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	-x2,x1-x2,x3,x4+1/3,+1	{ 3⁺₀₀₁ \| 0 0 0 1/3 }
3	-x1+x2,-x1,x3,x4+2/3,+1	{ 3^-₀₀₁ \| 0 0 0 2/3 }
4	-x1,-x2,x3,x4+1/2,+1	{ 2₀₀₁ \| 0 0 0 1/2 }
5	x2,-x1+x2,x3,x4+5/6,+1	{ 6^-₀₀₁ \| 0 0 0 5/6 }
6	x1-x2,x1,x3,x4+1/6,+1	{ 6⁺₀₀₁ \| 0 0 0 1/6 }
7	x2,x1,-x3,-x4+5/6,-1	{ 2'₁₁₀ \| 0 0 0 5/6 }
8	x1-x2,-x2,-x3,-x4+1/2,-1	{ 2'₁₀₀ \| 0 0 0 1/2 }
9	-x1,-x1+x2,-x3,-x4+1/6,-1	{ 2'₀₁₀ \| 0 0 0 1/6 }
10	-x2,-x1,-x3,-x4+1/3,-1	{ 2'_1-10 \| 0 0 0 1/3 }
11	-x1+x2,x2,-x3,-x4,-1	{ 2'₁₂₀ \| 0 }
12	x1,x1-x2,-x3,-x4+2/3,-1	{ 2'₂₁₀ \| 0 0 0 2/3 }

N	(x,y,z)	Seitz notation
1	x,y,z,+1	1
2	-y,x-y,z,+1	3⁺₀₀₁
3	-x+y,-x,z,+1	3^-₀₀₁
4	-x,-y,z,+1	2₀₀₁
5	y,-x+y,z,+1	6^-₀₀₁
6	x-y,x,z,+1	6⁺₀₀₁
7	y,x,-z,-1	2'₁₁₀
8	x-y,-y,-z,-1	2'₁₀₀
9	-x,-x+y,-z,-1	2'₀₁₀
10	-y,-x,-z,-1	2'_1-10
11	-x+y,y,-z,-1	2'₁₂₀
12	x,x-y,-z,-1	2'₂₁₀

Label	Atom type	x	y	z	Multiplicity
Ge1	Ge	0.333333	0.666667	0	2
Ge2	Ge	0.333333	0.666667	0.5	2
Ge3	Ge	0	0	0.3447	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
Dy1	√3M_xsin1	0	0	6.195546	0.0	0.0	M_xsin1	2M_xsin1	0	3.577	7.154	0.0
Mn1	M_xcos1	M_ycos1	0	-1.877	-0.206	0.0	M_xsin1	M_ysin1	0	-0.846	-2.049	0.0

Atom	x	y	z	Symmetry constraints on M	M_0x	M_0y	M_0z
1	0.00000	0.00000	0.00000	0,0,m_z	0.00000	0.00000	3.93200

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	√3M_xsin1	0	0	6.19555	0.0	0.0	M_xsin1	2M_xsin1	0	3.57700	7.15400	0.0

Atom	x	y	z	Symmetry constraints on M	M_0z
1	0.50000	0.00000	0.25100	0,0,m_z	-1.14900
2	0.00000	0.50000	0.25100	0,0,m_z	-1.14900
3	0.50000	0.50000	0.25100	0,0,m_z	-1.14900
4	0.00000	0.50000	0.74900	0,0,m_z	-1.14900
5	0.50000	0.00000	0.74900	0,0,m_z	-1.14900
6	0.50000	0.50000	0.74900	0,0,m_z	-1.14900

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	-1.87700	-0.20600	0.0	M_xsin1	M_ysin1	0	-0.84600	-2.04900	0.0
2	1/2M_ycos1+√3/2M_ysin1	-1/2M_xcos1+1/2M_ycos1-√3/2M_xsin1+√3/2M_ysin1	0	-1.87749	-0.20633	0.0	-√3/2M_ycos1+1/2M_ysin1	√3/2M_xcos1-√3/2M_ycos1-1/2M_xsin1+1/2M_ysin1	0	-0.84610	-2.04863	0.0
3	1/2M_xcos1-1/2M_ycos1-√3/2M_xsin1+√3/2M_ysin1	1/2M_xcos1-√3/2M_xsin1	0	-1.87733	-0.20584	0.0	√3/2M_xcos1-√3/2M_ycos1+1/2M_xsin1-1/2M_ysin1	√3/2M_xcos1+1/2M_xsin1	0	-0.84563	-2.04853	0.0
4	-1/2M_ycos1+√3/2M_ysin1	-1/2M_xcos1+√3/2M_xsin1	0	-1.67149	0.20584	0.0	√3/2M_ycos1+1/2M_ysin1	√3/2M_xcos1+1/2M_xsin1	0	-1.20290	-2.04853	0.0
5	M_xcos1-M_ycos1	-M_ycos1	0	-1.67100	0.20600	0.0	-M_xsin1+M_ysin1	M_ysin1	0	-1.20300	-2.04900	0.0
6	1/2M_xcos1+√3/2M_xsin1	1/2M_xcos1-1/2M_ycos1+√3/2M_xsin1-√3/2M_ysin1	0	-1.67116	0.20633	0.0	√3/2M_xcos1-1/2M_xsin1	√3/2M_xcos1-√3/2M_ycos1-1/2M_xsin1+1/2M_ysin1	0	-1.20253	-2.04863	0.0

