MAGNDATA - Collection of Magnetic Structures

Magnetic structure with only magnetic atoms

Reference: A. Szytula, J. Leciejewicz and H. BiÅ„czycka, Physica Status Solidi (a) (1980) 58 67-70.
DOI: 10.1002/pssa.2210580107
Atomic positions from: ICSD #623576

Parent space group (paramagnetic phase): I4/mmm (#139)
Propagation vector: k1 (0.000000, 0.000000, 0.730000)

Transition Temperature: 28 K
Experiment Temperature: 4.2 K

Lattice parameters of the basic unit cell:
4.053(7) 4.053(7) 10.230(10) 90 90 90
Transformation from parent structure: (a,b,c;0,0,0)
[View matrix form]

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

Symmetry operations of the magnetic space group in the setting used:

N	(x,y,z)	Seitz notation
1	x1,x2,x3,x4,+1	{ 1 \| 0 }
2	-x1,-x2,x3,x4,+1	{ 2₀₀₁ \| 0 }
3	-x2,x1,x3,x4,+1	{ 4⁺₀₀₁ \| 0 }
4	x2,-x1,x3,x4,+1	{ 4^-₀₀₁ \| 0 }
5	-x1,x2,-x3,-x4+1/2,+1	{ 2₀₁₀ \| 0 0 0 1/2 }
6	x1,-x2,-x3,-x4+1/2,+1	{ 2₁₀₀ \| 0 0 0 1/2 }
7	x2,x1,-x3,-x4+1/2,+1	{ 2₁₁₀ \| 0 0 0 1/2 }
8	-x2,-x1,-x3,-x4+1/2,+1	{ 2_1-10 \| 0 0 0 1/2 }
9	-x1,-x2,-x3,-x4,+1	{ -1 \| 0 }
10	x1,x2,-x3,-x4,+1	{ m₀₀₁ \| 0 }
11	x2,-x1,-x3,-x4,+1	{ -4⁺₀₀₁ \| 0 }
12	-x2,x1,-x3,-x4,+1	{ -4^-₀₀₁ \| 0 }
13	x1,-x2,x3,x4+1/2,+1	{ m₀₁₀ \| 0 0 0 1/2 }
14	-x1,x2,x3,x4+1/2,+1	{ m₁₀₀ \| 0 0 0 1/2 }
15	-x2,-x1,x3,x4+1/2,+1	{ m₁₁₀ \| 0 0 0 1/2 }
16	x2,x1,x3,x4+1/2,+1	{ m_1-10 \| 0 0 0 1/2 }
17	x1,x2,x3,x4+1/2,-1	{ 1' \| 0 0 0 1/2 }
18	-x1,-x2,x3,x4+1/2,-1	{ 2'₀₀₁ \| 0 0 0 1/2 }
19	-x2,x1,x3,x4+1/2,-1	{ 4'⁺₀₀₁ \| 0 0 0 1/2 }
20	x2,-x1,x3,x4+1/2,-1	{ 4'^-₀₀₁ \| 0 0 0 1/2 }
21	-x1,x2,-x3,-x4,-1	{ 2'₀₁₀ \| 0 }
22	x1,-x2,-x3,-x4,-1	{ 2'₁₀₀ \| 0 }
23	x2,x1,-x3,-x4,-1	{ 2'₁₁₀ \| 0 }
24	-x2,-x1,-x3,-x4,-1	{ 2'_1-10 \| 0 }
25	-x1,-x2,-x3,-x4+1/2,-1	{ -1' \| 0 0 0 1/2 }
26	x1,x2,-x3,-x4+1/2,-1	{ m'₀₀₁ \| 0 0 0 1/2 }
27	x2,-x1,-x3,-x4+1/2,-1	{ -4'⁺₀₀₁ \| 0 0 0 1/2 }
28	-x2,x1,-x3,-x4+1/2,-1	{ -4'^-₀₀₁ \| 0 0 0 1/2 }
29	x1,-x2,x3,x4,-1	{ m'₀₁₀ \| 0 }
30	-x1,x2,x3,x4,-1	{ m'₁₀₀ \| 0 }
31	-x2,-x1,x3,x4,-1	{ m'₁₁₀ \| 0 }
32	x2,x1,x3,x4,-1	{ m'_1-10 \| 0 }
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	{ 2₀₀₁ \| 1/2 1/2 1/2 0 }
35	-x2+1/2,x1+1/2,x3+1/2,x4,+1	{ 4⁺₀₀₁ \| 1/2 1/2 1/2 0 }
36	x2+1/2,-x1+1/2,x3+1/2,x4,+1	{ 4^-₀₀₁ \| 1/2 1/2 1/2 0 }
37	-x1+1/2,x2+1/2,-x3+1/2,-x4+1/2,+1	{ 2₀₁₀ \| 1/2 1/2 1/2 1/2 }
38	x1+1/2,-x2+1/2,-x3+1/2,-x4+1/2,+1	{ 2₁₀₀ \| 1/2 1/2 1/2 1/2 }
39	x2+1/2,x1+1/2,-x3+1/2,-x4+1/2,+1	{ 2₁₁₀ \| 1/2 1/2 1/2 1/2 }
