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,-x3,-x4+1/2,+1	{ 2₁₀₀ \| 0 0 0 1/2 }
3	-x1,x2,-x3,-x4+1/2,+1	{ 2₀₁₀ \| 0 0 0 1/2 }
4	-x1,-x2,x3,x4,+1	{ 2₀₀₁ \| 0 }
5	-x2,-x1,-x3,-x4+1/2,+1	{ 2_1-10 \| 0 0 0 1/2 }
6	-x2,x1,x3,x4,+1	{ 4⁺₀₀₁ \| 0 }
7	x2,-x1,x3,x4,+1	{ 4^-₀₀₁ \| 0 }
8	x2,x1,-x3,-x4+1/2,+1	{ 2₁₁₀ \| 0 0 0 1/2 }
9	-x1,-x2,-x3,-x4,+1	{ -1 \| 0 }
10	-x1,x2,x3,x4+1/2,+1	{ m₁₀₀ \| 0 0 0 1/2 }
11	x1,-x2,x3,x4+1/2,+1	{ m₀₁₀ \| 0 0 0 1/2 }
12	x1,x2,-x3,-x4,+1	{ m₀₀₁ \| 0 }
13	x2,x1,x3,x4+1/2,+1	{ m_1-10 \| 0 0 0 1/2 }
14	x2,-x1,-x3,-x4,+1	{ -4⁺₀₀₁ \| 0 }
15	-x2,x1,-x3,-x4,+1	{ -4^-₀₀₁ \| 0 }
16	-x2,-x1,x3,x4+1/2,+1	{ m₁₁₀ \| 0 0 0 1/2 }
(0,0,0,1/2)' + set click here to show and hide
17	x1,x2,x3,x4+1/2,-1	{ 1' \| 0 0 0 1/2 }
18	x1,-x2,-x3,-x4,-1	{ 2'₁₀₀ \| 0 }
19	-x1,x2,-x3,-x4,-1	{ 2'₀₁₀ \| 0 }
20	-x1,-x2,x3,x4+1/2,-1	{ 2'₀₀₁ \| 0 0 0 1/2 }
21	-x2,-x1,-x3,-x4,-1	{ 2'_1-10 \| 0 }
22	-x2,x1,x3,x4+1/2,-1	{ 4'⁺₀₀₁ \| 0 0 0 1/2 }
23	x2,-x1,x3,x4+1/2,-1	{ 4'^-₀₀₁ \| 0 0 0 1/2 }
24	x2,x1,-x3,-x4,-1	{ 2'₁₁₀ \| 0 }
25	-x1,-x2,-x3,-x4+1/2,-1	{ -1' \| 0 0 0 1/2 }
26	-x1,x2,x3,x4,-1	{ m'₁₀₀ \| 0 }
27	x1,-x2,x3,x4,-1	{ m'₀₁₀ \| 0 }
28	x1,x2,-x3,-x4+1/2,-1	{ m'₀₀₁ \| 0 0 0 1/2 }
29	x2,x1,x3,x4,-1	{ m'_1-10 \| 0 }
30	x2,-x1,-x3,-x4+1/2,-1	{ -4'⁺₀₀₁ \| 0 0 0 1/2 }
31	-x2,x1,-x3,-x4+1/2,-1	{ -4'^-₀₀₁ \| 0 0 0 1/2 }
32	-x2,-x1,x3,x4,-1	{ m'₁₁₀ \| 0 }
(1/2,1/2,1/2,0) + set click here to show and hide
33	x1+1/2,x2+1/2,x3+1/2,x4,+1	{ 1 \| 1/2 1/2 1/2 0 }
34	x1+1/2,-x2+1/2,-x3+1/2,-x4+1/2,+1	{ 2₁₀₀ \| 1/2 1/2 1/2 1/2 }
35	-x1+1/2,x2+1/2,-x3+1/2,-x4+1/2,+1	{ 2₀₁₀ \| 1/2 1/2 1/2 1/2 }
36	-x1+1/2,-x2+1/2,x3+1/2,x4,+1	{ 2₀₀₁ \| 1/2 1/2 1/2 0 }
37	-x2+1/2,-x1+1/2,-x3+1/2,-x4+1/2,+1	{ 2_1-10 \| 1/2 1/2 1/2 1/2 }
38	-x2+1/2,x1+1/2,x3+1/2,x4,+1	{ 4⁺₀₀₁ \| 1/2 1/2 1/2 0 }
39	x2+1/2,-x1+1/2,x3+1/2,x4,+1	{ 4^-₀₀₁ \| 1/2 1/2 1/2 0 }
40	x2+1/2,x1+1/2,-x3+1/2,-x4+1/2,+1	{ 2₁₁₀ \| 1/2 1/2 1/2 1/2 }
41	-x1+1/2,-x2+1/2,-x3+1/2,-x4,+1	{ -1 \| 1/2 1/2 1/2 0 }
42	-x1+1/2,x2+1/2,x3+1/2,x4+1/2,+1	{ m₁₀₀ \| 1/2 1/2 1/2 1/2 }
