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,x3+1/2,x4,+1	{ 2₀₀₁ \| 1/2 0 1/2 0 }
3	-x1,x2+1/2,-x3+1/2,-x4,+1	{ 2₀₁₀ \| 0 1/2 1/2 0 }
4	x1+1/2,-x2+1/2,-x3,-x4,+1	{ 2₁₀₀ \| 1/2 1/2 0 0 }
(0,0,0,1/2)' + set click here to show and hide
5	x1,x2,x3,x4+1/2,-1	{ 1' \| 0 0 0 1/2 }
6	-x1+1/2,-x2,x3+1/2,x4+1/2,-1	{ 2'₀₀₁ \| 1/2 0 1/2 1/2 }
7	-x1,x2+1/2,-x3+1/2,-x4+1/2,-1	{ 2'₀₁₀ \| 0 1/2 1/2 1/2 }
8	x1+1/2,-x2+1/2,-x3,-x4+1/2,-1	{ 2'₁₀₀ \| 1/2 1/2 0 1/2 }

N	(x,y,z)	Seitz notation
1	x,y,z,+1	1
2	-x,-y,z,+1	2₀₀₁
3	-x,y,-z,+1	2₀₁₀
4	x,-y,-z,+1	2₁₀₀
1' + set click here to show and hide
5	x,y,z,-1	1'
6	-x,-y,z,-1	2'₀₀₁
7	-x,y,-z,-1	2'₀₁₀
8	x,-y,-z,-1	2'₁₀₀

Label	Atom type	x	y	z	Multiplicity
Rh1_1	Rh	0.0612	0.9388	0.4388	4
Ge1_1	Ge	0.6829	0.3171	0.8171	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_1	M_xcos1	M_ycos1	M_zcos1	-1.11(8)	-1.05(12)	0.960(2)	M_xsin1	M_ysin1	M_zsin1	1.24(6)	-0.08(11)	1.32(6)
Mn1_2	M_xcos1	M_ycos1	M_zcos1	-1.29(9)	0.73(17)	-1.04(17)	M_xsin1	M_ysin1	M_zsin1	-1.20(7)	-1.17(11)	0.67(19)
Mn1_3	M_xcos1	M_ycos1	M_zcos1	1.32(8)	1.07(12)	0.63(13)	M_xsin1	M_ysin1	M_zsin1	-1.20(8)	0.90(10)	1.00(12)

Atom	x	y	z
1	0.60620	0.70430	0.96020
2	0.89380	0.29570	0.46020
3	0.39380	0.20430	0.53980
4	0.10620	0.79570	0.03980

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	-1.11000	-1.05000	0.96000	M_xsin1	M_ysin1	M_zsin1	1.24000	-0.08000	1.32000
2	-M_xcos1	-M_ycos1	M_zcos1	1.11000	1.05000	0.96000	-M_xsin1	-M_ysin1	M_zsin1	-1.24000	0.08000	1.32000
3	-M_xcos1	M_ycos1	-M_zcos1	1.11000	-1.05000	-0.96000	M_xsin1	-M_ysin1	M_zsin1	1.24000	0.08000	1.32000
4	M_xcos1	-M_ycos1	-M_zcos1	-1.11000	1.05000	-0.96000	-M_xsin1	M_ysin1	M_zsin1	-1.24000	-0.08000	1.32000

Atom	x	y	z
1	0.54020	0.39380	0.20430
2	0.95980	0.60620	0.70430
3	0.45980	0.89380	0.29570
4	0.04020	0.10620	0.79570

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	-1.29000	0.73000	-1.04000	M_xsin1	M_ysin1	M_zsin1	-1.20000	-1.17000	0.67000
2	-M_xcos1	-M_ycos1	M_zcos1	1.29000	-0.73000	-1.04000	-M_xsin1	-M_ysin1	M_zsin1	1.20000	1.17000	0.67000
3	-M_xcos1	M_ycos1	-M_zcos1	1.29000	0.73000	1.04000	M_xsin1	-M_ysin1	M_zsin1	-1.20000	1.17000	0.67000
4	M_xcos1	-M_ycos1	-M_zcos1	-1.29000	-0.73000	1.04000	-M_xsin1	M_ysin1	M_zsin1	1.20000	-1.17000	0.67000

Atom	x	y	z
1	0.29570	0.45980	0.89380
2	0.20430	0.54020	0.39380
3	0.70430	0.95980	0.60620
4	0.79570	0.04020	0.10620

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	1.32000	1.07000	0.63000	M_xsin1	M_ysin1	M_zsin1	-1.20000	0.90000	1.00000
2	-M_xcos1	-M_ycos1	M_zcos1	-1.32000	-1.07000	0.63000	-M_xsin1	-M_ysin1	M_zsin1	1.20000	-0.90000	1.00000
3	-M_xcos1	M_ycos1	-M_zcos1	-1.32000	1.07000	-0.63000	M_xsin1	-M_ysin1	M_zsin1	-1.20000	-0.90000	1.00000
4	M_xcos1	-M_ycos1	-M_zcos1	1.32000	-1.07000	-0.63000	-M_xsin1	M_ysin1	M_zsin1	1.20000	0.90000	1.00000

Atom	x	y	z
1	0.06120	0.93880	0.43880
2	0.43880	0.06120	0.93880
3	0.93880	0.43880	0.06120
4	0.56120	0.56120	0.56120

