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+1/2,-x2+1/2,-x3+1/2,-x4,+1	{ 2₁₀₀ \| 1/2 1/2 1/2 0 }
3	-x1+1/2,x2+1/2,-x3+1/2,-x4+1/2,+1	{ 2₀₁₀ \| 1/2 1/2 1/2 1/2 }
4	-x1,-x2,x3,x4+1/2,+1	{ 2₀₀₁ \| 0 0 0 1/2 }
5	-x2,-x1,-x3,-x4+3/4,+1	{ 2_1-10 \| 0 0 0 3/4 }
6	-x2+1/2,x1+1/2,x3+1/2,x4+3/4,+1	{ 4⁺₀₀₁ \| 1/2 1/2 1/2 3/4 }
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,x1,-x3,-x4+1/4,+1	{ 2₁₁₀ \| 0 0 0 1/4 }
(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+1/2,-x2+1/2,-x3+1/2,-x4+1/2,-1	{ 2'₁₀₀ \| 1/2 1/2 1/2 1/2 }
11	-x1+1/2,x2+1/2,-x3+1/2,-x4,-1	{ 2'₀₁₀ \| 1/2 1/2 1/2 0 }
12	-x1,-x2,x3,x4,-1	{ 2'₀₀₁ \| 0 }
13	-x2,-x1,-x3,-x4+1/4,-1	{ 2'_1-10 \| 0 0 0 1/4 }
14	-x2+1/2,x1+1/2,x3+1/2,x4+1/4,-1	{ 4'⁺₀₀₁ \| 1/2 1/2 1/2 1/4 }
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,x1,-x3,-x4+3/4,-1	{ 2'₁₁₀ \| 0 0 0 3/4 }

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	-y,-x,-z,+1	2_1-10
6	-y,x,z,+1	4⁺₀₀₁
7	y,-x,z,+1	4^-₀₀₁
8	y,x,-z,+1	2₁₁₀
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	-y,-x,-z,-1	2'_1-10
14	-y,x,z,-1	4'⁺₀₀₁
15	y,-x,z,-1	4'^-₀₀₁
16	y,x,-z,-1	2'₁₁₀

Label	Atom type	x	y	z	Multiplicity
O1	O	0.30460	0.30460	0.00000	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
Mn1	M_xcos1	M_ycos1	0	0.0	1.0	0.0	-M_ycos1	-M_xcos1	0	-1.0	0.0	0.0

Atom	x	y	z
1	0.00000	0.00000	0.00000
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_xcos1	M_ycos1	0	0.0	1.00000	0.0	-M_ycos1	-M_xcos1	0	-1.00000	0.0	0.0
2	M_xcos1	-M_ycos1	0	0.0	-1.00000	0.0	M_ycos1	-M_xcos1	0	1.00000	0.0	0.0

Atom	x	y	z
1	0.30460	0.30460	0.00000
2	0.80460	0.19540	0.50000
3	0.19540	0.80460	0.50000
4	0.69540	0.69540	0.00000

Reference: H. Sato, K. Wakiya, T. Enoki, T. Kiyama, Y. Wakabayashi, H. Nakao, Y. Murakami, Journal of the Physical Society of Japan (2001) 70 37 - 40
DOI: 10.1143/JPSJ.70.37
Atomic positions from: ICSD #73716

Parent space group (paramagnetic phase): P4₂/mnm (#136)
Propagation vector: k1 (0.00000, 0.00000, 0.29700)

Transition Temperature: 93 K

Lattice parameters of the basic unit cell:
4.40410 4.40410 2.87650 90.00000 90.00000 90.00000
Transformation from parent structure: (a,b,c;0,0,0)
    [View matrix form]

Magnetic Superspace Group: P4_22_121'(0,0,g)-q00s
    [View symmetry operations]

Magnetic Point Group: 4221' (12.2.41)
    [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
Mn1	Mn	0.00000	0.00000	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
Mn1	M_xcos1	M_ycos1	0	0.0	1.0	0.0	-M_ycos1	-M_xcos1	0	-1.0	0.0	0.0

Atom	x	y	z
1	0.00000	0.00000	0.00000
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_xcos1	M_ycos1	0	0.0	1.00000	0.0	-M_ycos1	-M_xcos1	0	-1.00000	0.0	0.0
2	M_xcos1	-M_ycos1	0	0.0	-1.00000	0.0	M_ycos1	-M_xcos1	0	1.00000	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
mLD5	2	4	special	primary	2

Comments:

XRSC
Mn moment magnitude is not determined. An arbitrary unit value is given here

Comments (symmetry):

1k incommensurate magnetic structure
k-maximal magnetic symmetry
4-dim irrep along a special direction as primary

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

MnO₂ (#1.1.111)

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

MnO2 (#1.1.111)

MnO₂ (#1.1.111)