MAGNDATA - Collection of Magnetic Structures

Magnetic structure with only magnetic atoms

Reference: M. Loewenhaupt, Th. Reif, R. R. Arons, E. Gratz, M. Rotter, B. Lebech, Z. Phys. B (1995) 96 491 - 496
DOI: 10.1007/BF01313846
Atomic positions from: same reference

Parent space group (paramagnetic phase): Imma (#74)
Propagation vector: k1 (0.60000, 0.00000, 0.00000)

Transition Temperature: 4.1 K
Experiment Temperature: 1.8 K

Wave vectors table:

label	Wave vector	k1 coefficient
1	(0.6, 0, 0)	1
2	(1.8, 0, 0)	3
3	(3, 0, 0)	5

N	(x,y,z)	Seitz notation
1	x1,x2,x3,x4,+1	{ 1 \| 0 }
2	x1,-x2,-x3,x4+1/2,+1	{ 2₁₀₀ \| 0 0 0 1/2 }
3	-x1,x2+1/2,-x3,-x4,+1	{ 2₀₁₀ \| 0 1/2 0 0 }
4	-x1,-x2+1/2,x3,-x4+1/2,+1	{ 2₀₀₁ \| 0 1/2 0 1/2 }
5	-x1,-x2,-x3,-x4,+1	{ -1 \| 0 }
6	-x1,x2,x3,-x4+1/2,+1	{ m₁₀₀ \| 0 0 0 1/2 }
7	x1,-x2+1/2,x3,x4,+1	{ m₀₁₀ \| 0 1/2 0 0 }
8	x1+1/2,x2,-x3+1/2,x4+1/2,+1	{ m₀₀₁ \| 1/2 0 1/2 1/2 }
(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	{ 2'₁₀₀ \| 0 }
11	-x1,x2+1/2,-x3,-x4+1/2,-1	{ 2'₀₁₀ \| 0 1/2 0 1/2 }
12	-x1,-x2+1/2,x3,-x4,-1	{ 2'₀₀₁ \| 0 1/2 0 0 }
13	-x1,-x2,-x3,-x4+1/2,-1	{ -1' \| 0 0 0 1/2 }
14	-x1,x2,x3,-x4,-1	{ m'₁₀₀ \| 0 }
15	x1,-x2+1/2,x3,x4+1/2,-1	{ m'₀₁₀ \| 0 1/2 0 1/2 }
16	x1+1/2,x2,-x3+1/2,x4,-1	{ m'₀₀₁ \| 1/2 0 1/2 0 }
(1/2,1/2,1/2,0) + set click here to show and hide
17	x1+1/2,x2+1/2,x3+1/2,x4,+1	{ 1 \| 1/2 1/2 1/2 0 }
18	x1+1/2,-x2+1/2,-x3+1/2,x4+1/2,+1	{ 2₁₀₀ \| 1/2 1/2 1/2 1/2 }
19	-x1+1/2,x2,-x3+1/2,-x4,+1	{ 2₀₁₀ \| 1/2 0 1/2 0 }
20	-x1+1/2,-x2,x3+1/2,-x4+1/2,+1	{ 2₀₀₁ \| 1/2 0 1/2 1/2 }
21	-x1+1/2,-x2+1/2,-x3+1/2,-x4,+1	{ -1 \| 1/2 1/2 1/2 0 }
22	-x1+1/2,x2+1/2,x3+1/2,-x4+1/2,+1	{ m₁₀₀ \| 1/2 1/2 1/2 1/2 }
23	x1+1/2,-x2,x3+1/2,x4,+1	{ m₀₁₀ \| 1/2 0 1/2 0 }
24	x1,x2+1/2,-x3,x4+1/2,+1	{ m₀₀₁ \| 0 1/2 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	{ 2'₁₀₀ \| 1/2 1/2 1/2 0 }
27	-x1+1/2,x2,-x3+1/2,-x4+1/2,-1	{ 2'₀₁₀ \| 1/2 0 1/2 1/2 }
28	-x1+1/2,-x2,x3+1/2,-x4,-1	{ 2'₀₀₁ \| 1/2 0 1/2 0 }
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'₁₀₀ \| 1/2 1/2 1/2 0 }
31	x1+1/2,-x2,x3+1/2,x4+1/2,-1	{ m'₀₁₀ \| 1/2 0 1/2 1/2 }
32	x1,x2+1/2,-x3,x4,-1	{ m'₀₀₁ \| 0 1/2 0 0 }

N	(x,y,z)	Seitz notation
1	x,y,z,+1	1
2	x,-y,-z,+1	2₁₀₀
3	-x,y,-z,+1	2₀₁₀
4	-x,-y,z,+1	2₀₀₁
5	-x,-y,-z,+1	-1
6	-x,y,z,+1	m₁₀₀
7	x,-y,z,+1	m₀₁₀
8	x,y,-z,+1	m₀₀₁
1' + set click here to show and hide
9	x,y,z,-1	1'
10	x,-y,-z,-1	2'₁₀₀
11	-x,y,-z,-1	2'₀₁₀
12	-x,-y,z,-1	2'₀₀₁
13	-x,-y,-z,-1	-1'
14	-x,y,z,-1	m'₁₀₀
15	x,-y,z,-1	m'₀₁₀
16	x,y,-z,-1	m'₀₀₁

Label	Atom type	x	y	z	Multiplicity
Cu1	Cu	0.00000	0.05060	0.16700	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
Nd1	0	M_yc1	0	0.0	2.32(1)	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
Nd1	0	M_yc1	0	0.0	-0.90(1)	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
Nd1	0	M_yc1	0	0.0	0.36(1)	0.0	0	0	0	0.0	0.0	0.0