40	-x2+1/2,-x1+1/2,-x3+1/2,-x4+1/2,+1	{ 2_1-10 \| 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	{ m₀₀₁ \| 1/2 1/2 1/2 0 }
43	x2+1/2,-x1+1/2,-x3+1/2,-x4,+1	{ -4⁺₀₀₁ \| 1/2 1/2 1/2 0 }
44	-x2+1/2,x1+1/2,-x3+1/2,-x4,+1	{ -4^-₀₀₁ \| 1/2 1/2 1/2 0 }
45	x1+1/2,-x2+1/2,x3+1/2,x4+1/2,+1	{ m₀₁₀ \| 1/2 1/2 1/2 1/2 }
46	-x1+1/2,x2+1/2,x3+1/2,x4+1/2,+1	{ m₁₀₀ \| 1/2 1/2 1/2 1/2 }
47	-x2+1/2,-x1+1/2,x3+1/2,x4+1/2,+1	{ m₁₁₀ \| 1/2 1/2 1/2 1/2 }
48	x2+1/2,x1+1/2,x3+1/2,x4+1/2,+1	{ m_1-10 \| 1/2 1/2 1/2 1/2 }
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,-1	{ 2'₀₀₁ \| 1/2 1/2 1/2 1/2 }
51	-x2+1/2,x1+1/2,x3+1/2,x4+1/2,-1	{ 4'⁺₀₀₁ \| 1/2 1/2 1/2 1/2 }
52	x2+1/2,-x1+1/2,x3+1/2,x4+1/2,-1	{ 4'^-₀₀₁ \| 1/2 1/2 1/2 1/2 }
53	-x1+1/2,x2+1/2,-x3+1/2,-x4,-1	{ 2'₀₁₀ \| 1/2 1/2 1/2 0 }
54	x1+1/2,-x2+1/2,-x3+1/2,-x4,-1	{ 2'₁₀₀ \| 1/2 1/2 1/2 0 }
55	x2+1/2,x1+1/2,-x3+1/2,-x4,-1	{ 2'₁₁₀ \| 1/2 1/2 1/2 0 }
56	-x2+1/2,-x1+1/2,-x3+1/2,-x4,-1	{ 2'_1-10 \| 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+1/2,-1	{ m'₀₀₁ \| 1/2 1/2 1/2 1/2 }
59	x2+1/2,-x1+1/2,-x3+1/2,-x4+1/2,-1	{ -4'⁺₀₀₁ \| 1/2 1/2 1/2 1/2 }
60	-x2+1/2,x1+1/2,-x3+1/2,-x4+1/2,-1	{ -4'^-₀₀₁ \| 1/2 1/2 1/2 1/2 }
61	x1+1/2,-x2+1/2,x3+1/2,x4,-1	{ m'₀₁₀ \| 1/2 1/2 1/2 0 }
62	-x1+1/2,x2+1/2,x3+1/2,x4,-1	{ m'₁₀₀ \| 1/2 1/2 1/2 0 }
63	-x2+1/2,-x1+1/2,x3+1/2,x4,-1	{ m'₁₁₀ \| 1/2 1/2 1/2 0 }
64	x2+1/2,x1+1/2,x3+1/2,x4,-1	{ m'_1-10 \| 1/2 1/2 1/2 0 }
(0,0,0,1/2)' + set click here to show and hide
65	x1,x2,x3,x4+1/2,-1	{ 1' \| 0 0 0 1/2 }
66	-x1,-x2,x3,x4+1/2,-1	{ 2'₀₀₁ \| 0 0 0 1/2 }
67	-x2,x1,x3,x4+1/2,-1	{ 4'⁺₀₀₁ \| 0 0 0 1/2 }
68	x2,-x1,x3,x4+1/2,-1	{ 4'^-₀₀₁ \| 0 0 0 1/2 }
69	-x1,x2,-x3,-x4,-1	{ 2'₀₁₀ \| 0 }
70	x1,-x2,-x3,-x4,-1	{ 2'₁₀₀ \| 0 }
71	x2,x1,-x3,-x4,-1	{ 2'₁₁₀ \| 0 }
72	-x2,-x1,-x3,-x4,-1	{ 2'_1-10 \| 0 }
73	-x1,-x2,-x3,-x4+1/2,-1	{ -1' \| 0 0 0 1/2 }
74	x1,x2,-x3,-x4+1/2,-1	{ m'₀₀₁ \| 0 0 0 1/2 }
75	x2,-x1,-x3,-x4+1/2,-1	{ -4'⁺₀₀₁ \| 0 0 0 1/2 }
76	-x2,x1,-x3,-x4+1/2,-1	{ -4'^-₀₀₁ \| 0 0 0 1/2 }
77	x1,-x2,x3,x4,-1	{ m'₀₁₀ \| 0 }
78	-x1,x2,x3,x4,-1	{ m'₁₀₀ \| 0 }
79	-x2,-x1,x3,x4,-1	{ m'₁₁₀ \| 0 }
80	x2,x1,x3,x4,-1	{ m'_1-10 \| 0 }
81	x1,x2,x3,x4,+1	{ 1 \| 0 }
82	-x1,-x2,x3,x4,+1	{ 2₀₀₁ \| 0 }
83	-x2,x1,x3,x4,+1	{ 4⁺₀₀₁ \| 0 }
84	x2,-x1,x3,x4,+1	{ 4^-₀₀₁ \| 0 }
85	-x1,x2,-x3,-x4+1/2,+1	{ 2₀₁₀ \| 0 0 0 1/2 }
86	x1,-x2,-x3,-x4+1/2,+1	{ 2₁₀₀ \| 0 0 0 1/2 }
87	x2,x1,-x3,-x4+1/2,+1	{ 2₁₁₀ \| 0 0 0 1/2 }