43	x1+1/2,-x2+1/2,x3+1/2,x4+1/2,+1	{ m₀₁₀ \| 1/2 1/2 1/2 1/2 }
44	x1+1/2,x2+1/2,-x3+1/2,-x4,+1	{ m₀₀₁ \| 1/2 1/2 1/2 0 }
45	x2+1/2,x1+1/2,x3+1/2,x4+1/2,+1	{ m_1-10 \| 1/2 1/2 1/2 1/2 }
46	x2+1/2,-x1+1/2,-x3+1/2,-x4,+1	{ -4⁺₀₀₁ \| 1/2 1/2 1/2 0 }
47	-x2+1/2,x1+1/2,-x3+1/2,-x4,+1	{ -4^-₀₀₁ \| 1/2 1/2 1/2 0 }
48	-x2+1/2,-x1+1/2,x3+1/2,x4+1/2,+1	{ m₁₁₀ \| 1/2 1/2 1/2 1/2 }
(1/2,1/2,1/2,1/2)' + set click here to show and hide
49	x1+1/2,x2+1/2,x3+1/2,x4+1/2,-1	{ 1' \| 1/2 1/2 1/2 1/2 }
50	x1+1/2,-x2+1/2,-x3+1/2,-x4,-1	{ 2'₁₀₀ \| 1/2 1/2 1/2 0 }
51	-x1+1/2,x2+1/2,-x3+1/2,-x4,-1	{ 2'₀₁₀ \| 1/2 1/2 1/2 0 }
52	-x1+1/2,-x2+1/2,x3+1/2,x4+1/2,-1	{ 2'₀₀₁ \| 1/2 1/2 1/2 1/2 }
53	-x2+1/2,-x1+1/2,-x3+1/2,-x4,-1	{ 2'_1-10 \| 1/2 1/2 1/2 0 }
54	-x2+1/2,x1+1/2,x3+1/2,x4+1/2,-1	{ 4'⁺₀₀₁ \| 1/2 1/2 1/2 1/2 }
55	x2+1/2,-x1+1/2,x3+1/2,x4+1/2,-1	{ 4'^-₀₀₁ \| 1/2 1/2 1/2 1/2 }
56	x2+1/2,x1+1/2,-x3+1/2,-x4,-1	{ 2'₁₁₀ \| 1/2 1/2 1/2 0 }
57	-x1+1/2,-x2+1/2,-x3+1/2,-x4+1/2,-1	{ -1' \| 1/2 1/2 1/2 1/2 }
58	-x1+1/2,x2+1/2,x3+1/2,x4,-1	{ m'₁₀₀ \| 1/2 1/2 1/2 0 }
59	x1+1/2,-x2+1/2,x3+1/2,x4,-1	{ m'₀₁₀ \| 1/2 1/2 1/2 0 }
60	x1+1/2,x2+1/2,-x3+1/2,-x4+1/2,-1	{ m'₀₀₁ \| 1/2 1/2 1/2 1/2 }
61	x2+1/2,x1+1/2,x3+1/2,x4,-1	{ m'_1-10 \| 1/2 1/2 1/2 0 }
62	x2+1/2,-x1+1/2,-x3+1/2,-x4+1/2,-1	{ -4'⁺₀₀₁ \| 1/2 1/2 1/2 1/2 }
63	-x2+1/2,x1+1/2,-x3+1/2,-x4+1/2,-1	{ -4'^-₀₀₁ \| 1/2 1/2 1/2 1/2 }
64	-x2+1/2,-x1+1/2,x3+1/2,x4,-1	{ m'₁₁₀ \| 1/2 1/2 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	-y,-x,-z,+1	2_1-10
6	-y,x,z,+1	4⁺₀₀₁
7	y,-x,z,+1	4^-₀₀₁
8	y,x,-z,+1	2₁₁₀
9	-x,-y,-z,+1	-1
10	-x,y,z,+1	m₁₀₀
11	x,-y,z,+1	m₀₁₀
12	x,y,-z,+1	m₀₀₁
13	y,x,z,+1	m_1-10
14	y,-x,-z,+1	-4⁺₀₀₁
15	-y,x,-z,+1	-4^-₀₀₁
16	-y,-x,z,+1	m₁₁₀
1' + set click here to show and hide
17	x,y,z,-1	1'
18	x,-y,-z,-1	2'₁₀₀
19	-x,y,-z,-1	2'₀₁₀
20	-x,-y,z,-1	2'₀₀₁
21	-y,-x,-z,-1	2'_1-10
22	-y,x,z,-1	4'⁺₀₀₁
23	y,-x,z,-1	4'^-₀₀₁
24	y,x,-z,-1	2'₁₁₀
25	-x,-y,-z,-1	-1'
26	-x,y,z,-1	m'₁₀₀
27	x,-y,z,-1	m'₀₁₀
28	x,y,-z,-1	m'₀₀₁
29	y,x,z,-1	m'_1-10
30	y,-x,-z,-1	-4'⁺₀₀₁
31	-y,x,-z,-1	-4'^-₀₀₁
32	-y,-x,z,-1	m'₁₁₀

