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	{ 2₀₀₁ \| 0 }
3	-x1+1/2,x2+1/2,-x3,-x4+1/2,+1	{ 2₀₁₀ \| 1/2 1/2 0 1/2 }
4	x1+1/2,-x2+1/2,-x3,x4+1/2,+1	{ 2₁₀₀ \| 1/2 1/2 0 1/2 }
5	-x1,-x2,-x3,-x4,+1	{ -1 \| 0 }
6	x1,x2,-x3,x4,+1	{ m₀₀₁ \| 0 }
7	x1+1/2,-x2+1/2,x3,x4+1/2,+1	{ m₀₁₀ \| 1/2 1/2 0 1/2 }
8	-x1+1/2,x2+1/2,x3,-x4+1/2,+1	{ m₁₀₀ \| 1/2 1/2 0 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,-1	{ 2'₀₀₁ \| 0 0 0 1/2 }
11	-x1+1/2,x2+1/2,-x3,-x4,-1	{ 2'₀₁₀ \| 1/2 1/2 0 0 }
12	x1+1/2,-x2+1/2,-x3,x4,-1	{ 2'₁₀₀ \| 1/2 1/2 0 0 }
13	-x1,-x2,-x3,-x4+1/2,-1	{ -1' \| 0 0 0 1/2 }
14	x1,x2,-x3,x4+1/2,-1	{ m'₀₀₁ \| 0 0 0 1/2 }
15	x1+1/2,-x2+1/2,x3,x4,-1	{ m'₀₁₀ \| 1/2 1/2 0 0 }
16	-x1+1/2,x2+1/2,x3,-x4,-1	{ m'₁₀₀ \| 1/2 1/2 0 0 }

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

Label	Atom type	x	y	z	Multiplicity
Pd1	Pd	0.37340(10)	0.8734	0	4
Sn1	Sn	0	0	0	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	0	0	M_zcos1	0.0	0.0	1.70(5)	0	0	M_zsin1	0.0	0.0	0.0

Atom	x	y	z
1	0.17810	0.67810	0.50000
2	0.82190	0.32190	0.50000
3	0.32190	0.17810	0.50000
4	0.67810	0.82190	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	0	0	M_zcos1	0.0	0.0	1.70000	0	0	M_zsin1	0.0	0.0	0.0
2	0	0	M_zcos1	0.0	0.0	1.70000	0	0	-M_zsin1	0.0	0.0	0.0
3	0	0	M_zcos1	0.0	0.0	1.70000	0	0	-M_zsin1	0.0	0.0	0.0
4	0	0	M_zcos1	0.0	0.0	1.70000	0	0	M_zsin1	0.0	0.0	0.0

Atom	x	y
1	0.37340	0.87340
2	0.62660	0.12660
3	0.12660	0.37340
4	0.87340	0.62660

Atom	x	y	z
1	0.00000	0.00000	0.00000
2	0.50000	0.50000	0.00000

Reference: Rodriguez-Carvajal, J et al., EPJ Web of Conferences (2012) 22 00010
DOI: 10.1051/epjconf/20122200010
Atomic positions from: ICSD #107316

Parent space group (paramagnetic phase): P4/mbm (#127)
Propagation vector: k1 (0.105, 0.00000, 0.000000)

Transition Temperature: 4.8 K
Experiment Temperature: 4 K

Lattice parameters of the basic unit cell:
7.7620(5) 7.7620(5) 3.9300(10) 90 90 90
Transformation from parent structure: (a,b,c;0,0,0)
    [View matrix form]

Magnetic Superspace Group: Pbam1'(a00)0s0s
    [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

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     [Show all the atoms]

Average atomic positions of symmetry independent atoms

Label	Atom type	x	y	z	Multiplicity
Ce1	Ce	0.17810(10)	0.6781	0.5	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	0	0	M_zcos1	0.0	0.0	1.70(5)	0	0	M_zsin1	0.0	0.0	0.0

Atom	x	y	z
1	0.17810	0.67810	0.50000
2	0.82190	0.32190	0.50000
3	0.32190	0.17810	0.50000
4	0.67810	0.82190	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	0	0	M_zcos1	0.0	0.0	1.70000	0	0	M_zsin1	0.0	0.0	0.0
2	0	0	M_zcos1	0.0	0.0	1.70000	0	0	-M_zsin1	0.0	0.0	0.0
3	0	0	M_zcos1	0.0	0.0	1.70000	0	0	-M_zsin1	0.0	0.0	0.0
4	0	0	M_zcos1	0.0	0.0	1.70000	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
mDT4	1	4	primary	2

Comments:

NSD
See also Laffargue et al. Solid State Communic. 100 (1996) 575-579.
Simple transversal modulation.

Comments (symmetry):

1k incommensurate magnetic structure
Active small irrep 1-dim. This irrep does NOT split Ce atoms into two orbits if the irrep is taken into account for the operations changing k into -k.
Symmetry correlates modulations of all Ce atoms. Only one Ce atom is independent. But modulations of Ce atoms related by inversion are not symmetry forced to be in phase.
Two free parameters in the magnetic modulation.

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

Ce₂Pd₂Sn (#1.1.9)

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

Ce2Pd2Sn (#1.1.9)

Ce₂Pd₂Sn (#1.1.9)