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+1/2,+1	{ 2₀₀₁ \| 0 0 0 1/2 }
3	-x2,x1,x3,x4+1/4,+1	{ 4⁺₀₀₁ \| 0 0 0 1/4 }
4	x2,-x1,x3,x4+3/4,+1	{ 4^-₀₀₁ \| 0 0 0 3/4 }
(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+1/2,+1	{ 2₀₀₁ \| 1/2 1/2 1/2 1/2 }
7	-x2+1/2,x1+1/2,x3+1/2,x4+1/4,+1	{ 4⁺₀₀₁ \| 1/2 1/2 1/2 1/4 }
8	x2+1/2,-x1+1/2,x3+1/2,x4+3/4,+1	{ 4^-₀₀₁ \| 1/2 1/2 1/2 3/4 }
(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	{ 2'₀₀₁ \| 0 }
11	-x2,x1,x3,x4+3/4,-1	{ 4'⁺₀₀₁ \| 0 0 0 3/4 }
12	x2,-x1,x3,x4+1/4,-1	{ 4'^-₀₀₁ \| 0 0 0 1/4 }
(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	{ 2'₀₀₁ \| 1/2 1/2 1/2 0 }
15	-x2+1/2,x1+1/2,x3+1/2,x4+3/4,-1	{ 4'⁺₀₀₁ \| 1/2 1/2 1/2 3/4 }
16	x2+1/2,-x1+1/2,x3+1/2,x4+1/4,-1	{ 4'^-₀₀₁ \| 1/2 1/2 1/2 1/4 }

N	(x,y,z)	Seitz notation
1	x,y,z,+1	1
2	-x,-y,z,+1	2₀₀₁
3	-y,x,z,+1	4⁺₀₀₁
4	y,-x,z,+1	4^-₀₀₁
1' + set click here to show and hide
5	x,y,z,-1	1'
6	-x,-y,z,-1	2'₀₀₁
7	-y,x,z,-1	4'⁺₀₀₁
8	y,-x,z,-1	4'^-₀₀₁

Label	Atom type	y	z	Multiplicity
Au1	Au	0	0.631	2
Al1	Al	0	0.407	2
Al2	Al	0.5	0.258	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
Ce1	M_ysin1	-M_xsin1	0	0.0	1.05(9)	0.0	M_xsin1	M_ysin1	0	-1.05(9)	0.0	0.0

Atom	x	y	z
1	0.00000	0.00000	0.00000
(1/2,1/2,1/2,0) + set click here to show and hide
2	0.50000	0.50000	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_ysin1	-M_xsin1	0	0.0	1.05000	0.0	M_xsin1	M_ysin1	0	-1.05000	0.0	0.0
(1/2,1/2,1/2,0) + set click here to show and hide
2	M_ysin1	-M_xsin1	0	0.0	1.05000	0.0	M_xsin1	M_ysin1	0	-1.05000	0.0	0.0

Atom	x	y	z
1	0.00000	0.00000	0.63100
(1/2,1/2,1/2,0) + set click here to show and hide
2	0.50000	0.50000	0.13100

Atom	x	y	z
1	0.00000	0.00000	0.40700
(1/2,1/2,1/2,0) + set click here to show and hide
2	0.50000	0.50000	0.90700

Atom	x	y	z
1	0.00000	0.50000	0.25800
2	0.50000	0.00000	0.25800
(1/2,1/2,1/2,0) + set click here to show and hide
3	0.50000	0.00000	0.75800
4	0.00000	0.50000	0.75800

Reference: D.T. Adroja, C. de la Fuente, A. Fraile, A.D. Hillier, A. Daoud-Aladine, W. Kockelmann, J.W. Taylor, M.M. Koza, E. Burzur, F. Luis, J.I. Arnaudas and A. del Moral, Physical Review B (2015) 91 134425.
DOI: 10.1103/physrevb.91.134425
Atomic positions from: same reference

Parent space group (paramagnetic phase): I4mm (#107)
Propagation vector: k1 (0.000000, 0.000000, 0.52)

Transition Temperature: 1.2 K
Experiment Temperature: 0.3 K

Lattice parameters of the basic unit cell:
4.3172 4.3172 10.8090 90 90 90
Transformation from parent structure: (a,b,c;0,0,0)
    [View matrix form]

Magnetic Superspace Group: I41'(00γ)qs
    [View symmetry operations]

Magnetic Point Group: 41' (9.2.30)
    [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
Ce1	Ce	0	0	0	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	M_ysin1	-M_xsin1	0	0.0	1.05(9)	0.0	M_xsin1	M_ysin1	0	-1.05(9)	0.0	0.0

Atom	x	y	z
1	0.00000	0.00000	0.00000
(1/2,1/2,1/2,0) + set click here to show and hide
2	0.50000	0.50000	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_ysin1	-M_xsin1	0	0.0	1.05000	0.0	M_xsin1	M_ysin1	0	-1.05000	0.0	0.0
(1/2,1/2,1/2,0) + set click here to show and hide
2	M_ysin1	-M_xsin1	0	0.0	1.05000	0.0	M_xsin1	M_ysin1	0	-1.05000	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
mLD5LD5	2	4	special	primary	1

Comments:

NPD
positional structure from a measurement at 9K

Comments (symmetry):

1k incommensurate magnetic structure
k-maximal symmetry (4 possible)
active irrep 4-dim (4 alternative MSSGs possible for the same irrep)
the arbitrary modulation phase allowed by the MSSG has been chosen choosing the moment orientation of the Ce atom at the origin.
Symmetry-protected circular helix spin modulation.
Equivalent twin related configuration with opposite chirality, and enantiomorphic MSSG exists.

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

CeAuAl₃ (#1.1.33)

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

CeAuAl3 (#1.1.33)

CeAuAl₃ (#1.1.33)