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+1/2,+1	{ 2₀₀₁ \| 1/2 0 1/2 1/2 }
3	-x1,-x2,-x3,-x4,+1	{ -1 \| 0 }
4	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
5	x1,x2,x3,x4+1/2,-1	{ 1' \| 0 0 0 1/2 }
6	-x1+1/2,-x2,x3+1/2,-x4,-1	{ 2'₀₀₁ \| 1/2 0 1/2 0 }
7	-x1,-x2,-x3,-x4+1/2,-1	{ -1' \| 0 0 0 1/2 }
8	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	2₀₀₁
3	-x,-y,-z,+1	-1
4	x,y,-z,+1	m₀₀₁
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	-1'
8	x,y,-z,-1	m'₀₀₁

Label	Atom type	x	y	z	Multiplicity
Ni1	Ni	0.3918	0.25	0.5531	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
Tb1	M_xcos1	M_ycos1	M_zcos1	1.4(2)	-0.3(2)	4.4(1)	M_xsin1	M_ysin1	M_zsin1	0.4(2)	0.0(2)	1.8(1)
Tb2_1	M_xcos1	M_ycos1	M_zcos1	-0.4(3)	-1.1(3)	0.9(1)	M_xsin1	M_ysin1	M_zsin1	-1.3(2)	-2.5(1)	5.0(1)
Tb2_2	M_xcos1	M_ycos1	M_zcos1	-1.1(3)	0.7(2)	2.5(1)	M_xsin1	M_ysin1	M_zsin1	1.0(2)	-0.8(2)	-2.3(1)

Atom	x	y	z
1	0.03090	0.25000	0.35620
2	0.46910	0.75000	0.85620
3	0.96910	0.75000	0.64380
4	0.53090	0.25000	0.14380

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	1.40000	-0.30000	4.40000	M_xsin1	M_ysin1	M_zsin1	0.40000	0.0	1.80000
2	M_xcos1	M_ycos1	-M_zcos1	1.40000	-0.30000	-4.40000	-M_xsin1	-M_ysin1	M_zsin1	-0.40000	0.0	1.80000
3	M_xcos1	M_ycos1	M_zcos1	1.40000	-0.30000	4.40000	-M_xsin1	-M_ysin1	-M_zsin1	-0.40000	0.0	-1.80000
4	M_xcos1	M_ycos1	-M_zcos1	1.40000	-0.30000	-4.40000	M_xsin1	M_ysin1	-M_zsin1	0.40000	0.0	-1.80000

Atom	x	y	z
1	0.18000	0.06510	0.82090
2	0.32000	0.93490	0.32090
3	0.82000	0.93490	0.17910
4	0.68000	0.06510	0.67910

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	-0.40000	-1.10000	0.90000	M_xsin1	M_ysin1	M_zsin1	-1.30000	-2.50000	5.00000
2	M_xcos1	M_ycos1	-M_zcos1	-0.40000	-1.10000	-0.90000	-M_xsin1	-M_ysin1	M_zsin1	1.30000	2.50000	5.00000
3	M_xcos1	M_ycos1	M_zcos1	-0.40000	-1.10000	0.90000	-M_xsin1	-M_ysin1	-M_zsin1	1.30000	2.50000	-5.00000
4	M_xcos1	M_ycos1	-M_zcos1	-0.40000	-1.10000	-0.90000	M_xsin1	M_ysin1	-M_zsin1	-1.30000	-2.50000	-5.00000

Atom	x	y	z
1	0.82000	0.56510	0.17910
2	0.68000	0.43490	0.67910
3	0.18000	0.43490	0.82090
4	0.32000	0.56510	0.32090

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	-1.10000	0.70000	2.50000	M_xsin1	M_ysin1	M_zsin1	1.00000	-0.80000	-2.30000
2	M_xcos1	M_ycos1	-M_zcos1	-1.10000	0.70000	-2.50000	-M_xsin1	-M_ysin1	M_zsin1	-1.00000	0.80000	-2.30000
3	M_xcos1	M_ycos1	M_zcos1	-1.10000	0.70000	2.50000	-M_xsin1	-M_ysin1	-M_zsin1	-1.00000	0.80000	2.30000
4	M_xcos1	M_ycos1	-M_zcos1	-1.10000	0.70000	-2.50000	M_xsin1	M_ysin1	-M_zsin1	1.00000	-0.80000	2.30000

Atom	x	y	z
1	0.39180	0.25000	0.55310
2	0.10820	0.75000	0.05310
3	0.60820	0.75000	0.44690
4	0.89180	0.25000	0.94690

Reference: A.F. Gubkin, L.S. Wu, S.E. Nikitin, A.V. Suslov, A. Podlesnyak, O. Prokhnenko, K. Prokes, F. Yokaichiya, L. Keller and N.V. Baranov, Physical Review B (2018) 97 134425.
DOI: 10.1103/physrevb.97.134425
Atomic positions from: same reference

