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-x2,x1,x3+1/2,x4+1/6,+1	{ 6⁺₀₀₁ \| 0 0 1/2 1/6 }
3	-x1,-x1+x2,-x3,-x4,+1	{ 2₀₁₀ \| 0 }
4	-x2,-x1,-x3+1/2,-x4+1/6,+1	{ 2_1-10 \| 0 0 1/2 1/6 }
5	-x2,x1-x2,x3,x4+1/3,+1	{ 3⁺₀₀₁ \| 0 0 0 1/3 }
6	x1-x2,-x2,-x3,-x4+1/3,+1	{ 2₁₀₀ \| 0 0 0 1/3 }
7	-x1+x2,x2,-x3+1/2,-x4+5/6,+1	{ 2₁₂₀ \| 0 0 1/2 5/6 }
8	x2,-x1+x2,x3+1/2,x4+5/6,+1	{ 6^-₀₀₁ \| 0 0 1/2 5/6 }
9	-x1,-x2,x3+1/2,x4+1/2,+1	{ 2₀₀₁ \| 0 0 1/2 1/2 }
10	x1,x1-x2,-x3+1/2,-x4+1/2,+1	{ 2₂₁₀ \| 0 0 1/2 1/2 }
11	x2,x1,-x3,-x4+2/3,+1	{ 2₁₁₀ \| 0 0 0 2/3 }
12	-x1+x2,-x1,x3,x4+2/3,+1	{ 3^-₀₀₁ \| 0 0 0 2/3 }
(0,0,0,1/2)' + set click here to show and hide
13	x1,x2,x3,x4+1/2,-1	{ 1' \| 0 0 0 1/2 }
14	x1-x2,x1,x3+1/2,x4+2/3,-1	{ 6'⁺₀₀₁ \| 0 0 1/2 2/3 }
15	-x1,-x1+x2,-x3,-x4+1/2,-1	{ 2'₀₁₀ \| 0 0 0 1/2 }
16	-x2,-x1,-x3+1/2,-x4+2/3,-1	{ 2'_1-10 \| 0 0 1/2 2/3 }
17	-x2,x1-x2,x3,x4+5/6,-1	{ 3'⁺₀₀₁ \| 0 0 0 5/6 }
18	x1-x2,-x2,-x3,-x4+5/6,-1	{ 2'₁₀₀ \| 0 0 0 5/6 }
19	-x1+x2,x2,-x3+1/2,-x4+1/3,-1	{ 2'₁₂₀ \| 0 0 1/2 1/3 }
20	x2,-x1+x2,x3+1/2,x4+1/3,-1	{ 6'^-₀₀₁ \| 0 0 1/2 1/3 }
21	-x1,-x2,x3+1/2,x4,-1	{ 2'₀₀₁ \| 0 0 1/2 0 }
22	x1,x1-x2,-x3+1/2,-x4,-1	{ 2'₂₁₀ \| 0 0 1/2 0 }
23	x2,x1,-x3,-x4+1/6,-1	{ 2'₁₁₀ \| 0 0 0 1/6 }
24	-x1+x2,-x1,x3,x4+1/6,-1	{ 3'^-₀₀₁ \| 0 0 0 1/6 }

N	(x,y,z)	Seitz notation
1	x,y,z,+1	1
2	x-y,x,z,+1	6⁺₀₀₁
3	-x,-x+y,-z,+1	2₀₁₀
4	-y,-x,-z,+1	2_1-10
5	-y,x-y,z,+1	3⁺₀₀₁
6	x-y,-y,-z,+1	2₁₀₀
7	-x+y,y,-z,+1	2₁₂₀
8	y,-x+y,z,+1	6^-₀₀₁
9	-x,-y,z,+1	2₀₀₁
10	x,x-y,-z,+1	2₂₁₀
11	y,x,-z,+1	2₁₁₀
12	-x+y,-x,z,+1	3^-₀₀₁
1' + set click here to show and hide
13	x,y,z,-1	1'
14	x-y,x,z,-1	6'⁺₀₀₁
15	-x,-x+y,-z,-1	2'₀₁₀
16	-y,-x,-z,-1	2'_1-10
17	-y,x-y,z,-1	3'⁺₀₀₁
18	x-y,-y,-z,-1	2'₁₀₀
19	-x+y,y,-z,-1	2'₁₂₀
20	y,-x+y,z,-1	6'^-₀₀₁
21	-x,-y,z,-1	2'₀₀₁
22	x,x-y,-z,-1	2'₂₁₀
23	y,x,-z,-1	2'₁₁₀
24	-x+y,-x,z,-1	3'^-₀₀₁

