MAGNDATA - Collection of Magnetic Structures

Magnetic structure with only magnetic atoms

Reference: Lemoine, P. et al., Journal of Magnetism and Magnetic Materials (2012) 324 2937 - 2952
DOI: 10.1016/j.jmmm.2012.03.037
Atomic positions from: same reference

Parent space group (paramagnetic phase): I4/mmm (#139)
Propagation vector: k1 (0.816000, 0.000000, 0.000000)

Transition Temperature: 7 K
Experiment Temperature: 2 K

Wave vectors table:

label	Wave vector	k1 coefficient
1	(0.816, 0, 0)	1
2	(1.632, 0, 0)	2
3	(2.448, 0, 0)	3

N	(x,y,z)	Seitz notation
1	x1,x2,x3,x4,+1	{ 1 \| 0 }
2	-x1,-x2,x3,-x4+1/2,+1	{ 2₀₀₁ \| 0 0 0 1/2 }
3	-x1,x2,-x3,-x4+1/2,+1	{ 2₀₁₀ \| 0 0 0 1/2 }
4	x1,-x2,-x3,x4,+1	{ 2₁₀₀ \| 0 }
5	-x1,-x2,-x3,-x4,+1	{ -1 \| 0 }
6	x1,x2,-x3,x4+1/2,+1	{ m₀₀₁ \| 0 0 0 1/2 }
7	x1,-x2,x3,x4+1/2,+1	{ m₀₁₀ \| 0 0 0 1/2 }
8	-x1,x2,x3,-x4,+1	{ m₁₀₀ \| 0 }
(1/2,1/2,1/2,0) + set click here to show and hide
9	x1+1/2,x2+1/2,x3+1/2,x4,+1	{ 1 \| 1/2 1/2 1/2 0 }
10	-x1+1/2,-x2+1/2,x3+1/2,-x4+1/2,+1	{ 2₀₀₁ \| 1/2 1/2 1/2 1/2 }
11	-x1+1/2,x2+1/2,-x3+1/2,-x4+1/2,+1	{ 2₀₁₀ \| 1/2 1/2 1/2 1/2 }
12	x1+1/2,-x2+1/2,-x3+1/2,x4,+1	{ 2₁₀₀ \| 1/2 1/2 1/2 0 }
13	-x1+1/2,-x2+1/2,-x3+1/2,-x4,+1	{ -1 \| 1/2 1/2 1/2 0 }
14	x1+1/2,x2+1/2,-x3+1/2,x4+1/2,+1	{ m₀₀₁ \| 1/2 1/2 1/2 1/2 }
15	x1+1/2,-x2+1/2,x3+1/2,x4+1/2,+1	{ m₀₁₀ \| 1/2 1/2 1/2 1/2 }
16	-x1+1/2,x2+1/2,x3+1/2,-x4,+1	{ m₁₀₀ \| 1/2 1/2 1/2 0 }
(0,0,0,1/2)' + set click here to show and hide
17	x1,x2,x3,x4+1/2,-1	{ 1' \| 0 0 0 1/2 }
18	-x1,-x2,x3,-x4,-1	{ 2'₀₀₁ \| 0 }
19	-x1,x2,-x3,-x4,-1	{ 2'₀₁₀ \| 0 }
20	x1,-x2,-x3,x4+1/2,-1	{ 2'₁₀₀ \| 0 0 0 1/2 }
21	-x1,-x2,-x3,-x4+1/2,-1	{ -1' \| 0 0 0 1/2 }
22	x1,x2,-x3,x4,-1	{ m'₀₀₁ \| 0 }
23	x1,-x2,x3,x4,-1	{ m'₀₁₀ \| 0 }
24	-x1,x2,x3,-x4+1/2,-1	{ m'₁₀₀ \| 0 0 0 1/2 }
(1/2,1/2,1/2,1/2)' + set click here to show and hide
25	x1+1/2,x2+1/2,x3+1/2,x4+1/2,-1	{ 1' \| 1/2 1/2 1/2 1/2 }
26	-x1+1/2,-x2+1/2,x3+1/2,-x4,-1	{ 2'₀₀₁ \| 1/2 1/2 1/2 0 }
27	-x1+1/2,x2+1/2,-x3+1/2,-x4,-1	{ 2'₀₁₀ \| 1/2 1/2 1/2 0 }
28	x1+1/2,-x2+1/2,-x3+1/2,x4+1/2,-1	{ 2'₁₀₀ \| 1/2 1/2 1/2 1/2 }
29	-x1+1/2,-x2+1/2,-x3+1/2,-x4+1/2,-1	{ -1' \| 1/2 1/2 1/2 1/2 }
30	x1+1/2,x2+1/2,-x3+1/2,x4,-1	{ m'₀₀₁ \| 1/2 1/2 1/2 0 }
31	x1+1/2,-x2+1/2,x3+1/2,x4,-1	{ m'₀₁₀ \| 1/2 1/2 1/2 0 }
32	-x1+1/2,x2+1/2,x3+1/2,-x4+1/2,-1	{ m'₁₀₀ \| 1/2 1/2 1/2 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
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
Mg1_1	Mg	0	0.5	0	2
Mg1_2	Mg	-0.5	0	0	2
Pb1	Pb	0	0	0.139(1)	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
Er1	M_xcos1	0	0	0.0	0.0	0.0	0	0	M_zsin1	0.0	0.0	9.69