Label	Atom type	x	y	z	Multiplicity
Pd1	Pd	0.00000	0.50000	0.25000	4
Ge1	Ge	0.00000	0.00000	0.38300	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
U1	0	0	M_zcos1	0.0	0.0	2.49(8)	0	0	0	0.0	0.0	0.0

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

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	0	M_zcos1	0.0	0.0	2.49000	0	0	0	0.0	0.0	0.0
(0,0,0,1/2)' + set click here to show and hide
2	0	0	M_zcos1	0.0	0.0	2.49000	0	0	0	0.0	0.0	0.0

Atom	x	y	z
1	0.00000	0.50000	0.25000
(0,0,0,1/2)' + set click here to show and hide
2	0.00000	0.50000	0.75000
(1/2,1/2,1/2,0) + set click here to show and hide
3	0.50000	0.00000	0.75000
(1/2,1/2,1/2,1/2)' + set click here to show and hide
4	0.50000	0.00000	0.25000

Atom	x	y	z
1	0.00000	0.00000	0.38300
(0,0,0,1/2)' + set click here to show and hide
2	0.00000	0.00000	0.61700
(1/2,1/2,1/2,0) + set click here to show and hide
3	0.50000	0.50000	0.88300
(1/2,1/2,1/2,1/2)' + set click here to show and hide
4	0.50000	0.50000	0.11700

Reference: G. Andre, F. Bouree, A. Oles, W. Sikora, B. Penc, A. Szytula, Z. Tomkowicz, Solid State Communications (1996) 97 923 - 929
DOI: 10.1016/0038-1098(95)00818-7
Atomic positions from: ICSD #108866

Parent space group (paramagnetic phase): I4/mmm (#139)
Propagation vector: k1 (0.00000, 0.00000, 0.7302(17))

Transition Temperature: 135 K
Experiment Temperature: 100 K

Lattice parameters of the basic unit cell:
4.20000 4.20000 10.23000 90.00000 90.00000 90.00000
Transformation from parent structure: (a,b,c;0,0,0)
    [View matrix form]

Magnetic Superspace Group: I4/mmm1'(0,0,g)00sss
    [View symmetry operations]

Magnetic Point Group: 4/mmm1' (15.2.54)
    [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
U1	U	0.00000	0.00000	0.00000	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
U1	0	0	M_zcos1	0.0	0.0	2.49(8)	0	0	0	0.0	0.0	0.0

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

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	0	M_zcos1	0.0	0.0	2.49000	0	0	0	0.0	0.0	0.0
(0,0,0,1/2)' + set click here to show and hide
2	0	0	M_zcos1	0.0	0.0	2.49000	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
mLD4	1	2	general	primary	1

Comments:

NPD
Position structure is not fully specified. It is taken here from a determination at 293K of another work.
Below 80K the propagation vector becomes commensurate with kz=3/4 (see #1.535).
The initial phase of the global modulation is arbitrary. Here it is fixed by the form of the MSSG operations that transform k into -k.

Comments (symmetry):

1k incommensurate magnetic structure
k-maximal magnetic symmetry
2-dim irrep along a general direction as primary.

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

UPd₂Ge₂ (#1.1.115)

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

UPd2Ge2 (#1.1.115)

UPd₂Ge₂ (#1.1.115)