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,x1,x3+1/2,x4+5/6,+1	{ 6⁺₀₀₁ \| 0 0 1/2 5/6 }
3	-x2,x1-x2,x3,x4+2/3,+1	{ 3⁺₀₀₁ \| 0 0 0 2/3 }
4	-x1,-x2,x3+1/2,x4+1/2,+1	{ 2₀₀₁ \| 0 0 1/2 1/2 }
5	-x1+x2,-x1,x3,x4+1/3,+1	{ 3^-₀₀₁ \| 0 0 0 1/3 }
6	x2,-x1+x2,x3+1/2,x4+1/6,+1	{ 6^-₀₀₁ \| 0 0 1/2 1/6 }
7	x1-x2,-x2,-x3,-x4,+1	{ 2₁₀₀ \| 0 }
8	x1,x1-x2,-x3+1/2,-x4+5/6,+1	{ 2₂₁₀ \| 0 0 1/2 5/6 }
9	x2,x1,-x3,-x4+2/3,+1	{ 2₁₁₀ \| 0 0 0 2/3 }
10	-x1+x2,x2,-x3+1/2,-x4+1/2,+1	{ 2₁₂₀ \| 0 0 1/2 1/2 }
11	-x1,-x1+x2,-x3,-x4+1/3,+1	{ 2₀₁₀ \| 0 0 0 1/3 }
12	-x2,-x1,-x3+1/2,-x4+1/6,+1	{ 2_1-10 \| 0 0 1/2 1/6 }
(0,0,0,1/2)' + set click here to show and hide
13	x1,x2,x3,x4+1/2,-1	{ 1' \| 0 0 0 1/2 }
14	x1-x2,x1,x3+1/2,x4+1/3,-1	{ 6'⁺₀₀₁ \| 0 0 1/2 1/3 }
15	-x2,x1-x2,x3,x4+1/6,-1	{ 3'⁺₀₀₁ \| 0 0 0 1/6 }
16	-x1,-x2,x3+1/2,x4,-1	{ 2'₀₀₁ \| 0 0 1/2 0 }
17	-x1+x2,-x1,x3,x4+5/6,-1	{ 3'^-₀₀₁ \| 0 0 0 5/6 }
18	x2,-x1+x2,x3+1/2,x4+2/3,-1	{ 6'^-₀₀₁ \| 0 0 1/2 2/3 }
19	x1-x2,-x2,-x3,-x4+1/2,-1	{ 2'₁₀₀ \| 0 0 0 1/2 }
20	x1,x1-x2,-x3+1/2,-x4+1/3,-1	{ 2'₂₁₀ \| 0 0 1/2 1/3 }
21	x2,x1,-x3,-x4+1/6,-1	{ 2'₁₁₀ \| 0 0 0 1/6 }
22	-x1+x2,x2,-x3+1/2,-x4,-1	{ 2'₁₂₀ \| 0 0 1/2 0 }
23	-x1,-x1+x2,-x3,-x4+5/6,-1	{ 2'₀₁₀ \| 0 0 0 5/6 }
24	-x2,-x1,-x3+1/2,-x4+2/3,-1	{ 2'_1-10 \| 0 0 1/2 2/3 }

N	(x,y,z)	Seitz notation
1	x,y,z,+1	1
2	x-y,x,z,+1	6⁺₀₀₁
3	-y,x-y,z,+1	3⁺₀₀₁
4	-x,-y,z,+1	2₀₀₁
5	-x+y,-x,z,+1	3^-₀₀₁
6	y,-x+y,z,+1	6^-₀₀₁
7	x-y,-y,-z,+1	2₁₀₀
8	x,x-y,-z,+1	2₂₁₀
9	y,x,-z,+1	2₁₁₀
10	-x+y,y,-z,+1	2₁₂₀
11	-x,-x+y,-z,+1	2₀₁₀
12	-y,-x,-z,+1	2_1-10
1' + set click here to show and hide
13	x,y,z,-1	1'
14	x-y,x,z,-1	6'⁺₀₀₁
15	-y,x-y,z,-1	3'⁺₀₀₁
16	-x,-y,z,-1	2'₀₀₁
17	-x+y,-x,z,-1	3'^-₀₀₁
18	y,-x+y,z,-1	6'^-₀₀₁
19	x-y,-y,-z,-1	2'₁₀₀
20	x,x-y,-z,-1	2'₂₁₀
21	y,x,-z,-1	2'₁₁₀
22	-x+y,y,-z,-1	2'₁₂₀
23	-x,-x+y,-z,-1	2'₀₁₀
24	-y,-x,-z,-1	2'_1-10

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
Dy1	M_xcos1	0	0	9.5	0.0	0.0	-0.57735M_xcos1	-1.15470M_xcos1	0	-5.48483	-10.9697	0.0

Atom	x	y	z
1	0.33333	0.66667	0.25000
2	0.66666	0.33333	0.75000

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	0	0	9.50000	0.0	0.0	-0.57735M_xcos1	-1.15470M_xcos1	0	-5.48483	-10.96970	0.0
2	1.00000M_xcos1	0.00000M_xcos1	0	9.50004	0.0	0.0	-0.57735M_xcos1	-1.15470M_xcos1	0	-5.48481	-10.96966	0.0

Reference: M. K. Wilkinson, W. C. Koehler, E. O. Wollan, J. W. Cable, Journal of Applied Physics (1961) 32 48S - 49S
DOI: 10.1063/1.2000493
Atomic positions from: ICSD #53357

Parent space group (paramagnetic phase): P6₃/mmc (#194)
Propagation vector: k1 (0.00000, 0.00000, 0.15)

Transition Temperature: 179 K
Experiment Temperature: 100 K

Lattice parameters of the basic unit cell:
3.59030 3.59030 5.64750 90.00000 90.00000 120.00000
Transformation from parent structure: (a,b,c;0,0,0)
    [View matrix form]

Magnetic Superspace Group: P6_3221'(0,0,g)h00s
    [View symmetry operations]

Magnetic Point Group: 6221' (24.2.88)
    [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
Dy1	Dy	0.33333	0.66667	0.25000	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
Dy1	M_xcos1	0	0	9.5	0.0	0.0	-0.57735M_xcos1	-1.15470M_xcos1	0	-5.48483	-10.9697	0.0

Atom	x	y	z
1	0.33333	0.66667	0.25000
2	0.66666	0.33333	0.75000

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	0	0	9.50000	0.0	0.0	-0.57735M_xcos1	-1.15470M_xcos1	0	-5.48483	-10.96970	0.0
2	1.00000M_xcos1	0.00000M_xcos1	0	9.50004	0.0	0.0	-0.57735M_xcos1	-1.15470M_xcos1	0	-5.48481	-10.96966	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
mDT6	2	4	special	primary	1

Comments:

NPD
Position structure not specified. Here one at room temperature retrieved from the ICSD is used.
Values of propagation vector and Dy moment only approximate, estimated from the figures of the paper and the text comments.
Below 87K a FM is observed with the Dy moments on the ab plane.

Comments (symmetry):

1k incommensurate structure
4-dim (k,-k) full irrep along a special direction as primary

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

Dy (#1.1.135)