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

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

Label	Atom type	x	y	z	Multiplicity
Sc1	Sc	0	0	0	2
Ge1	Ge	0.333333	0.666667	0.25	4
Ge2	Ge	0.333333	0.666667	0	4
Ge3	Ge	0	0	0.1693(8)	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	-0.0315	0.2514	0.0	M_xsin1	M_ysin1	0	-0.3084	-0.1814	0.0

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	-0.03150	0.25140	0.0	M_xsin1	M_ysin1	0	-0.30840	-0.18140	0.0
2	1/2M_ycos1+√3/2M_ysin1	-1/2M_xcos1+1/2M_ycos1-√3/2M_xsin1+√3/2M_ysin1	0	-0.03140	0.25144	0.0	-√3/2M_ycos1+1/2M_ysin1	√3/2M_xcos1-√3/2M_ycos1-1/2M_xsin1+1/2M_ysin1	0	-0.30842	-0.18150	0.0
3	1/2M_xcos1-1/2M_ycos1-√3/2M_xsin1+√3/2M_ysin1	1/2M_xcos1-√3/2M_xsin1	0	-0.03146	0.25133	0.0	√3/2M_xcos1-√3/2M_ycos1+1/2M_xsin1-1/2M_ysin1	√3/2M_xcos1+1/2M_xsin1	0	-0.30850	-0.18148	0.0
4	1/2M_ycos1-√3/2M_ysin1	1/2M_xcos1-√3/2M_xsin1	0	0.28280	0.25133	0.0	-√3/2M_ycos1-1/2M_ysin1	-√3/2M_xcos1-1/2M_xsin1	0	-0.12702	0.18148	0.0
5	-M_xcos1+M_ycos1	M_ycos1	0	0.28290	0.25140	0.0	M_xsin1-M_ysin1	-M_ysin1	0	-0.12700	0.18140	0.0
6	-1/2M_xcos1-√3/2M_xsin1	-1/2M_xcos1+1/2M_ycos1-√3/2M_xsin1+√3/2M_ysin1	0	0.28283	0.25144	0.0	-√3/2M_xcos1+1/2M_xsin1	-√3/2M_xcos1+√3/2M_ycos1+1/2M_xsin1-1/2M_ysin1	0	-0.12692	0.18150	0.0
(0,0,1/2,1/2)' + set click here to show and hide
7	M_xcos1	M_ycos1	0	-0.03150	0.25140	0.0	M_xsin1	M_ysin1	0	-0.30840	-0.18140	0.0
8	1/2M_ycos1+√3/2M_ysin1	-1/2M_xcos1+1/2M_ycos1-√3/2M_xsin1+√3/2M_ysin1	0	-0.03140	0.25144	0.0	-√3/2M_ycos1+1/2M_ysin1	√3/2M_xcos1-√3/2M_ycos1-1/2M_xsin1+1/2M_ysin1	0	-0.30842	-0.18150	0.0
9	1/2M_xcos1-1/2M_ycos1-√3/2M_xsin1+√3/2M_ysin1	1/2M_xcos1-√3/2M_xsin1	0	-0.03146	0.25133	0.0	√3/2M_xcos1-√3/2M_ycos1+1/2M_xsin1-1/2M_ysin1	√3/2M_xcos1+1/2M_xsin1	0	-0.30850	-0.18148	0.0
10	1/2M_ycos1-√3/2M_ysin1	1/2M_xcos1-√3/2M_xsin1	0	0.28280	0.25133	0.0	-√3/2M_ycos1-1/2M_ysin1	-√3/2M_xcos1-1/2M_xsin1	0	-0.12702	0.18148	0.0
11	-M_xcos1+M_ycos1	M_ycos1	0	0.28290	0.25140	0.0	M_xsin1-M_ysin1	-M_ysin1	0	-0.12700	0.18140	0.0
12	-1/2M_xcos1-√3/2M_xsin1	-1/2M_xcos1+1/2M_ycos1-√3/2M_xsin1+√3/2M_ysin1	0	0.28283	0.25144	0.0	-√3/2M_xcos1+1/2M_xsin1	-√3/2M_xcos1+√3/2M_ycos1+1/2M_xsin1-1/2M_ysin1	0	-0.12692	0.18150	0.0

Atom	x	y	z
1	0.00000	0.00000	0.00000
(0,0,1/2,1/2)' + set click here to show and hide
2	0.00000	0.00000	0.50000

