MAGNDATA - Collection of Magnetic Structures

Magnetic structure with only magnetic atoms

Reference: J.A. Blanco, B. FÃ¥k, E. Ressouche, B. Grenier, M. Rotter, D. Schmitt, J.A. Rodriguez-Velamazan, J. Campo and P. Lejay, Physical Review B (2010) 82 054414.
DOI: 10.1103/physrevb.82.054414
Atomic positions from: ICSD #169860

Parent space group (paramagnetic phase): I4/mmm (#139)
Propagation vector: k1 (0.000000, 0.000000, 0.870000)

Transition Temperature: 20 K
Experiment Temperature: 1.6 K

Wave vectors table:

label	Wave vector	k1 coefficient
1	(0, 0, 0.87)	1
2	(0, 0, 1.74)	2
3	(0, 0, 2.61)	3

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 }
(1/2,1/2,1/2,0) + set click here to show and hide
17	x1+1/2,x2+1/2,x3+1/2,x4,+1	{ 1 \| 1/2 1/2 1/2 0 }
18	-x1+1/2,-x2+1/2,x3+1/2,x4,+1	{ 2₀₀₁ \| 1/2 1/2 1/2 0 }
19	-x2+1/2,x1+1/2,x3+1/2,x4,+1	{ 4⁺₀₀₁ \| 1/2 1/2 1/2 0 }
20	x2+1/2,-x1+1/2,x3+1/2,x4,+1	{ 4^-₀₀₁ \| 1/2 1/2 1/2 0 }
21	-x1+1/2,x2+1/2,-x3+1/2,-x4+1/2,+1	{ 2₀₁₀ \| 1/2 1/2 1/2 1/2 }
22	x1+1/2,-x2+1/2,-x3+1/2,-x4+1/2,+1	{ 2₁₀₀ \| 1/2 1/2 1/2 1/2 }
23	x2+1/2,x1+1/2,-x3+1/2,-x4+1/2,+1	{ 2₁₁₀ \| 1/2 1/2 1/2 1/2 }
24	-x2+1/2,-x1+1/2,-x3+1/2,-x4+1/2,+1	{ 2_1-10 \| 1/2 1/2 1/2 1/2 }
25	-x1+1/2,-x2+1/2,-x3+1/2,-x4,+1	{ -1 \| 1/2 1/2 1/2 0 }
26	x1+1/2,x2+1/2,-x3+1/2,-x4,+1	{ m₀₀₁ \| 1/2 1/2 1/2 0 }
27	x2+1/2,-x1+1/2,-x3+1/2,-x4,+1	{ -4⁺₀₀₁ \| 1/2 1/2 1/2 0 }
28	-x2+1/2,x1+1/2,-x3+1/2,-x4,+1	{ -4^-₀₀₁ \| 1/2 1/2 1/2 0 }
29	x1+1/2,-x2+1/2,x3+1/2,x4+1/2,+1	{ m₀₁₀ \| 1/2 1/2 1/2 1/2 }
30	-x1+1/2,x2+1/2,x3+1/2,x4+1/2,+1	{ m₁₀₀ \| 1/2 1/2 1/2 1/2 }
31	-x2+1/2,-x1+1/2,x3+1/2,x4+1/2,+1	{ m₁₁₀ \| 1/2 1/2 1/2 1/2 }
32	x2+1/2,x1+1/2,x3+1/2,x4+1/2,+1	{ m_1-10 \| 1/2 1/2 1/2 1/2 }
(0,0,0,1/2)' + set click here to show and hide
33	x1,x2,x3,x4+1/2,-1	{ 1' \| 0 0 0 1/2 }
34	-x1,-x2,x3,x4+1/2,-1	{ 2'₀₀₁ \| 0 0 0 1/2 }
35	-x2,x1,x3,x4+1/2,-1	{ 4'⁺₀₀₁ \| 0 0 0 1/2 }
36	x2,-x1,x3,x4+1/2,-1	{ 4'^-₀₀₁ \| 0 0 0 1/2 }
37	-x1,x2,-x3,-x4,-1	{ 2'₀₁₀ \| 0 }
38	x1,-x2,-x3,-x4,-1	{ 2'₁₀₀ \| 0 }
39	x2,x1,-x3,-x4,-1	{ 2'₁₁₀ \| 0 }
40	-x2,-x1,-x3,-x4,-1	{ 2'_1-10 \| 0 }
41	-x1,-x2,-x3,-x4+1/2,-1	{ -1' \| 0 0 0 1/2 }
42	x1,x2,-x3,-x4+1/2,-1	{ m'₀₀₁ \| 0 0 0 1/2 }
43	x2,-x1,-x3,-x4+1/2,-1	{ -4'⁺₀₀₁ \| 0 0 0 1/2 }
44	-x2,x1,-x3,-x4+1/2,-1	{ -4'^-₀₀₁ \| 0 0 0 1/2 }
45	x1,-x2,x3,x4,-1	{ m'₀₁₀ \| 0 }
46	-x1,x2,x3,x4,-1	{ m'₁₀₀ \| 0 }
47	-x2,-x1,x3,x4,-1	{ m'₁₁₀ \| 0 }
48	x2,x1,x3,x4,-1	{ m'_1-10 \| 0 }
(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,-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 }

