/2,x2,x3,x4+1/2,+1	{ 1 \| 1/2 0 0 1/2 }
6	-x1+3/4,x2+1/2,-x3,-x4,+1	{ 2₀₁₀ \| 3/4 1/2 0 0 }
7	-x1+3/4,x2+1/2,x3,x4+1/2,+1	{ m₁₀₀ \| 3/4 1/2 0 1/2 }
8	x1+1/2,x2,-x3,-x4,+1	{ m₀₀₁ \| 1/2 0 0 0 }
(0,0,0,1/2)' + set click here to show and hide
9	x1,x2,x3,x4+1/2,-1	{ 1' \| 0 0 0 1/2 }
10	-x1+1/4,x2+1/2,-x3,-x4,-1	{ 2'₀₁₀ \| 1/4 1/2 0 0 }
11	-x1+1/4,x2+1/2,x3,x4+1/2,-1	{ m'₁₀₀ \| 1/4 1/2 0 1/2 }
12	x1,x2,-x3,-x4,-1	{ m'₀₀₁ \| 0 }
(1/2,0,0,0)' + set click here to show and hide
13	x1+1/2,x2,x3,x4,-1	{ 1' \| 1/2 0 0 0 }
14	-x1+3/4,x2+1/2,-x3,-x4+1/2,-1	{ 2'₀₁₀ \| 3/4 1/2 0 1/2 }
15	-x1+3/4,x2+1/2,x3,x4,-1	{ m'₁₀₀ \| 3/4 1/2 0 0 }
16	x1+1/2,x2,-x3,-x4+1/2,-1	{ m'₀₀₁ \| 1/2 0 0 1/2 }

N	(x,y,z)	Seitz notation
1	x,y,z,+1	1
2	-x,y,-z,+1	2₀₁₀
3	-x,y,z,+1	m₁₀₀
4	x,y,-z,+1	m₀₀₁
1' + set click here to show and hide
5	x,y,z,-1	1'
6	-x,y,-z,-1	2'₀₁₀
7	-x,y,z,-1	m'₁₀₀
8	x,y,-z,-1	m'₀₀₁

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
Gd1_1	M_xcos1	M_ycos1	0	1.88(12)	-0.08(12)	0.0	0	0	M_zsin1	0.0	0.0	0.02(22)
Gd1_2	M_xcos1	M_xcos1	0	-1.23(8)	0.55(18)	0.0	0	0	M_zsin1	0.0	0.0	-0.14(29)
Mn1	M_xcos1	M_ycos1	M_zcos1	-1.46(5)	0.10(10)	0.24(35)	M_xsin1	M_ysin1	M_zsin1	-0.29(19)	-0.12(14)	0.13(13)
Mn2_1	M_xcos1	M_ycos1	0	2.73(13)	-0.95(26)	0.0	0	0	M_zsin1	0.0	0.0	0.05(28)
Mn2_2	M_xcos1	M_ycos1	0	-2.44(11)	0.50(13)	0.0	0	0	M_zsin1	0.0	0.0	0.01(28)

Atom	x	y	z
1	0.06950	0.17200	0.00000
2	0.18050	0.67200	0.00000
(1/2,0,0,1/2) + set click here to show and hide
3	0.56950	0.17200	0.00000
4	0.68050	0.67200	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	0	1.88000	-0.08000	0.0	0	0	M_zsin1	0.0	0.0	0.02000
2	M_xcos1	-M_ycos1	0	1.88000	0.08000	0.0	0	0	-M_zsin1	0.0	0.0	-0.02000
(1/2,0,0,1/2) + set click here to show and hide
3	-M_xcos1	-M_ycos1	0	-1.88000	0.08000	0.0	0	0	-M_zsin1	0.0	0.0	-0.02000
4	-M_xcos1	M_ycos1	0	-1.88000	-0.08000	0.0	0	0	M_zsin1	0.0	0.0	0.02000