88	-x2,-x1,-x3,-x4+1/2,+1	{ 2_1-10 \| 0 0 0 1/2 }
89	-x1,-x2,-x3,-x4,+1	{ -1 \| 0 }
90	x1,x2,-x3,-x4,+1	{ m₀₀₁ \| 0 }
91	x2,-x1,-x3,-x4,+1	{ -4⁺₀₀₁ \| 0 }
92	-x2,x1,-x3,-x4,+1	{ -4^-₀₀₁ \| 0 }
93	x1,-x2,x3,x4+1/2,+1	{ m₀₁₀ \| 0 0 0 1/2 }
94	-x1,x2,x3,x4+1/2,+1	{ m₁₀₀ \| 0 0 0 1/2 }
95	-x2,-x1,x3,x4+1/2,+1	{ m₁₁₀ \| 0 0 0 1/2 }
96	x2,x1,x3,x4+1/2,+1	{ m_1-10 \| 0 0 0 1/2 }
97	x1+1/2,x2+1/2,x3+1/2,x4+1/2,-1	{ 1' \| 1/2 1/2 1/2 1/2 }
98	-x1+1/2,-x2+1/2,x3+1/2,x4+1/2,-1	{ 2'₀₀₁ \| 1/2 1/2 1/2 1/2 }
99	-x2+1/2,x1+1/2,x3+1/2,x4+1/2,-1	{ 4'⁺₀₀₁ \| 1/2 1/2 1/2 1/2 }
100	x2+1/2,-x1+1/2,x3+1/2,x4+1/2,-1	{ 4'^-₀₀₁ \| 1/2 1/2 1/2 1/2 }
101	-x1+1/2,x2+1/2,-x3+1/2,-x4,-1	{ 2'₀₁₀ \| 1/2 1/2 1/2 0 }
102	x1+1/2,-x2+1/2,-x3+1/2,-x4,-1	{ 2'₁₀₀ \| 1/2 1/2 1/2 0 }
103	x2+1/2,x1+1/2,-x3+1/2,-x4,-1	{ 2'₁₁₀ \| 1/2 1/2 1/2 0 }
104	-x2+1/2,-x1+1/2,-x3+1/2,-x4,-1	{ 2'_1-10 \| 1/2 1/2 1/2 0 }
105	-x1+1/2,-x2+1/2,-x3+1/2,-x4+1/2,-1	{ -1' \| 1/2 1/2 1/2 1/2 }
106	x1+1/2,x2+1/2,-x3+1/2,-x4+1/2,-1	{ m'₀₀₁ \| 1/2 1/2 1/2 1/2 }
107	x2+1/2,-x1+1/2,-x3+1/2,-x4+1/2,-1	{ -4'⁺₀₀₁ \| 1/2 1/2 1/2 1/2 }
108	-x2+1/2,x1+1/2,-x3+1/2,-x4+1/2,-1	{ -4'^-₀₀₁ \| 1/2 1/2 1/2 1/2 }
109	x1+1/2,-x2+1/2,x3+1/2,x4,-1	{ m'₀₁₀ \| 1/2 1/2 1/2 0 }
110	-x1+1/2,x2+1/2,x3+1/2,x4,-1	{ m'₁₀₀ \| 1/2 1/2 1/2 0 }
111	-x2+1/2,-x1+1/2,x3+1/2,x4,-1	{ m'₁₁₀ \| 1/2 1/2 1/2 0 }
112	x2+1/2,x1+1/2,x3+1/2,x4,-1	{ m'_1-10 \| 1/2 1/2 1/2 0 }
113	x1+1/2,x2+1/2,x3+1/2,x4,+1	{ 1 \| 1/2 1/2 1/2 0 }
114	-x1+1/2,-x2+1/2,x3+1/2,x4,+1	{ 2₀₀₁ \| 1/2 1/2 1/2 0 }
115	-x2+1/2,x1+1/2,x3+1/2,x4,+1	{ 4⁺₀₀₁ \| 1/2 1/2 1/2 0 }
116	x2+1/2,-x1+1/2,x3+1/2,x4,+1	{ 4^-₀₀₁ \| 1/2 1/2 1/2 0 }
117	-x1+1/2,x2+1/2,-x3+1/2,-x4+1/2,+1	{ 2₀₁₀ \| 1/2 1/2 1/2 1/2 }
118	x1+1/2,-x2+1/2,-x3+1/2,-x4+1/2,+1	{ 2₁₀₀ \| 1/2 1/2 1/2 1/2 }
119	x2+1/2,x1+1/2,-x3+1/2,-x4+1/2,+1	{ 2₁₁₀ \| 1/2 1/2 1/2 1/2 }
120	-x2+1/2,-x1+1/2,-x3+1/2,-x4+1/2,+1	{ 2_1-10 \| 1/2 1/2 1/2 1/2 }
121	-x1+1/2,-x2+1/2,-x3+1/2,-x4,+1	{ -1 \| 1/2 1/2 1/2 0 }
122	x1+1/2,x2+1/2,-x3+1/2,-x4,+1	{ m₀₀₁ \| 1/2 1/2 1/2 0 }
123	x2+1/2,-x1+1/2,-x3+1/2,-x4,+1	{ -4⁺₀₀₁ \| 1/2 1/2 1/2 0 }
124	-x2+1/2,x1+1/2,-x3+1/2,-x4,+1	{ -4^-₀₀₁ \| 1/2 1/2 1/2 0 }
125	x1+1/2,-x2+1/2,x3+1/2,x4+1/2,+1	{ m₀₁₀ \| 1/2 1/2 1/2 1/2 }
126	-x1+1/2,x2+1/2,x3+1/2,x4+1/2,+1	{ m₁₀₀ \| 1/2 1/2 1/2 1/2 }
127	-x2+1/2,-x1+1/2,x3+1/2,x4+1/2,+1	{ m₁₁₀ \| 1/2 1/2 1/2 1/2 }
128	x2+1/2,x1+1/2,x3+1/2,x4+1/2,+1	{ m_1-10 \| 1/2 1/2 1/2 1/2 }

