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 (0.835000, 0.000000, 0.000000)

Transition Temperature: 19 K
Experiment Temperature: 2 K

Wave vectors table:

label	Wave vector	k1 coefficient
1	(0.835, 0, 0)	1
2	(1.67, 0, 0)	2
3	(2.505, 0, 0)	3
4	(3.34, 0, 0)	4
5	(4.175, 0, 0)	5

N	(x,y,z)	Seitz notation
1	x1,x2,x3,x4,+1	{ 1 \| 0 }
2	-x1,-x2,x3,-x4,+1	{ 2₀₀₁ \| 0 }
3	-x1,-x2,-x3,-x4,+1	{ -1 \| 0 }
4	x1,x2,-x3,x4,+1	{ m₀₀₁ \| 0 }
(1/2,1/2,1/2,0) + set click here to show and hide
5	x1+1/2,x2+1/2,x3+1/2,x4,+1	{ 1 \| 1/2 1/2 1/2 0 }
6	-x1+1/2,-x2+1/2,x3+1/2,-x4,+1	{ 2₀₀₁ \| 1/2 1/2 1/2 0 }
7	-x1+1/2,-x2+1/2,-x3+1/2,-x4,+1	{ -1 \| 1/2 1/2 1/2 0 }
8	x1+1/2,x2+1/2,-x3+1/2,x4,+1	{ m₀₀₁ \| 1/2 1/2 1/2 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,-x2,x3,-x4+1/2,-1	{ 2'₀₀₁ \| 0 0 0 1/2 }
11	-x1,-x2,-x3,-x4+1/2,-1	{ -1' \| 0 0 0 1/2 }
12	x1,x2,-x3,x4+1/2,-1	{ m'₀₀₁ \| 0 0 0 1/2 }
(1/2,1/2,1/2,1/2)' + set click here to show and hide
13	x1+1/2,x2+1/2,x3+1/2,x4+1/2,-1	{ 1' \| 1/2 1/2 1/2 1/2 }
14	-x1+1/2,-x2+1/2,x3+1/2,-x4+1/2,-1	{ 2'₀₀₁ \| 1/2 1/2 1/2 1/2 }
15	-x1+1/2,-x2+1/2,-x3+1/2,-x4+1/2,-1	{ -1' \| 1/2 1/2 1/2 1/2 }
16	x1+1/2,x2+1/2,-x3+1/2,x4+1/2,-1	{ m'₀₀₁ \| 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	-1
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	2'₀₀₁
7	-x,-y,-z,-1	-1'
8	x,y,-z,-1	m'₀₀₁

Label	Atom type	x	y	z	Multiplicity
Mg1_1	Mg	0	0.5	0	2
Mg2_1	Mg	-0.5	0	0	2
Pb1_1	Pb	0	0	0.139(2)	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
Ho1_1	0	0	M_zcos1	0.0	0.0	0.0	M_xsin1	M_ysin1	0	8.30	8.90	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
Ho1_1	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
Ho1_1	0	0	M_zcos3	0.0	0.0	0.0	M_xsin3	M_ysin3	0	2.72	2.92	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
Ho1_1	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
Ho1_1	0	0	M_zcos5	0.0	0.0	0.0	M_xsin5	M_ysin5	0	1.70	1.83	0.0