Atom	x	y	z
1	0.33333	0.66667	0.00000
2	0.66667	0.33333	0.00000

Atom	x	y	z
1	0.33333	0.66667	0.50000
2	0.66667	0.33333	0.50000

Atom	x	y	z
1	0.00000	0.00000	0.34470
2	0.00000	0.00000	0.65530

Reference: J. Rodriguez-Carvajal and F. Bouree, EPJ Web of Conferences (2012) 22 00010.
DOI: 10.1051/epjconf/20122200010
Atomic positions from: ICSD #57229

Parent space group (paramagnetic phase): P6/mmm (#191)
Propagation vector: k1 (0.000000, 0.000000, 0.1651)

Lattice parameters of the basic unit cell:
5.2081 5.2081 8.1522 90 90 120
Transformation from parent structure: (a,b,c;0,0,0)
    [View matrix form]

Magnetic Superspace Group: P62'2'(00γ)h00
    [View symmetry operations]

Magnetic Point Group: 62'2' (24.4.90)
    [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 and magnetic moments of symmetry independent atoms

Label	Atom type	x	y	z	Multiplicity	Symmetry constraints on M	M_0x	M_0y	M_0z	\|M\|
Dy1	Dy	0	0	0	1	0,0,m_z	0.0	0.0	3.932	3.93
Mn1	Mn	0.5	0	0.2510	6	0,0,m_z	0.0	0.0	-1.149	1.15

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	√3M_xsin1	0	0	6.195546	0.0	0.0	M_xsin1	2M_xsin1	0	3.577	7.154	0.0
Mn1	M_xcos1	M_ycos1	0	-1.877	-0.206	0.0	M_xsin1	M_ysin1	0	-0.846	-2.049	0.0

Atom	x	y	z	Symmetry constraints on M	M_0x	M_0y	M_0z
1	0.00000	0.00000	0.00000	0,0,m_z	0.00000	0.00000	3.93200

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	√3M_xsin1	0	0	6.19555	0.0	0.0	M_xsin1	2M_xsin1	0	3.57700	7.15400	0.0

Atom	x	y	z	Symmetry constraints on M	M_0z
1	0.50000	0.00000	0.25100	0,0,m_z	-1.14900
2	0.00000	0.50000	0.25100	0,0,m_z	-1.14900
3	0.50000	0.50000	0.25100	0,0,m_z	-1.14900
4	0.00000	0.50000	0.74900	0,0,m_z	-1.14900
5	0.50000	0.00000	0.74900	0,0,m_z	-1.14900
6	0.50000	0.50000	0.74900	0,0,m_z	-1.14900

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	-1.87700	-0.20600	0.0	M_xsin1	M_ysin1	0	-0.84600	-2.04900	0.0
2	1/2M_ycos1+√3/2M_ysin1	-1/2M_xcos1+1/2M_ycos1-√3/2M_xsin1+√3/2M_ysin1	0	-1.87749	-0.20633	0.0	-√3/2M_ycos1+1/2M_ysin1	√3/2M_xcos1-√3/2M_ycos1-1/2M_xsin1+1/2M_ysin1	0	-0.84610	-2.04863	0.0
3	1/2M_xcos1-1/2M_ycos1-√3/2M_xsin1+√3/2M_ysin1	1/2M_xcos1-√3/2M_xsin1	0	-1.87733	-0.20584	0.0	√3/2M_xcos1-√3/2M_ycos1+1/2M_xsin1-1/2M_ysin1	√3/2M_xcos1+1/2M_xsin1	0	-0.84563	-2.04853	0.0
4	-1/2M_ycos1+√3/2M_ysin1	-1/2M_xcos1+√3/2M_xsin1	0	-1.67149	0.20584	0.0	√3/2M_ycos1+1/2M_ysin1	√3/2M_xcos1+1/2M_xsin1	0	-1.20290	-2.04853	0.0
5	M_xcos1-M_ycos1	-M_ycos1	0	-1.67100	0.20600	0.0	-M_xsin1+M_ysin1	M_ysin1	0	-1.20300	-2.04900	0.0
6	1/2M_xcos1+√3/2M_xsin1	1/2M_xcos1-1/2M_ycos1+√3/2M_xsin1-√3/2M_ysin1	0	-1.67116	0.20633	0.0	√3/2M_xcos1-1/2M_xsin1	√3/2M_xcos1-√3/2M_ycos1-1/2M_xsin1+1/2M_ysin1	0	-1.20253	-2.04863	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
mGM2+	1	1		primary	2
mDT6	2	4	special	primary	5

Comments:

NPD
See also Schobinger-Papamantellos et al., Journal of Alloys and Compounds, 215, 111 (1994); J. Magn. Magn. Mat. 150 , 311 (1995).

Comments (symmetry):

1k incommensurate magnetic structure
2 irreps active
incommensurate irrep is 4-dim: 5 distinct superspace groups possible for this irrep.

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

DyMn₆Ge₆ (#1.1.10)

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

DyMn6Ge6 (#1.1.10)

DyMn₆Ge₆ (#1.1.10)