[Hide]

N	(x,y,z)	Seitz notation
1	x,y,z,+1	1
2	-x,-y,z,+1	2₀₀₁
3	-y,x,z,+1	4⁺₀₀₁
4	y,-x,z,+1	4^-₀₀₁
5	-x,y,-z,+1	2₀₁₀
6	x,-y,-z,+1	2₁₀₀
7	y,x,-z,+1	2₁₁₀
8	-y,-x,-z,+1	2_1-10
9	-x,-y,-z,+1	-1
10	x,y,-z,+1	m₀₀₁
11	y,-x,-z,+1	-4⁺₀₀₁
12	-y,x,-z,+1	-4^-₀₀₁
13	x,-y,z,+1	m₀₁₀
14	-x,y,z,+1	m₁₀₀
15	-y,-x,z,+1	m₁₁₀
16	y,x,z,+1	m_1-10
1' + set click here to show and hide
17	x,y,z,-1	1'
18	-x,-y,z,-1	2'₀₀₁
19	-y,x,z,-1	4'⁺₀₀₁
20	y,-x,z,-1	4'^-₀₀₁
21	-x,y,-z,-1	2'₀₁₀
22	x,-y,-z,-1	2'₁₀₀
23	y,x,-z,-1	2'₁₁₀
24	-y,-x,-z,-1	2'_1-10
25	-x,-y,-z,-1	-1'
26	x,y,-z,-1	m'₀₀₁
27	y,-x,-z,-1	-4'⁺₀₀₁
28	-y,x,-z,-1	-4'^-₀₀₁
29	x,-y,z,-1	m'₀₁₀
30	-x,y,z,-1	m'₁₀₀
31	-y,-x,z,-1	m'₁₁₀
32	y,x,z,-1	m'_1-10