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
Ho1	0	M_ycos1	0	0.0	6.938(13)	0.0	-1.15470M_ycos1	-0.57735M_ycos1	0	-8.012(13)	-4.006(13)	0.0

Atom	x	y	z
1	0.33333	0.66667	0.25000
2	0.66666	0.33333	0.75000

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	0	M_ycos1	0	0.0	6.93800	0.0	-1.15470M_ycos1	-0.57735M_ycos1	0	-8.01200	-4.00600	0.0
2	-0.00000M_ycos1	1.00000M_ycos1	0	0.00030	6.93860	0.0	-1.15470M_ycos1	-0.57735M_ycos1	0	-8.01148	-4.00600	0.0

Reference: M. Pardo-Sainz, F. Cova, J. A. Rodriguez-Velamazan, I. Puenteâ€‘Orench, Y. Kousaka, M. Mito, J. Campo, Scientific Reports (2023) 13 12168
DOI: 10.1038/s41598-023-39284-2
Atomic positions from: ICSD #43582

Parent space group (paramagnetic phase): P6₃/mmc (#194)
Propagation vector: k1 (0.00000, 0.00000, 0.25356(6))

Transition Temperature: 105 K
Experiment Temperature: 5 K

Lattice parameters of the basic unit cell:
3.3976(6) 3.3976(6) 5.3898(12) 90.0000 90.0000 120.000
Transformation from parent structure: (a,b,c;0,0,0)
    [View matrix form]

Magnetic Superspace Group: P6_322.1'(0,0,g)h00s
    [View symmetry operations]

Magnetic Point Group: 622.1' (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

     [Show only magnetic atoms]
     [Show all the atoms]

Average atomic positions of symmetry independent atoms

Label	Atom type	x	y	z	Multiplicity
Ho1	Ho	0.33333	0.66667	0.25000	2

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
Ho1	0	M_ycos1	0	0.0	6.938(13)	0.0	-1.15470M_ycos1	-0.57735M_ycos1	0	-8.012(13)	-4.006(13)	0.0

Atom	x	y	z
1	0.33333	0.66667	0.25000
2	0.66666	0.33333	0.75000

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	0	M_ycos1	0	0.0	6.93800	0.0	-1.15470M_ycos1	-0.57735M_ycos1	0	-8.01200	-4.00600	0.0
2	-0.00000M_ycos1	1.00000M_ycos1	0	0.00030	6.93860	0.0	-1.15470M_ycos1	-0.57735M_ycos1	0	-8.01148	-4.00600	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
mDT6	2	4	special	primary	1

Comments:

NPD at P = 8 GPa
Helical incommensurate structure.
Ho spin modulus: 6.94(1)

Comments (symmetry):

1k incommensurate magnetic structure.
The 2d-irreps, mDT5 and mDT6 , describe helices in which the magnetic moments are contained in ferromagnetic ab planes, and propagate along the c-axis.
However, both models differ greatly when considering the phase-shift between the Ho atoms in the unit cell. The magnetic structure
given by mDT6 can be considered as a single helix, while for mDT5 the system is composed of two independent helices, one for each atom in the unit cell.
The fit to NPD data shows that only the irrep mDT6 correctly describes the data.

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

Ho (#1.1.147)