Atom	x	y	z
1	0.31950	0.32800	0.00000
2	0.93050	0.82800	0.00000
(1/2,0,0,1/2) + set click here to show and hide
3	0.81950	0.32800	0.00000
4	0.43050	0.82800	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_xcos1	0	-1.23000	0.55000	0.0	0	0	M_zsin1	0.0	0.0	-0.14000
2	M_xcos1	-M_xcos1	0	-1.23000	-0.55000	0.0	0	0	-M_zsin1	0.0	0.0	0.14000
(1/2,0,0,1/2) + set click here to show and hide
3	-M_xcos1	-M_xcos1	0	1.23000	-0.55000	0.0	0	0	-M_zsin1	0.0	0.0	0.14000
4	-M_xcos1	M_xcos1	0	1.23000	0.55000	0.0	0	0	M_zsin1	0.0	0.0	-0.14000

Atom	x	y	z
1	0.00000	0.50000	0.25600
2	0.25000	0.00000	0.74400
3	0.25000	0.00000	0.25600
4	0.00000	0.50000	0.74400
(1/2,0,0,1/2) + set click here to show and hide
5	0.50000	0.50000	0.25600
6	0.75000	0.00000	0.74400
7	0.75000	0.00000	0.25600
8	0.50000	0.50000	0.74400

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	-1.46000	0.10000	0.24000	M_xsin1	M_ysin1	M_zsin1	-0.29000	-0.12000	0.13000
2	M_xcos1	-M_ycos1	M_zcos1	-1.46000	-0.10000	0.24000	-M_xsin1	M_ysin1	-M_zsin1	0.29000	-0.12000	-0.13000
3	M_xcos1	-M_ycos1	-M_zcos1	-1.46000	-0.10000	-0.24000	M_xsin1	-M_ysin1	-M_zsin1	-0.29000	0.12000	-0.13000
4	M_xcos1	M_ycos1	-M_zcos1	-1.46000	0.10000	-0.24000	-M_xsin1	-M_ysin1	M_zsin1	0.29000	0.12000	0.13000
(1/2,0,0,1/2) + set click here to show and hide
5	-M_xcos1	-M_ycos1	-M_zcos1	1.46000	-0.10000	-0.24000	-M_xsin1	-M_ysin1	-M_zsin1	0.29000	0.12000	-0.13000
6	-M_xcos1	M_ycos1	-M_zcos1	1.46000	0.10000	-0.24000	M_xsin1	-M_ysin1	M_zsin1	-0.29000	0.12000	0.13000
7	-M_xcos1	M_ycos1	M_zcos1	1.46000	0.10000	0.24000	-M_xsin1	M_ysin1	M_zsin1	0.29000	-0.12000	0.13000
8	-M_xcos1	-M_ycos1	M_zcos1	1.46000	-0.10000	0.24000	M_xsin1	M_ysin1	-M_zsin1	-0.29000	-0.12000	-0.13000

Atom	x	y	z
1	0.20550	0.34900	0.50000
2	0.04450	0.84900	0.50000
(1/2,0,0,1/2) + set click here to show and hide
3	0.70550	0.34900	0.50000
4	0.54450	0.84900	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	0	2.73000	-0.95000	0.0	0	0	M_zsin1	0.0	0.0	0.05000
2	M_xcos1	-M_ycos1	0	2.73000	0.95000	0.0	0	0	-M_zsin1	0.0	0.0	-0.05000
(1/2,0,0,1/2) + set click here to show and hide
3	-M_xcos1	-M_ycos1	0	-2.73000	0.95000	0.0	0	0	-M_zsin1	0.0	0.0	-0.05000
4	-M_xcos1	M_ycos1	0	-2.73000	-0.95000	0.0	0	0	M_zsin1	0.0	0.0	0.05000

Atom	x	y	z
1	0.29450	0.65100	0.50000
2	0.95550	0.15100	0.50000
(1/2,0,0,1/2) + set click here to show and hide
3	0.79450	0.65100	0.50000
4	0.45550	0.15100	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	0	-2.44000	0.50000	0.0	0	0	M_zsin1	0.0	0.0	0.01000
2	M_xcos1	-M_ycos1	0	-2.44000	-0.50000	0.0	0	0	-M_zsin1	0.0	0.0	-0.01000
(1/2,0,0,1/2) + set click here to show and hide
3	-M_xcos1	-M_ycos1	0	2.44000	-0.50000	0.0	0	0	-M_zsin1	0.0	0.0	-0.01000
4	-M_xcos1	M_ycos1	0	2.44000	0.50000	0.0	0	0	M_zsin1	0.0	0.0	0.01000