Atom	x	y	z
1	0.00000	0.25000	0.54040
(0,0,0,1/2)' + set click here to show and hide
2	0.00000	0.75000	0.45960
(1/2,1/2,1/2,0) + set click here to show and hide
3	0.50000	0.25000	0.95960
(1/2,1/2,1/2,1/2)' + set click here to show and hide
4	0.50000	0.75000	0.04040

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	_y	0	0.0	2.32000	0.0	0	0	0	0.0	0.0	0.0
(0,0,0,1/2)' + set click here to show and hide
2	0	_y	0	0.0	2.32000	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	_y	0	0.0	2.32000	0.0	0	0	0	0.0	0.0	0.0
(1/2,1/2,1/2,1/2)' + set click here to show and hide
4	0	_y	0	0.0	2.32000	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	_y	0	0.0	-0.90000	0.0	0	0	0	0.0	0.0	0.0
(0,0,0,1/2)' + set click here to show and hide
2	0	_y	0	0.0	-0.90000	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	_y	0	0.0	-0.90000	0.0	0	0	0	0.0	0.0	0.0
(1/2,1/2,1/2,1/2)' + set click here to show and hide
4	0	_y	0	0.0	-0.90000	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	_y	0	0.0	0.36000	0.0	0	0	0	0.0	0.0	0.0
(0,0,0,1/2)' + set click here to show and hide
2	0	_y	0	0.0	0.36000	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	_y	0	0.0	0.36000	0.0	0	0	0	0.0	0.0	0.0
(1/2,1/2,1/2,1/2)' + set click here to show and hide
4	0	_y	0	0.0	0.36000	0.0	0	0	0	0.0	0.0	0.0

Atom	x	y	z
1	0.00000	0.05060	0.16700
2	0.00000	0.94940	0.83300
(0,0,0,1/2)' + set click here to show and hide
3	0.00000	0.55060	0.83300
4	0.00000	0.44940	0.16700
(1/2,1/2,1/2,0) + set click here to show and hide
5	0.50000	0.55060	0.66700
6	0.50000	0.44940	0.33300
(1/2,1/2,1/2,1/2)' + set click here to show and hide
7	0.50000	0.05060	0.33300
8	0.50000	0.94940	0.66700

Lattice parameters of the basic unit cell:
4.37000 6.98000 7.37000 90.00000 90.00000 90.00000
Transformation from parent structure: (a,b,c;0,0,0)
    [View matrix form]

Magnetic Superspace Group: Imma1'(0,0,g)00ss
    [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
Nd1	Nd	0.00000	0.25000	0.54040	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
Nd1	0	M_yc1	0	0.0	2.32(1)	0.0	0	0	0	0.0	0.0	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
Nd1	0	M_yc1	0	0.0	-0.90(1)	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
Nd1	0	M_yc1	0	0.0	0.36(1)	0.0	0	0	0	0.0	0.0	0.0

Atom	x	y	z
1	0.00000	0.25000	0.54040
(0,0,0,1/2)' + set click here to show and hide
2	0.00000	0.75000	0.45960
(1/2,1/2,1/2,0) + set click here to show and hide
3	0.50000	0.25000	0.95960
(1/2,1/2,1/2,1/2)' + set click here to show and hide
4	0.50000	0.75000	0.04040

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	_y	0	0.0	2.32000	0.0	0	0	0	0.0	0.0	0.0
(0,0,0,1/2)' + set click here to show and hide
2	0	_y	0	0.0	2.32000	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	_y	0	0.0	2.32000	0.0	0	0	0	0.0	0.0	0.0
(1/2,1/2,1/2,1/2)' + set click here to show and hide
4	0	_y	0	0.0	2.32000	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	_y	0	0.0	-0.90000	0.0	0	0	0	0.0	0.0	0.0
(0,0,0,1/2)' + set click here to show and hide
2	0	_y	0	0.0	-0.90000	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	_y	0	0.0	-0.90000	0.0	0	0	0	0.0	0.0	0.0
(1/2,1/2,1/2,1/2)' + set click here to show and hide
4	0	_y	0	0.0	-0.90000	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	_y	0	0.0	0.36000	0.0	0	0	0	0.0	0.0	0.0
(0,0,0,1/2)' + set click here to show and hide
2	0	_y	0	0.0	0.36000	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	_y	0	0.0	0.36000	0.0	0	0	0	0.0	0.0	0.0
(1/2,1/2,1/2,1/2)' + set click here to show and hide
4	0	_y	0	0.0	0.36000	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	direction	action	number of modes
mSM3(k1)	1	2	special	primary	1
mSM3(3k1)	1	2	special	primary	1
mSM3(5k1)	1	2	special	primary	1

Comments:

NPD and NSD
Commensurate 5-fold structure described as a modulated structure with three harmonics.
The commensurate MSG of this structure is P_Inma (62.456). For an alternate commensurate description of this structure under its MSG see #1.620.
The graphical representation in the paper is shifted (2/5,0,0) in the 5-fold supercell with respect to the one described here, following the exact modulation functions given in the paper, but both descriptions are equivalent.
Between 6.5K and 4.1K a more complex incommensurate magnetic structure with wave vector (0.62, 0.042, 0.0) is observed.

Comments (symmetry):

1k magnetic structure
2-dim irrep for k1=(3/5,0,0) along a special direction as primary
Secondary irreps (3rd (9/5,0,0) and 5th (1,0,0) harmonics) are also present.

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

NdCu₂ (#1.1.132)

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

NdCu2 (#1.1.132)

NdCu₂ (#1.1.132)