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
Si1	Si	0	0	0.3712(4)	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
Pr1	0	0	M_zcos1	0.0	0.0	2.35(2)	0	0	0	0.0	0.0	0.0
Ni1	0	0	M_zcos1	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0

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
Pr1	0	0	0	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0
Ni1	0	0	0	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0

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
Pr1	0	0	M_zcos3	0.0	0.0	0.34(19)	0	0	0	0.0	0.0	0.0
Ni1	0	0	M_zcos3	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
(1/2,1/2,1/2,0) + 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	2.35000	0	0	0	0.0	0.0	0.0
(1/2,1/2,1/2,0) + set click here to show and hide
2	0	0	M_zcos1	0.0	0.0	2.35000	0	0	0	0.0	0.0	0.0

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

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_zcos3	0.0	0.0	0.34000	0	0	0	0.0	0.0	0.0
(1/2,1/2,1/2,0) + set click here to show and hide
2	0	0	M_zcos3	0.0	0.0	0.34000	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
(1/2,1/2,1/2,0) + set click here to show and hide
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
(1/2,1/2,1/2,0) + set click here to show and hide
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	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	0	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0
2	0	0	0	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0
(1/2,1/2,1/2,0) + set click here to show and hide
3	0	0	0	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0
4	0	0	0	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0

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_zcos3	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0
2	0	0	M_zcos3	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0
(1/2,1/2,1/2,0) + set click here to show and hide
3	0	0	M_zcos3	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0
4	0	0	M_zcos3	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0

Atom	x	y	z
1	0.00000	0.00000	0.37120
2	0.00000	0.00000	0.62880
(1/2,1/2,1/2,0) + set click here to show and hide
3	0.50000	0.50000	0.87120
4	0.50000	0.50000	0.12880

Lattice parameters of the basic unit cell:
4.047 4.047 9.621 90 90 90
Transformation from parent structure: (a,b,c;0,0,0)
    [View matrix form]

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

Magnetic Point Group: I4/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
Pr1	Pr	0	0	0	2
Ni1	Ni	0	0.5	0.25	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
Pr1	0	0	M_zcos1	0.0	0.0	2.35(2)	0	0	0	0.0	0.0	0.0
Ni1	0	0	M_zcos1	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0

Wave vector 2

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
Pr1	0	0	0	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0
Ni1	0	0	0	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0

Wave vector 3

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
Pr1	0	0	M_zcos3	0.0	0.0	0.34(19)	0	0	0	0.0	0.0	0.0
Ni1	0	0	M_zcos3	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
(1/2,1/2,1/2,0) + 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	2.35000	0	0	0	0.0	0.0	0.0
(1/2,1/2,1/2,0) + set click here to show and hide
2	0	0	M_zcos1	0.0	0.0	2.35000	0	0	0	0.0	0.0	0.0

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

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_zcos3	0.0	0.0	0.34000	0	0	0	0.0	0.0	0.0
(1/2,1/2,1/2,0) + set click here to show and hide
2	0	0	M_zcos3	0.0	0.0	0.34000	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
(1/2,1/2,1/2,0) + set click here to show and hide
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
(1/2,1/2,1/2,0) + set click here to show and hide
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	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	0	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0
2	0	0	0	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0
(1/2,1/2,1/2,0) + set click here to show and hide
3	0	0	0	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0
4	0	0	0	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0

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_zcos3	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0
2	0	0	M_zcos3	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0
(1/2,1/2,1/2,0) + set click here to show and hide
3	0	0	M_zcos3	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0
4	0	0	M_zcos3	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0

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

Comments:

position structure from measurement at 40K

Comments (symmetry):

1k magnetic structure
k maximal magnetic symmetry
1-dim small irrep: one to one correspondence between MSSG and irrep

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

PrNi₂Si₂ (#1.1.34)

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

PrNi2Si2 (#1.1.34)

PrNi₂Si₂ (#1.1.34)