Atom	x	y	z
1	0.33333	0.66667	0.25000
2	0.66667	0.33333	0.25000
(0,0,1/2,1/2)' + set click here to show and hide
3	0.33333	0.66667	0.75000
4	0.66667	0.33333	0.75000

Atom	x	y	z
1	0.33333	0.66667	0.00000
2	0.66667	0.33333	0.00000
(0,0,1/2,1/2)' + set click here to show and hide
3	0.33333	0.66667	0.50000
4	0.66667	0.33333	0.50000

Atom	x	y	z
1	0.00000	0.00000	0.16930
2	0.00000	0.00000	0.33070
(0,0,1/2,1/2)' + set click here to show and hide
3	0.00000	0.00000	0.66930
4	0.00000	0.00000	0.83070

Reference: P. Schobinger-Papamantellos, J. Rodriguez-Carvajal and K. Buschow, Journal of Magnetism and Magnetic Materials (2014) 369 243-248.
DOI: 10.1016/j.jmmm.2014.06.052
Atomic positions from: ICSD #192905

Parent space group (paramagnetic phase): (#191)
Propagation vector: k1 (0.000000, 0.000000, 0.810000)

Transition Temperature: 100 K
Experiment Temperature: 1.5 K

Lattice parameters of the basic unit cell:
5.1684(2) 5.1684(2) 16.7940(4) 90 90 120
Transformation from parent structure: (a,b,c;0,0,0)
    [View matrix form]

Magnetic Superspace Group: P6221'_c(00γ)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

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     [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\|
Mn1	Mn	0.5	0	0.1229(10)	12	0,0,m_z	0.0	0.0	2.09	2.09

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	-0.0315	0.2514	0.0	M_xsin1	M_ysin1	0	-0.3084	-0.1814	0.0

[Show all magnetic atoms in unit cell and their moment relations]

Average positions and magnetic moments of all atoms in unit cell, with magnetic moment relations explicitly given:

Set of atoms in the unit cell related by symmetry with the magnetic atom Mn1:

Average atomic positions and magnetic moments

Atom	x	y	z	Symmetry constraints on M	M_0x	M_0y	M_0z
1	0.50000	0.00000	0.12290	0,0,m_z	0.00000	0.00000	2.09000
2	0.00000	0.50000	0.12290	0,0,m_z	0.00000	0.00000	2.09000
3	0.50000	0.50000	0.12290	0,0,m_z	0.00000	0.00000	2.09000
4	0.00000	0.50000	0.37710	0,0,-m_z	0.00000	0.00000	-2.09000
5	0.50000	0.00000	0.37710	0,0,-m_z	0.00000	0.00000	-2.09000
6	0.50000	0.50000	0.37710	0,0,-m_z	0.00000	0.00000	-2.09000
(0,0,1/2,1/2)' + set click here to show and hide
7	0.50000	0.00000	0.62290	0,0,-m_z	0.00000	0.00000	-2.09000
8	0.00000	0.50000	0.62290	0,0,-m_z	0.00000	0.00000	-2.09000
9	0.50000	0.50000	0.62290	0,0,-m_z	0.00000	0.00000	-2.09000
10	0.00000	0.50000	0.87710	0,0,m_z	0.00000	0.00000	2.09000
11	0.50000	0.00000	0.87710	0,0,m_z	0.00000	0.00000	2.09000
12	0.50000	0.50000	0.87710	0,0,m_z	0.00000	0.00000	2.09000