Atom	x	y	z
1	0.68290	0.31710	0.81710
2	0.81710	0.68290	0.31710
3	0.31710	0.81710	0.68290
4	0.18290	0.18290	0.18290

Reference: A. E. Hall, P. Manuel, D. D. Khalyavin, F. Orlandi, D. A. Mayoh, L.-J. Chang, Y.-S. Chen, D. G. C. Jonas, M. R. Lees, G. Balakrishnan, PHYSICAL REVIEW MATERIALS (2023) 7 114402
DOI: 10.1103/PhysRevMaterials.7.114402
Atomic positions from: same reference

Parent space group (paramagnetic phase): P2₁3 (#198)
Propagation vector: k1 (0.000000, 0.000000, 0.066319)

Transition Temperature: 225(2) K
Experiment Temperature: 200 K

Lattice parameters of the basic unit cell:
6.6106 6.6106 6.6106 90 90 90
Transformation from parent structure: (-a,c,b;0.75,0.25,0.75)
    [View matrix form]

Magnetic Superspace Group: P212121.1'(00γ)000s
    [View symmetry operations]

Magnetic Point Group: 222.1' (6.1.17)
    [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_1	Mn	0.6062	0.7043	0.9602	4
Mn1_2	Mn	0.5402	0.3938	0.2043	4
Mn1_3	Mn	0.2957	0.4598	0.8938	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_1	M_xcos1	M_ycos1	M_zcos1	-1.11(8)	-1.05(12)	0.960(2)	M_xsin1	M_ysin1	M_zsin1	1.24(6)	-0.08(11)	1.32(6)
Mn1_2	M_xcos1	M_ycos1	M_zcos1	-1.29(9)	0.73(17)	-1.04(17)	M_xsin1	M_ysin1	M_zsin1	-1.20(7)	-1.17(11)	0.67(19)
Mn1_3	M_xcos1	M_ycos1	M_zcos1	1.32(8)	1.07(12)	0.63(13)	M_xsin1	M_ysin1	M_zsin1	-1.20(8)	0.90(10)	1.00(12)

Atom	x	y	z
1	0.60620	0.70430	0.96020
2	0.89380	0.29570	0.46020
3	0.39380	0.20430	0.53980
4	0.10620	0.79570	0.03980

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	-1.11000	-1.05000	0.96000	M_xsin1	M_ysin1	M_zsin1	1.24000	-0.08000	1.32000
2	-M_xcos1	-M_ycos1	M_zcos1	1.11000	1.05000	0.96000	-M_xsin1	-M_ysin1	M_zsin1	-1.24000	0.08000	1.32000
3	-M_xcos1	M_ycos1	-M_zcos1	1.11000	-1.05000	-0.96000	M_xsin1	-M_ysin1	M_zsin1	1.24000	0.08000	1.32000
4	M_xcos1	-M_ycos1	-M_zcos1	-1.11000	1.05000	-0.96000	-M_xsin1	M_ysin1	M_zsin1	-1.24000	-0.08000	1.32000

Atom	x	y	z
1	0.54020	0.39380	0.20430
2	0.95980	0.60620	0.70430
3	0.45980	0.89380	0.29570
4	0.04020	0.10620	0.79570

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	-1.29000	0.73000	-1.04000	M_xsin1	M_ysin1	M_zsin1	-1.20000	-1.17000	0.67000
2	-M_xcos1	-M_ycos1	M_zcos1	1.29000	-0.73000	-1.04000	-M_xsin1	-M_ysin1	M_zsin1	1.20000	1.17000	0.67000
3	-M_xcos1	M_ycos1	-M_zcos1	1.29000	0.73000	1.04000	M_xsin1	-M_ysin1	M_zsin1	-1.20000	1.17000	0.67000
4	M_xcos1	-M_ycos1	-M_zcos1	-1.29000	-0.73000	1.04000	-M_xsin1	M_ysin1	M_zsin1	1.20000	-1.17000	0.67000

Atom	x	y	z
1	0.29570	0.45980	0.89380
2	0.20430	0.54020	0.39380
3	0.70430	0.95980	0.60620
4	0.79570	0.04020	0.10620

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	1.32000	1.07000	0.63000	M_xsin1	M_ysin1	M_zsin1	-1.20000	0.90000	1.00000
2	-M_xcos1	-M_ycos1	M_zcos1	-1.32000	-1.07000	0.63000	-M_xsin1	-M_ysin1	M_zsin1	1.20000	-0.90000	1.00000
3	-M_xcos1	M_ycos1	-M_zcos1	-1.32000	1.07000	-0.63000	M_xsin1	-M_ysin1	M_zsin1	-1.20000	-0.90000	1.00000
4	M_xcos1	-M_ycos1	-M_zcos1	1.32000	-1.07000	-0.63000	-M_xsin1	M_ysin1	M_zsin1	1.20000	0.90000	1.00000

[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
mDT1	2	6	special	primary	18

Comments:

NPD
At lower temperatures a commensurate k=0 phase is reported
The setting used is the standard of the MSSG, different from that of the parent cubic structure. The transformation from the parent setting is (-a,c,b;0.75,0.25,0.75).

Comments (symmetry):

1k incommensurate magnetic structure
one single irrep

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

Mn₃RhGe (#1.1.148)

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

Mn3RhGe (#1.1.148)

Mn₃RhGe (#1.1.148)