Reference: J. Sheng, X. Tong, F. Ye, J.A. Fernandez-Baca, H. Cao, N. Poudel, M. Gooch, B. Lorenz, C.W. Chu, X. Wang and S.-W. Cheong, Physical Review B (2019) 99 094429.
DOI: 10.1103/physrevb.99.094429
Atomic positions from: same reference

Parent space group (paramagnetic phase): Pbam (#55)
Propagation vector: k1 (0.000000, 0.000000, 0.100000)

Transition Temperature: 40 K
Experiment Temperature: 33.5 K

Lattice parameters of the basic unit cell:
14.7062 8.5371 5.6807 90 90 90
Transformation from parent structure: (2a,b,c;0,0,0)
    [View matrix form]

Magnetic Superspace Group: Xb2_1m1'(00g)000s
    [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
Gd1_1	Gd	0.0695	0.172	0	4
Gd1_2	Gd	0.3195	0.328	0	4
Mn1	Mn	0	0.5	0.256	8
Mn2_1	Mn	0.2055	0.349	0.5	4
Mn2_2	Mn	0.2945	0.651	0.5	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
Gd1_1	M_xcos1	M_ycos1	0	1.88(12)	-0.08(12)	0.0	0	0	M_zsin1	0.0	0.0	0.02(22)
Gd1_2	M_xcos1	M_xcos1	0	-1.23(8)	0.55(18)	0.0	0	0	M_zsin1	0.0	0.0	-0.14(29)
Mn1	M_xcos1	M_ycos1	M_zcos1	-1.46(5)	0.10(10)	0.24(35)	M_xsin1	M_ysin1	M_zsin1	-0.29(19)	-0.12(14)	0.13(13)
Mn2_1	M_xcos1	M_ycos1	0	2.73(13)	-0.95(26)	0.0	0	0	M_zsin1	0.0	0.0	0.05(28)
Mn2_2	M_xcos1	M_ycos1	0	-2.44(11)	0.50(13)	0.0	0	0	M_zsin1	0.0	0.0	0.01(28)

Atom	x	y	z
1	0.06950	0.17200	0.00000
2	0.18050	0.67200	0.00000
(1/2,0,0,1/2) + set click here to show and hide
3	0.56950	0.17200	0.00000
4	0.68050	0.67200	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	0	1.88000	-0.08000	0.0	0	0	M_zsin1	0.0	0.0	0.02000
2	M_xcos1	-M_ycos1	0	1.88000	0.08000	0.0	0	0	-M_zsin1	0.0	0.0	-0.02000
(1/2,0,0,1/2) + set click here to show and hide
3	-M_xcos1	-M_ycos1	0	-1.88000	0.08000	0.0	0	0	-M_zsin1	0.0	0.0	-0.02000
4	-M_xcos1	M_ycos1	0	-1.88000	-0.08000	0.0	0	0	M_zsin1	0.0	0.0	0.02000

Atom	x	y	z
1	0.31950	0.32800	0.00000
2	0.93050	0.82800	0.00000
(1/2,0,0,1/2) + set click here to show and hide
3	0.81950	0.32800	0.00000
4	0.43050	0.82800	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_xcos1	0	-1.23000	0.55000	0.0	0	0	M_zsin1	0.0	0.0	-0.14000
2	M_xcos1	-M_xcos1	0	-1.23000	-0.55000	0.0	0	0	-M_zsin1	0.0	0.0	0.14000
(1/2,0,0,1/2) + set click here to show and hide
3	-M_xcos1	-M_xcos1	0	1.23000	-0.55000	0.0	0	0	-M_zsin1	0.0	0.0	0.14000
4	-M_xcos1	M_xcos1	0	1.23000	0.55000	0.0	0	0	M_zsin1	0.0	0.0	-0.14000

Atom	x	y	z
1	0.00000	0.50000	0.25600
2	0.25000	0.00000	0.74400
3	0.25000	0.00000	0.25600
4	0.00000	0.50000	0.74400
(1/2,0,0,1/2) + set click here to show and hide
5	0.50000	0.50000	0.25600
6	0.75000	0.00000	0.74400
7	0.75000	0.00000	0.25600
8	0.50000	0.50000	0.74400