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
Er1	0	0	0	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0

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
Er1	M_xcos3	0	0	0.0	0.0	0.0	0	0	M_zsin3	0.0	0.0	2.74

Atom	x	y	z
1	0.00000	0.00000	0.33400
2	0.00000	0.00000	0.66600
(1/2,1/2,1/2,0) + set click here to show and hide
3	0.50000	0.50000	0.83400
4	0.50000	0.50000	0.16600

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	0	0.0	0.0	0.0	0	0	M_zsin1	0.0	0.0	9.69000
2	M_xcos1	0	0	0.0	0.0	0.0	0	0	M_zsin1	0.0	0.0	9.69000
(1/2,1/2,1/2,0) + set click here to show and hide
3	M_xcos1	0	0	0.0	0.0	0.0	0	0	M_zsin1	0.0	0.0	9.69000
4	M_xcos1	0	0	0.0	0.0	0.0	0	0	M_zsin1	0.0	0.0	9.69000

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	0	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0
2	0	0	0	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0
(1/2,1/2,1/2,0) + set click here to show and hide
3	0	0	0	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0
4	0	0	0	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0

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_xcos3	0	0	0.0	0.0	0.0	0	0	M_zsin3	0.0	0.0	2.74000
2	M_xcos3	0	0	0.0	0.0	0.0	0	0	-M_zsin3	0.0	0.0	-2.74000
(1/2,1/2,1/2,0) + set click here to show and hide
3	M_xcos3	0	0	0.0	0.0	0.0	0	0	M_zsin3	0.0	0.0	2.74000
4	M_xcos3	0	0	0.0	0.0	0.0	0	0	-M_zsin3	0.0	0.0	-2.74000

Atom	x	y	z
1	0.00000	0.50000	0.00000
(1/2,1/2,1/2,0) + set click here to show and hide
2	0.50000	0.00000	0.50000

Atom	x	y	z
1	0.50000	0.00000	0.00000
(1/2,1/2,1/2,0) + set click here to show and hide
2	0.00000	0.50000	0.50000

Atom	x	y	z
1	0.00000	0.00000	0.13900
2	0.00000	0.00000	0.86100
(1/2,1/2,1/2,0) + set click here to show and hide
3	0.50000	0.50000	0.63900
4	0.50000	0.50000	0.36100

Lattice parameters of the basic unit cell:
4.364(1) 4.364(1) 15.801(3) 90 90 90
Transformation from parent structure: (a,b,c;0,0,0)
    [View matrix form]

Magnetic Superspace Group: Immm1'(α00)0sss
    [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

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

Average atomic positions of symmetry independent atoms

Label	Atom type	x	y	z	Multiplicity
Er1	Er	0	0	0.334(1)	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
Er1	M_xcos1	0	0	0.0	0.0	0.0	0	0	M_zsin1	0.0	0.0	9.69

Wave vector 2

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
Er1	0	0	0	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0

Wave vector 3

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
Er1	M_xcos3	0	0	0.0	0.0	0.0	0	0	M_zsin3	0.0	0.0	2.74

Atom	x	y	z
1	0.00000	0.00000	0.33400
2	0.00000	0.00000	0.66600
(1/2,1/2,1/2,0) + set click here to show and hide
3	0.50000	0.50000	0.83400
4	0.50000	0.50000	0.16600

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	0	0.0	0.0	0.0	0	0	M_zsin1	0.0	0.0	9.69000
2	M_xcos1	0	0	0.0	0.0	0.0	0	0	M_zsin1	0.0	0.0	9.69000
(1/2,1/2,1/2,0) + set click here to show and hide
3	M_xcos1	0	0	0.0	0.0	0.0	0	0	M_zsin1	0.0	0.0	9.69000
4	M_xcos1	0	0	0.0	0.0	0.0	0	0	M_zsin1	0.0	0.0	9.69000

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	0	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0
2	0	0	0	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0
(1/2,1/2,1/2,0) + set click here to show and hide
3	0	0	0	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0
4	0	0	0	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0

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_xcos3	0	0	0.0	0.0	0.0	0	0	M_zsin3	0.0	0.0	2.74000
2	M_xcos3	0	0	0.0	0.0	0.0	0	0	-M_zsin3	0.0	0.0	-2.74000
(1/2,1/2,1/2,0) + set click here to show and hide
3	M_xcos3	0	0	0.0	0.0	0.0	0	0	M_zsin3	0.0	0.0	2.74000
4	M_xcos3	0	0	0.0	0.0	0.0	0	0	-M_zsin3	0.0	0.0	-2.74000

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

Comments:

NPD
anharmonic sinusoidal model
figure of model in reference does not seem to agree with the parameters listed in table and used here.

Comments (symmetry):

1k incommensurate magnetic structure
k-maximal magnetic symmetry (4 possible)
2-dim active irrep (1-dim small irrep): one to one correspondence between irrep and MSSG

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

ErMgPb (#1.1.29)