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	-x1,-x2,-x3,-x4+1/2,+1	{ -1 \| 0 0 0 1/2 }
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+1/2,+1	{ 2₀₀₁ \| 1/2 1/2 1/2 1/2 }
7	-x1+1/2,-x2+1/2,-x3+1/2,-x4+1/2,+1	{ -1 \| 1/2 1/2 1/2 1/2 }
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	{ 2'₀₀₁ \| 0 }
11	-x1,-x2,-x3,-x4,-1	{ -1' \| 0 }
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	{ 2'₀₀₁ \| 1/2 1/2 1/2 0 }
15	-x1+1/2,-x2+1/2,-x3+1/2,-x4,-1	{ -1' \| 1/2 1/2 1/2 0 }
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	Mg	0	0.5	0	2
Mg2	Mg	-0.5	0	0	2
Pb1	Pb	0	0	0.1340(10)	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_xcos1	M_ycos1	0	-0.87	0.87	0.0	0	0	M_zsin1	0.0	0.0	0.0

Atom	x	y	z
1	0.00000	0.00000	0.33000
2	0.00000	0.00000	0.67000
(1/2,1/2,1/2,0) + set click here to show and hide
3	0.50000	0.50000	0.83000
4	0.50000	0.50000	0.17000

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	M_ycos1	0	-0.87000	0.87000	0.0	0	0	M_zsin1	0.0	0.0	0.0
2	-M_xcos1	-M_ycos1	0	0.87000	-0.87000	0.0	0	0	M_zsin1	0.0	0.0	0.0
(1/2,1/2,1/2,0) + set click here to show and hide
3	M_xcos1	M_ycos1	0	-0.87000	0.87000	0.0	0	0	M_zsin1	0.0	0.0	0.0
4	-M_xcos1	-M_ycos1	0	0.87000	-0.87000	0.0	0	0	M_zsin1	0.0	0.0	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	0.13400
2	0.00000	0.00000	0.86600
(1/2,1/2,1/2,0) + set click here to show and hide
3	0.50000	0.50000	0.63400
4	0.50000	0.50000	0.36600

Reference: P. Lemoine, A. Verniere, G. Venturini, J. MarÃªche, S. Capelli and B. Malaman, 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 (0.448000, 0.500000, 0.000000)

Transition Temperature: 7 K
Experiment Temperature: 2 K

Lattice parameters of the basic unit cell:
4.5380(5) 4.5380(5) 16.339(4) 90 90 90
Transformation from parent structure: (a,b,c;0,0,0)
    [View matrix form]

Magnetic Superspace Group: I112/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

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     [Show all the atoms]

Average atomic positions of symmetry independent atoms

Label	Atom type	x	y	z	Multiplicity
Ce1	Ce	0	0	0.3300(10)	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
Ce1	M_xcos1	M_ycos1	0	-0.87	0.87	0.0	0	0	M_zsin1	0.0	0.0	0.0

Atom	x	y	z
1	0.00000	0.00000	0.33000
2	0.00000	0.00000	0.67000
(1/2,1/2,1/2,0) + set click here to show and hide
3	0.50000	0.50000	0.83000
4	0.50000	0.50000	0.17000

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	M_ycos1	0	-0.87000	0.87000	0.0	0	0	M_zsin1	0.0	0.0	0.0
2	-M_xcos1	-M_ycos1	0	0.87000	-0.87000	0.0	0	0	M_zsin1	0.0	0.0	0.0
(1/2,1/2,1/2,0) + set click here to show and hide
3	M_xcos1	M_ycos1	0	-0.87000	0.87000	0.0	0	0	M_zsin1	0.0	0.0	0.0
4	-M_xcos1	-M_ycos1	0	0.87000	-0.87000	0.0	0	0	M_zsin1	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	action	number of modes
mC1	1	8	primary	3

Comments:

NPD
it coexists with another phase with commensurate propagation vector k=(1/2,1/2,0) (see entry # 1.142)
sinusoidal incommensurate magnetic modulation
amplitude of Ce spin modulation: 1.23(11)

Comments (symmetry):

1k magnetic structure
k-maximal magnetic symmetry (2 possible)
symmetry allows an arbitrary direction on the ab plane for the cosine component of the Ce spin modulation, and a non-zero sine component along c
The origin along x4 of the MSSG has been shifted with respect to a simpler choice, in order to have the Ce spin modulation on the ab plane described by a cosine function, instead of a sine.

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

CeMgPb (#1.1.27)