Label	Atom type	x	y	z	Multiplicity
Ge1	Ge	0	0	0.3740(10)	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
Co1	0	0	M_zcos1	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0
Pr1	0	0	M_zcos1	0.0	0.0	3.98(15)	0	0	0	0.0	0.0	0.0

Atom	x	y	z
1	0.00000	0.50000	0.25000
2	0.50000	0.00000	0.25000
3	0.00000	0.50000	0.75000
4	0.50000	0.00000	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	0	M_zcos1	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0
2	0	0	M_zcos1	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0
3	0	0	M_zcos1	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0
4	0	0	M_zcos1	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0

Atom	x	y	z
1	0.00000	0.00000	0.00000
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	3.98000	0	0	0	0.0	0.0	0.0
2	0	0	M_zcos1	0.0	0.0	3.98000	0	0	0	0.0	0.0	0.0

Atom	x	y	z
1	0.00000	0.00000	0.37400
2	0.00000	0.00000	0.62600
3	0.50000	0.50000	0.87400
4	0.50000	0.50000	0.12600

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
Co1	Co	0	0.5	0.25	4
Pr1	Pr	0	0	0	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
Co1	0	0	M_zcos1	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0
Pr1	0	0	M_zcos1	0.0	0.0	3.98(15)	0	0	0	0.0	0.0	0.0

Atom	x	y	z
1	0.00000	0.50000	0.25000
2	0.50000	0.00000	0.25000
3	0.00000	0.50000	0.75000
4	0.50000	0.00000	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	0	M_zcos1	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0
2	0	0	M_zcos1	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0
3	0	0	M_zcos1	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0
4	0	0	M_zcos1	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0

Atom	x	y	z
1	0.00000	0.00000	0.00000
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	3.98000	0	0	0	0.0	0.0	0.0
2	0	0	M_zcos1	0.0	0.0	3.98000	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:

Comments (symmetry):

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

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

PrCo₂Ge₂ (#1.1.91)

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

PrCo2Ge2 (#1.1.91)

PrCo₂Ge₂ (#1.1.91)