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

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	-x,-y,-z,+1	-1
6	-x,y,z,+1	m₁₀₀
7	x,-y,z,+1	m₀₁₀
8	x,y,-z,+1	m₀₀₁
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	-x,-y,-z,-1	-1'
14	-x,y,z,-1	m'₁₀₀
15	x,-y,z,-1	m'₀₁₀
16	x,y,-z,-1	m'₀₀₁

Label	Atom type	x	y	z	Occupancy	Multiplicity
Lu1	Lu	0.08468	0.25000	-0.01880	0.898	4
O1	O	0.45730	0.25000	0.11790	1.00000	4
O2	O	0.32537	0.05634	0.69629	1.00000	8

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	0	M_zcos1	0.0	0.0	0.0	M_xsin1	0	M_zsin1	0.0	0.0	0.0
Mn2	M_xcos1	M_ycos1	M_zcos1	2.84	0.0	1.06	0	0	0	0.0	0.0	0.0

Atom	x	y	z
1	0.08468	0.25000	0.98120
2	0.58468	0.25000	0.51880
3	0.91532	0.75000	0.01880
4	0.41532	0.75000	0.48120

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	M_zcos1	0.0	0.0	0.0	M_xsin1	0	M_zsin1	0.0	0.0	0.0
2	M_xcos1	0	-M_zcos1	0.0	0.0	0.0	M_xsin1	0	-M_zsin1	0.0	0.0	0.0
3	M_xcos1	0	M_zcos1	0.0	0.0	0.0	-M_xsin1	0	-M_zsin1	0.0	0.0	0.0
4	M_xcos1	0	-M_zcos1	0.0	0.0	0.0	-M_xsin1	0	M_zsin1	0.0	0.0	0.0

Atom	x	y	z
1	0.00000	0.00000	0.50000
2	0.50000	0.50000	0.00000
3	0.00000	0.50000	0.50000
4	0.50000	0.00000	0.00000

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	M_zcos1	2.84000	0.0	1.06000	0	0	0	0.0	0.0	0.0
2	M_xcos1	-M_ycos1	-M_zcos1	2.84000	0.0	-1.06000	0	0	0	0.0	0.0	0.0
3	M_xcos1	-M_ycos1	M_zcos1	2.84000	0.0	1.06000	0	0	0	0.0	0.0	0.0
4	M_xcos1	M_ycos1	-M_zcos1	2.84000	0.0	-1.06000	0	0	0	0.0	0.0	0.0

Atom	x	y	z
1	0.08468	0.25000	0.98120
2	0.58468	0.25000	0.51880
3	0.91532	0.75000	0.01880
4	0.41532	0.75000	0.48120

Atom	x	y	z
1	0.45730	0.25000	0.11790
2	0.95730	0.25000	0.38210
3	0.54270	0.75000	0.88210
4	0.04270	0.75000	0.61790

Atom	x	y	z
1	0.32537	0.05634	0.69629
2	0.82537	0.44366	0.80371
3	0.67463	0.55634	0.30371
4	0.17463	0.94366	0.19629
5	0.67463	0.94366	0.30371
6	0.17463	0.55634	0.19629
7	0.32537	0.44366	0.69629
8	0.82537	0.05634	0.80371

Reference: L. Zhang, A. Donni, V. Y. Pomjakushin, K. Yamaura, A. A. Belik, Inorg. Chem. (2018) 57 14073 - 14085
DOI: 10.1021/acs.inorgchem.8b01470
Atomic positions from: ICSD #266215

Parent space group (paramagnetic phase): Pnma (#62)
Propagation vector: k1 (0.438(1), 0.00000, 0.00000)

Transition Temperature: 36 K
Experiment Temperature: 2 K

Lattice parameters of the basic unit cell:
5.7000(1) 7.3087(1) 5.1892(1) 90.00000 90.00000 90.00000
Transformation from parent structure: (a,b,c;0,0,0)
    [View matrix form]

Magnetic Superspace Group: Pnma1'(a,0,0)0sss
    [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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Average atomic positions of symmetry independent atoms

Label	Atom type	x	y	z	Occupancy	Multiplicity
Mn1	Mn	0.08468	0.25000	-0.01880	0.102	4
Mn2	Mn	0.00000	0.00000	0.50000	1.00000	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
Mn1	M_xcos1	0	M_zcos1	0.0	0.0	0.0	M_xsin1	0	M_zsin1	0.0	0.0	0.0
Mn2	M_xcos1	M_ycos1	M_zcos1	2.84	0.0	1.06	0	0	0	0.0	0.0	0.0

Atom	x	y	z
1	0.08468	0.25000	0.98120
2	0.58468	0.25000	0.51880
3	0.91532	0.75000	0.01880
4	0.41532	0.75000	0.48120

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	M_zcos1	0.0	0.0	0.0	M_xsin1	0	M_zsin1	0.0	0.0	0.0
2	M_xcos1	0	-M_zcos1	0.0	0.0	0.0	M_xsin1	0	-M_zsin1	0.0	0.0	0.0
3	M_xcos1	0	M_zcos1	0.0	0.0	0.0	-M_xsin1	0	-M_zsin1	0.0	0.0	0.0
4	M_xcos1	0	-M_zcos1	0.0	0.0	0.0	-M_xsin1	0	M_zsin1	0.0	0.0	0.0

Atom	x	y	z
1	0.00000	0.00000	0.50000
2	0.50000	0.50000	0.00000
3	0.00000	0.50000	0.50000
4	0.50000	0.00000	0.00000

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	M_zcos1	2.84000	0.0	1.06000	0	0	0	0.0	0.0	0.0
2	M_xcos1	-M_ycos1	-M_zcos1	2.84000	0.0	-1.06000	0	0	0	0.0	0.0	0.0
3	M_xcos1	-M_ycos1	M_zcos1	2.84000	0.0	1.06000	0	0	0	0.0	0.0	0.0
4	M_xcos1	M_ycos1	-M_zcos1	2.84000	0.0	-1.06000	0	0	0	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	direction	action	number of modes
mSM2	1	2	general	primary	7

Comments:

NPD
Position structure, except cell parameters, from a determination at 65K
FM is symmetry forbidden.
Mn2 moment amplitude: 3.04(3)
The experimental data are unsensitive to the phase shift between the mx and mz modulations of Mn2. However the only possible MSSG that can result from a single order parameter according to the active irrep dictates that the two modulations must be in phase. This implies an amplitude modulated structure, which is the model described here.
Any phase shift, different from zero o pi, between the two modulations would require the involvement of two distinct order parameters according to the same irrep, with a lowering of the symmetry to the noncentrosymmetric MSSG P2_1nm1'(a00)0sss

Comments (symmetry):

1k incommensurate magnetic structure
k-maximal magnetic symmetry
2-dim irrep as primary

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

(Lu_0.9Mn_0.1)MnO₃ (#1.1.127)

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

(Lu0.9Mn0.1)MnO3 (#1.1.127)

(Lu_0.9Mn_0.1)MnO₃ (#1.1.127)