Magnetic moment modulation parameters

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
1	M_xcos1	M_ycos1	0	-0.03150	0.25140	0.0	M_xsin1	M_ysin1	0	-0.30840	-0.18140	0.0
2	1/2M_ycos1+√3/2M_ysin1	-1/2M_xcos1+1/2M_ycos1-√3/2M_xsin1+√3/2M_ysin1	0	-0.03140	0.25144	0.0	-√3/2M_ycos1+1/2M_ysin1	√3/2M_xcos1-√3/2M_ycos1-1/2M_xsin1+1/2M_ysin1	0	-0.30842	-0.18150	0.0
3	1/2M_xcos1-1/2M_ycos1-√3/2M_xsin1+√3/2M_ysin1	1/2M_xcos1-√3/2M_xsin1	0	-0.03146	0.25133	0.0	√3/2M_xcos1-√3/2M_ycos1+1/2M_xsin1-1/2M_ysin1	√3/2M_xcos1+1/2M_xsin1	0	-0.30850	-0.18148	0.0
4	1/2M_ycos1-√3/2M_ysin1	1/2M_xcos1-√3/2M_xsin1	0	0.28280	0.25133	0.0	-√3/2M_ycos1-1/2M_ysin1	-√3/2M_xcos1-1/2M_xsin1	0	-0.12702	0.18148	0.0
5	-M_xcos1+M_ycos1	M_ycos1	0	0.28290	0.25140	0.0	M_xsin1-M_ysin1	-M_ysin1	0	-0.12700	0.18140	0.0
6	-1/2M_xcos1-√3/2M_xsin1	-1/2M_xcos1+1/2M_ycos1-√3/2M_xsin1+√3/2M_ysin1	0	0.28283	0.25144	0.0	-√3/2M_xcos1+1/2M_xsin1	-√3/2M_xcos1+√3/2M_ycos1+1/2M_xsin1-1/2M_ysin1	0	-0.12692	0.18150	0.0
(0,0,1/2,1/2)' + set click here to show and hide
7	M_xcos1	M_ycos1	0	-0.03150	0.25140	0.0	M_xsin1	M_ysin1	0	-0.30840	-0.18140	0.0
8	1/2M_ycos1+√3/2M_ysin1	-1/2M_xcos1+1/2M_ycos1-√3/2M_xsin1+√3/2M_ysin1	0	-0.03140	0.25144	0.0	-√3/2M_ycos1+1/2M_ysin1	√3/2M_xcos1-√3/2M_ycos1-1/2M_xsin1+1/2M_ysin1	0	-0.30842	-0.18150	0.0
9	1/2M_xcos1-1/2M_ycos1-√3/2M_xsin1+√3/2M_ysin1	1/2M_xcos1-√3/2M_xsin1	0	-0.03146	0.25133	0.0	√3/2M_xcos1-√3/2M_ycos1+1/2M_xsin1-1/2M_ysin1	√3/2M_xcos1+1/2M_xsin1	0	-0.30850	-0.18148	0.0
10	1/2M_ycos1-√3/2M_ysin1	1/2M_xcos1-√3/2M_xsin1	0	0.28280	0.25133	0.0	-√3/2M_ycos1-1/2M_ysin1	-√3/2M_xcos1-1/2M_xsin1	0	-0.12702	0.18148	0.0
11	-M_xcos1+M_ycos1	M_ycos1	0	0.28290	0.25140	0.0	M_xsin1-M_ysin1	-M_ysin1	0	-0.12700	0.18140	0.0
12	-1/2M_xcos1-√3/2M_xsin1	-1/2M_xcos1+1/2M_ycos1-√3/2M_xsin1+√3/2M_ysin1	0	0.28283	0.25144	0.0	-√3/2M_xcos1+1/2M_xsin1	-√3/2M_xcos1+√3/2M_ycos1+1/2M_xsin1-1/2M_ysin1	0	-0.12692	0.18150	0.0

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Active Irreps:

label	dim. small irrep	dim. full irrep	direction	action	number of modes
mA2+	1	1		primary	1
mDT6	2	4	special	primary	4

Comments:

NPD
Double conical incommensurate structure.
Mn spin modulus: 2.12(4); spin spiral xy component Mxy: 0.31(4) ; Mz component: 2.09(4)

Comments (symmetry):

1k incommensurate structure
Stable below about 100K, Above this temperature, and up to 516K a commensurate AFM phase exists with propagation vector (0 0 1/2), similar to the average structure of this incommensurate phase.
Two irreps with different wave vectors (one incommensurate) are active
The average sructure is AFM, with type IV MSG.
The reported phase relations between the modulations of the Mn spins (all spins in phase within each z layer, and layers at z≈1/4 and -1/4 also in phase) and the circular modulation imply, in the parameterization used here, that MiCos1=Mxy*Cos[2Pi*Di] and MiSin1=-Mxy*Sin[2*Pi*Di], i=x,y, with Dx= -(kz*2zo) and Dy= Dx-1/6. The magnetic symmetry is however mantained for any values of these four parameters, which are free under the MSSG.
Domains related by the lost inversion operation have opposite chirality of the spin spirals and an enantiomorphic superspace group: P6221'_c(00g)-h00s. The operation {6z | 0 0 0 tau } has a traslation tau=5/6 instead of 1/6 in the enantiomorphic MSSG.

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

ScMn₆Ge₆ (#1.1.46)

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

ScMn6Ge6 (#1.1.46)

ScMn₆Ge₆ (#1.1.46)