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	-1.46000	0.10000	0.24000	M_xsin1	M_ysin1	M_zsin1	-0.29000	-0.12000	0.13000
2	M_xcos1	-M_ycos1	M_zcos1	-1.46000	-0.10000	0.24000	-M_xsin1	M_ysin1	-M_zsin1	0.29000	-0.12000	-0.13000
3	M_xcos1	-M_ycos1	-M_zcos1	-1.46000	-0.10000	-0.24000	M_xsin1	-M_ysin1	-M_zsin1	-0.29000	0.12000	-0.13000
4	M_xcos1	M_ycos1	-M_zcos1	-1.46000	0.10000	-0.24000	-M_xsin1	-M_ysin1	M_zsin1	0.29000	0.12000	0.13000
(1/2,0,0,1/2) + set click here to show and hide
5	-M_xcos1	-M_ycos1	-M_zcos1	1.46000	-0.10000	-0.24000	-M_xsin1	-M_ysin1	-M_zsin1	0.29000	0.12000	-0.13000
6	-M_xcos1	M_ycos1	-M_zcos1	1.46000	0.10000	-0.24000	M_xsin1	-M_ysin1	M_zsin1	-0.29000	0.12000	0.13000
7	-M_xcos1	M_ycos1	M_zcos1	1.46000	0.10000	0.24000	-M_xsin1	M_ysin1	M_zsin1	0.29000	-0.12000	0.13000
8	-M_xcos1	-M_ycos1	M_zcos1	1.46000	-0.10000	0.24000	M_xsin1	M_ysin1	-M_zsin1	-0.29000	-0.12000	-0.13000

Atom	x	y	z
1	0.20550	0.34900	0.50000
2	0.04450	0.84900	0.50000
(1/2,0,0,1/2) + set click here to show and hide
3	0.70550	0.34900	0.50000
4	0.54450	0.84900	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	0	2.73000	-0.95000	0.0	0	0	M_zsin1	0.0	0.0	0.05000
2	M_xcos1	-M_ycos1	0	2.73000	0.95000	0.0	0	0	-M_zsin1	0.0	0.0	-0.05000
(1/2,0,0,1/2) + set click here to show and hide
3	-M_xcos1	-M_ycos1	0	-2.73000	0.95000	0.0	0	0	-M_zsin1	0.0	0.0	-0.05000
4	-M_xcos1	M_ycos1	0	-2.73000	-0.95000	0.0	0	0	M_zsin1	0.0	0.0	0.05000

Atom	x	y	z
1	0.29450	0.65100	0.50000
2	0.95550	0.15100	0.50000
(1/2,0,0,1/2) + set click here to show and hide
3	0.79450	0.65100	0.50000
4	0.45550	0.15100	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	0	-2.44000	0.50000	0.0	0	0	M_zsin1	0.0	0.0	0.01000
2	M_xcos1	-M_ycos1	0	-2.44000	-0.50000	0.0	0	0	-M_zsin1	0.0	0.0	-0.01000
(1/2,0,0,1/2) + set click here to show and hide
3	-M_xcos1	-M_ycos1	0	2.44000	-0.50000	0.0	0	0	-M_zsin1	0.0	0.0	-0.01000
4	-M_xcos1	M_ycos1	0	2.44000	0.50000	0.0	0	0	M_zsin1	0.0	0.0	0.01000

[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
mG1	2	4	special	primary	18

Comments:

NSD
Below 33K the structure becomes commensurate (see #1.299 and #1.300)
Lattice parameters are absent in the article; those of a room temperature model of the paramagnetic phase (icsd #97046) are used here.
Only magnetic atoms are reported.
See entry #1.1.63 for the structure in the same phase at 36K

Comments (symmetry):

1k incommensurate magnetic structure
4-dim irrep along a special direction
Incommensurate spin modulation which breaks the centrosymmetry of the parent phase. It is polar along b (in parent setting). But electric polarization is not detected. Magnetic induced electric polarization is only observed in the lower commensurate phase.

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

GdMn₂O₅ (#1.1.63)

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

GdMn2O5 (#1.1.63)

GdMn₂O₅ (#1.1.63)