Parent space group (paramagnetic phase): (#62)
Propagation vector: k1 (0.506000, 0.299000, 0.000000)

Transition Temperature: 61 K
Experiment Temperature: 58 K

Lattice parameters of the basic unit cell:
6.8342(3) 9.5262(4) 6.3306(3) 90 90 90
Transformation from parent structure: (a,b,c;0,0,0)
    [View matrix form]

Magnetic Superspace Group: P1121/a1'(αβ0)0ss
    [View symmetry operations]

Magnetic Point Group: 2/m1' (5.2.13)
    [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
Tb1	Tb	0.0309	0.25	0.3562	4
Tb2_1	Tb	0.18	0.0651	0.8209	4
Tb2_2	Tb	0.82	0.5651	0.1791	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
Tb1	M_xcos1	M_ycos1	M_zcos1	1.4(2)	-0.3(2)	4.4(1)	M_xsin1	M_ysin1	M_zsin1	0.4(2)	0.0(2)	1.8(1)
Tb2_1	M_xcos1	M_ycos1	M_zcos1	-0.4(3)	-1.1(3)	0.9(1)	M_xsin1	M_ysin1	M_zsin1	-1.3(2)	-2.5(1)	5.0(1)
Tb2_2	M_xcos1	M_ycos1	M_zcos1	-1.1(3)	0.7(2)	2.5(1)	M_xsin1	M_ysin1	M_zsin1	1.0(2)	-0.8(2)	-2.3(1)

Atom	x	y	z
1	0.03090	0.25000	0.35620
2	0.46910	0.75000	0.85620
3	0.96910	0.75000	0.64380
4	0.53090	0.25000	0.14380

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	1.40000	-0.30000	4.40000	M_xsin1	M_ysin1	M_zsin1	0.40000	0.0	1.80000
2	M_xcos1	M_ycos1	-M_zcos1	1.40000	-0.30000	-4.40000	-M_xsin1	-M_ysin1	M_zsin1	-0.40000	0.0	1.80000
3	M_xcos1	M_ycos1	M_zcos1	1.40000	-0.30000	4.40000	-M_xsin1	-M_ysin1	-M_zsin1	-0.40000	0.0	-1.80000
4	M_xcos1	M_ycos1	-M_zcos1	1.40000	-0.30000	-4.40000	M_xsin1	M_ysin1	-M_zsin1	0.40000	0.0	-1.80000

Atom	x	y	z
1	0.18000	0.06510	0.82090
2	0.32000	0.93490	0.32090
3	0.82000	0.93490	0.17910
4	0.68000	0.06510	0.67910

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	-0.40000	-1.10000	0.90000	M_xsin1	M_ysin1	M_zsin1	-1.30000	-2.50000	5.00000
2	M_xcos1	M_ycos1	-M_zcos1	-0.40000	-1.10000	-0.90000	-M_xsin1	-M_ysin1	M_zsin1	1.30000	2.50000	5.00000
3	M_xcos1	M_ycos1	M_zcos1	-0.40000	-1.10000	0.90000	-M_xsin1	-M_ysin1	-M_zsin1	1.30000	2.50000	-5.00000
4	M_xcos1	M_ycos1	-M_zcos1	-0.40000	-1.10000	-0.90000	M_xsin1	M_ysin1	-M_zsin1	-1.30000	-2.50000	-5.00000

Atom	x	y	z
1	0.82000	0.56510	0.17910
2	0.68000	0.43490	0.67910
3	0.18000	0.43490	0.82090
4	0.32000	0.56510	0.32090

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	-1.10000	0.70000	2.50000	M_xsin1	M_ysin1	M_zsin1	1.00000	-0.80000	-2.30000
2	M_xcos1	M_ycos1	-M_zcos1	-1.10000	0.70000	-2.50000	-M_xsin1	-M_ysin1	M_zsin1	-1.00000	0.80000	-2.30000
3	M_xcos1	M_ycos1	M_zcos1	-1.10000	0.70000	2.50000	-M_xsin1	-M_ysin1	-M_zsin1	-1.00000	0.80000	2.30000
4	M_xcos1	M_ycos1	-M_zcos1	-1.10000	0.70000	-2.50000	M_xsin1	M_ysin1	-M_zsin1	1.00000	-0.80000	2.30000

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

Active Irreps:

label	dim. small irrep	dim. full irrep	action	number of modes
mV2	1	4	primary	18

Comments:

NPD
At lower temperatures more complicated phases are reported with coexistence of several propagation vectors that are not symmetry related.
Average structure (Pnma) from an experiment at 65K in the paramagnetic phase.

Comments (symmetry):

1k magnetic structures
1-dim small irrep active (2 possible)
Symmetry operations transforming k and -k are included in the superspace group, and the spin modulations of Tb atoms related by these operations have correlated spin modulations.
The spin modulations of the two split sites coming from the Tb2 site in the paramagnetic phase are very different.

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

Tb₃Ni (#1.1.47)

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

Tb3Ni (#1.1.47)

Tb₃Ni (#1.1.47)