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	0	0	M_zcos1	0.0	0.0	0.0	M_xsin1	M_ysin1	0	8.30000	8.90000	0.0
2	0	0	M_zcos1	0.0	0.0	0.0	M_xsin1	M_ysin1	0	8.30000	8.90000	0.0
(1/2,1/2,1/2,0) + set click here to show and hide
3	0	0	M_zcos1	0.0	0.0	0.0	M_xsin1	M_ysin1	0	8.30000	8.90000	0.0
4	0	0	M_zcos1	0.0	0.0	0.0	M_xsin1	M_ysin1	0	8.30000	8.90000	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	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	0	0	M_zcos3	0.0	0.0	0.0	M_xsin3	M_ysin3	0	2.72000	2.92000	0.0
2	0	0	M_zcos3	0.0	0.0	0.0	-M_xsin3	-M_ysin3	0	-2.72000	-2.92000	0.0
(1/2,1/2,1/2,0) + set click here to show and hide
3	0	0	M_zcos3	0.0	0.0	0.0	M_xsin3	M_ysin3	0	2.72000	2.92000	0.0
4	0	0	M_zcos3	0.0	0.0	0.0	-M_xsin3	-M_ysin3	0	-2.72000	-2.92000	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	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	0	0	M_zcos5	0.0	0.0	0.0	M_xsin5	M_ysin5	0	1.70000	1.83000	0.0
2	0	0	M_zcos5	0.0	0.0	0.0	-M_xsin5	-M_ysin5	0	-1.70000	-1.83000	0.0
(1/2,1/2,1/2,0) + set click here to show and hide
3	0	0	M_zcos5	0.0	0.0	0.0	M_xsin5	M_ysin5	0	1.70000	1.83000	0.0
4	0	0	M_zcos5	0.0	0.0	0.0	-M_xsin5	-M_ysin5	0	-1.70000	-1.83000	0.0

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:
4.383(1) 4.383 15.856(4) 90 90 90
Transformation from parent structure: (a,b,c;0,0,0)
    [View matrix form]

Magnetic Superspace Group: I2/m1'(αβ0)00s
    [View symmetry operations]

Magnetic Point Group: 2/m1' (5.2.13)
    [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
Ho1_1	Ho	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
Ho1_1	0	0	M_zcos1	0.0	0.0	0.0	M_xsin1	M_ysin1	0	8.30	8.90	0.0

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
Ho1_1	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
Ho1_1	0	0	M_zcos3	0.0	0.0	0.0	M_xsin3	M_ysin3	0	2.72	2.92	0.0

Wave vector 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
Ho1_1	0	0	0	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0

Wave vector 5

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
Ho1_1	0	0	M_zcos5	0.0	0.0	0.0	M_xsin5	M_ysin5	0	1.70	1.83	0.0

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	0	0	M_zcos1	0.0	0.0	0.0	M_xsin1	M_ysin1	0	8.30000	8.90000	0.0
2	0	0	M_zcos1	0.0	0.0	0.0	M_xsin1	M_ysin1	0	8.30000	8.90000	0.0
(1/2,1/2,1/2,0) + set click here to show and hide
3	0	0	M_zcos1	0.0	0.0	0.0	M_xsin1	M_ysin1	0	8.30000	8.90000	0.0
4	0	0	M_zcos1	0.0	0.0	0.0	M_xsin1	M_ysin1	0	8.30000	8.90000	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	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	0	0	M_zcos3	0.0	0.0	0.0	M_xsin3	M_ysin3	0	2.72000	2.92000	0.0
2	0	0	M_zcos3	0.0	0.0	0.0	-M_xsin3	-M_ysin3	0	-2.72000	-2.92000	0.0
(1/2,1/2,1/2,0) + set click here to show and hide
3	0	0	M_zcos3	0.0	0.0	0.0	M_xsin3	M_ysin3	0	2.72000	2.92000	0.0
4	0	0	M_zcos3	0.0	0.0	0.0	-M_xsin3	-M_ysin3	0	-2.72000	-2.92000	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	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	0	0	M_zcos5	0.0	0.0	0.0	M_xsin5	M_ysin5	0	1.70000	1.83000	0.0
2	0	0	M_zcos5	0.0	0.0	0.0	-M_xsin5	-M_ysin5	0	-1.70000	-1.83000	0.0
(1/2,1/2,1/2,0) + set click here to show and hide
3	0	0	M_zcos5	0.0	0.0	0.0	M_xsin5	M_ysin5	0	1.70000	1.83000	0.0
4	0	0	M_zcos5	0.0	0.0	0.0	-M_xsin5	-M_ysin5	0	-1.70000	-1.83000	0.0

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

Comments:

NPD
NPD
anharmonic sinusoidal magnetic modulation
amplitudes of moment harmonics: 12.17(12) (1k), 3.99(11) (3k) and 2.50(14) (5k). Phi=47

Comments (symmetry):

1k incommmensurate magnetic structure
2 primary irreps active
wave vectors of harmonics have been modified to be exact multiples of the propagation vector.

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

HoMgPb (#1.1.32)