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

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

Label	Atom type	x	y	z	Multiplicity
Pd1_1	Pd	0.00000	0.00000	0.00000	2
Pd2_1	Pd	0.16667	0.50000	0.50000	4
Al1_1	Al	0.11400	0.88600	0.50000	4
Al1_2	Al	0.00000	0.22800	0.50000	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
Ce1_1	0	0	M_zc1	0.0	0.0	1.58(2)	M_xs1	M_ys1	0	0.0	0.0	0.0
Ce1_2	0	0	0	0.0	0.0	0.0	M_xs1	0	0	0.0	0.0	0.0

Atom	x	y	z
1	0.28925	0.71075	0.00000
(0,0,0,1/2)' + set click here to show and hide
2	0.71075	0.71075	0.00000
(1/2,1/2,0,1/2) + set click here to show and hide
3	0.78925	0.21075	0.00000
(1/2,1/2,0,0)' + set click here to show and hide
4	0.21075	0.21075	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	0	0	M_zcos1	0.0	0.0	1.58000	M_xcos1+M_ysin1	M_ycos1+M_ysin1	0	0.0	0.0	0.0
(0,0,0,1/2)' + set click here to show and hide
2	0	0	-M_zcos1	0.0	0.0	-1.58000	M_xcos1+M_ysin1	-M_ycos1-M_ysin1	0	0.0	0.0	0.0
(1/2,1/2,0,1/2) + set click here to show and hide
3	0	0	-M_zcos1	0.0	0.0	-1.58000	-M_xcos1-M_ysin1	-M_ycos1-M_ysin1	0	0.0	0.0	0.0
(1/2,1/2,0,0)' + set click here to show and hide
4	0	0	M_zcos1	0.0	0.0	1.58000	-M_xcos1-M_ysin1	M_ycos1+M_ysin1	0	0.0	0.0	0.0

Atom	x	y	z
1	0.00000	0.57850	0.00000
(0,0,0,1/2)' + set click here to show and hide
2	0.50000	0.07850	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	0	0	0	0.0	0.0	0.0	M_xcos1+M_ysin1	0	0	0.0	0.0	0.0
(0,0,0,1/2)' + set click here to show and hide
2	0	0	0	0.0	0.0	0.0	-M_xcos1-M_ysin1	0	0	0.0	0.0	0.0

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

Atom	x	y	z
1	0.16667	0.50000	0.50000
(0,0,0,1/2)' + set click here to show and hide
2	0.83333	0.50000	0.50000
(1/2,1/2,0,1/2) + set click here to show and hide
3	0.66667	0.00000	0.50000
(1/2,1/2,0,0)' + set click here to show and hide
4	0.33333	0.00000	0.50000

Atom	x	y	z
1	0.11400	0.88600	0.50000
(0,0,0,1/2)' + set click here to show and hide
2	0.88600	0.88600	0.50000
(1/2,1/2,0,1/2) + set click here to show and hide
3	0.61400	0.38600	0.50000
(1/2,1/2,0,0)' + set click here to show and hide
4	0.38600	0.38600	0.50000

Atom	x	y	z
1	0.00000	0.22800	0.50000
(0,0,0,1/2)' + set click here to show and hide
2	0.50000	0.72800	0.50000

Reference: A. Donni, G. Ehlers, H. Maletta, P. Fischer, H. Kitazawa, M. Zolliker, J. Phys.: Condens. Matter (1996) 8 11213 - 11229
DOI: 10.1088/0953-8984/8/50/043
Atomic positions from: same reference

Parent space group (paramagnetic phase): P-62m (#189)
Propagation vector: k1 (0.00000, 0.00000, 0.350(1))

Transition Temperature: 2.7 K
Experiment Temperature: 1.5 K

Lattice parameters of the basic unit cell:
12.46211 7.19500 4.24000 90.00000 90.00000 90.00000
Transformation from parent structure: (2a+b,b,c;0,0,0)
    [View matrix form]

Magnetic Superspace Group: Xm2m.1'(0,0,g)000s
    [View symmetry operations]

Magnetic Point Group: mm2.1' (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

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     [Show all the atoms]

Average atomic positions of symmetry independent atoms

Label	Atom type	x	y	z	Multiplicity
Ce1_1	Ce	0.28925	0.71075	0.00000	4
Ce1_2	Ce	0.00000	0.57850	0.00000	2

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
Ce1_1	0	0	M_zc1	0.0	0.0	1.58(2)	M_xs1	M_ys1	0	0.0	0.0	0.0
Ce1_2	0	0	0	0.0	0.0	0.0	M_xs1	0	0	0.0	0.0	0.0

Atom	x	y	z
1	0.28925	0.71075	0.00000
(0,0,0,1/2)' + set click here to show and hide
2	0.71075	0.71075	0.00000
(1/2,1/2,0,1/2) + set click here to show and hide
3	0.78925	0.21075	0.00000
(1/2,1/2,0,0)' + set click here to show and hide
4	0.21075	0.21075	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	0	0	M_zcos1	0.0	0.0	1.58000	M_xcos1+M_ysin1	M_ycos1+M_ysin1	0	0.0	0.0	0.0
(0,0,0,1/2)' + set click here to show and hide
2	0	0	-M_zcos1	0.0	0.0	-1.58000	M_xcos1+M_ysin1	-M_ycos1-M_ysin1	0	0.0	0.0	0.0
(1/2,1/2,0,1/2) + set click here to show and hide
3	0	0	-M_zcos1	0.0	0.0	-1.58000	-M_xcos1-M_ysin1	-M_ycos1-M_ysin1	0	0.0	0.0	0.0
(1/2,1/2,0,0)' + set click here to show and hide
4	0	0	M_zcos1	0.0	0.0	1.58000	-M_xcos1-M_ysin1	M_ycos1+M_ysin1	0	0.0	0.0	0.0

Atom	x	y	z
1	0.00000	0.57850	0.00000
(0,0,0,1/2)' + set click here to show and hide
2	0.50000	0.07850	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	0	0	0	0.0	0.0	0.0	M_xcos1+M_ysin1	0	0	0.0	0.0	0.0
(0,0,0,1/2)' + set click here to show and hide
2	0	0	0	0.0	0.0	0.0	-M_xcos1-M_ysin1	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
mU1	2	6	special	primary	4

Comments:

NPD
Position structure from a determination at 7.5K
The propagation vector is of type (1/2,0,g) with respect to the parent hexagonal basis. But here we use a supercentered orthogonal unit cell for the basic structure to get rid of the fractional component, and the modulation wave vector in this basis becomes (0,0,g) with a centering (1/2,1/2,0,1/2) in superspace.

Comments (symmetry):

1k incommensurate magnetic structure
k-maximal magnetic symmetry
2-dim small irrep as primary
The irrep star has 3 (k,-k) pairs of vectors. Possible multi-k modulations involving more than one these pairs, which could equally fit the data were not considered.
The MSSG (or the corresponding irrep) forbids any moment along c for Ce1_2, but it allows a moment component along the direction (2,1,0) in the basal plane of the hexagonal basis, just in quadrature with the mz modulation of Ce1_1. Not clear if this degree of freedom was tested.
The magnetic modulation breaks the inversion of the structure, the MSSG being polar along the b direction of the hexagonal parent basis. Of course, two other domain-equivalent orientations of the spin arrangement according to the other two pairs of k-vectors of the irrep star are possible.

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

CePdAl (#1.1.144)