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⁺₀₀₁ \| 0 0 1/2 0 }
3	-x2,x1-x2,x3,x4,+1	{ 3⁺₀₀₁ \| 0 }
4	-x1,-x2,x3+1/2,x4,+1	{ 2₀₀₁ \| 0 0 1/2 0 }
5	-x1+x2,-x1,x3,x4,+1	{ 3^-₀₀₁ \| 0 }
6	x2,-x1+x2,x3+1/2,x4,+1	{ 6^-₀₀₁ \| 0 0 1/2 0 }
7	x1-x2,-x2,-x3+1/2,-x4+1/2,+1	{ 2₁₀₀ \| 0 0 1/2 1/2 }
8	x1,x1-x2,-x3,-x4+1/2,+1	{ 2₂₁₀ \| 0 0 0 1/2 }
9	x2,x1,-x3+1/2,-x4+1/2,+1	{ 2₁₁₀ \| 0 0 1/2 1/2 }
10	-x1+x2,x2,-x3,-x4+1/2,+1	{ 2₁₂₀ \| 0 0 0 1/2 }
11	-x1,-x1+x2,-x3+1/2,-x4+1/2,+1	{ 2₀₁₀ \| 0 0 1/2 1/2 }
12	-x2,-x1,-x3,-x4+1/2,+1	{ 2_1-10 \| 0 0 0 1/2 }
13	-x1,-x2,-x3,-x4,+1	{ -1 \| 0 }
14	-x1+x2,-x1,-x3+1/2,-x4,+1	{ -6⁺₀₀₁ \| 0 0 1/2 0 }
15	x2,-x1+x2,-x3,-x4,+1	{ -3⁺₀₀₁ \| 0 }
16	x1,x2,-x3+1/2,-x4,+1	{ m₀₀₁ \| 0 0 1/2 0 }
17	x1-x2,x1,-x3,-x4,+1	{ -3^-₀₀₁ \| 0 }
18	-x2,x1-x2,-x3+1/2,-x4,+1	{ -6^-₀₀₁ \| 0 0 1/2 0 }
19	-x1+x2,x2,x3+1/2,x4+1/2,+1	{ m₁₀₀ \| 0 0 1/2 1/2 }
20	-x1,-x1+x2,x3,x4+1/2,+1	{ m₂₁₀ \| 0 0 0 1/2 }
21	-x2,-x1,x3+1/2,x4+1/2,+1	{ m₁₁₀ \| 0 0 1/2 1/2 }
22	x1-x2,-x2,x3,x4+1/2,+1	{ m₁₂₀ \| 0 0 0 1/2 }
23	x1,x1-x2,x3+1/2,x4+1/2,+1	{ m₀₁₀ \| 0 0 1/2 1/2 }
24	x2,x1,x3,x4+1/2,+1	{ m_1-10 \| 0 0 0 1/2 }
(0,0,0,1/2)' + set click here to show and hide
25	x1,x2,x3,x4+1/2,-1	{ 1' \| 0 0 0 1/2 }
26	x1-x2,x1,x3+1/2,x4+1/2,-1	{ 6'⁺₀₀₁ \| 0 0 1/2 1/2 }
27	-x2,x1-x2,x3,x4+1/2,-1	{ 3'⁺₀₀₁ \| 0 0 0 1/2 }
28	-x1,-x2,x3+1/2,x4+1/2,-1	{ 2'₀₀₁ \| 0 0 1/2 1/2 }
29	-x1+x2,-x1,x3,x4+1/2,-1	{ 3'^-₀₀₁ \| 0 0 0 1/2 }
30	x2,-x1+x2,x3+1/2,x4+1/2,-1	{ 6'^-₀₀₁ \| 0 0 1/2 1/2 }
31	x1-x2,-x2,-x3+1/2,-x4,-1	{ 2'₁₀₀ \| 0 0 1/2 0 }
32	x1,x1-x2,-x3,-x4,-1	{ 2'₂₁₀ \| 0 }
33	x2,x1,-x3+1/2,-x4,-1	{ 2'₁₁₀ \| 0 0 1/2 0 }
34	-x1+x2,x2,-x3,-x4,-1	{ 2'₁₂₀ \| 0 }
35	-x1,-x1+x2,-x3+1/2,-x4,-1	{ 2'₀₁₀ \| 0 0 1/2 0 }
36	-x2,-x1,-x3,-x4,-1	{ 2'_1-10 \| 0 }
37	-x1,-x2,-x3,-x4+1/2,-1	{ -1' \| 0 0 0 1/2 }
38	-x1+x2,-x1,-x3+1/2,-x4+1/2,-1	{ -6'⁺₀₀₁ \| 0 0 1/2 1/2 }
39	x2,-x1+x2,-x3,-x4+1/2,-1	{ -3'⁺₀₀₁ \| 0 0 0 1/2 }
40	x1,x2,-x3+1/2,-x4+1/2,-1	{ m'₀₀₁ \| 0 0 1/2 1/2 }
41	x1-x2,x1,-x3,-x4+1/2,-1	{ -3'^-₀₀₁ \| 0 0 0 1/2 }
42	-x2,x1-x2,-x3+1/2,-x4+1/2,-1	{ -6'^-₀₀₁ \| 0 0 1/2 1/2 }
43	-x1+x2,x2,x3+1/2,x4,-1	{ m'₁₀₀ \| 0 0 1/2 0 }
44	-x1,-x1+x2,x3,x4,-1	{ m'₂₁₀ \| 0 }
45	-x2,-x1,x3+1/2,x4,-1	{ m'₁₁₀ \| 0 0 1/2 0 }
46	x1-x2,-x2,x3,x4,-1	{ m'₁₂₀ \| 0 }
47	x1,x1-x2,x3+1/2,x4,-1	{ m'₀₁₀ \| 0 0 1/2 0 }
48	x2,x1,x3,x4,-1	{ m'_1-10 \| 0 }

N	(x,y,z)	Seitz notation
1	x,y,z,+1	1
2	x-y,x,z,+1	6⁺₀₀₁
3	-y,x-y,z,+1	3⁺₀₀₁
4	-x,-y,z,+1	2₀₀₁
5	-x+y,-x,z,+1	3^-₀₀₁
6	y,-x+y,z,+1	6^-₀₀₁
7	x-y,-y,-z,+1	2₁₀₀
8	x,x-y,-z,+1	2₂₁₀
9	y,x,-z,+1	2₁₁₀
10	-x+y,y,-z,+1	2₁₂₀
11	-x,-x+y,-z,+1	2₀₁₀
12	-y,-x,-z,+1	2_1-10
13	-x,-y,-z,+1	-1
14	-x+y,-x,-z,+1	-6⁺₀₀₁
15	y,-x+y,-z,+1	-3⁺₀₀₁
16	x,y,-z,+1	m₀₀₁
17	x-y,x,-z,+1	-3^-₀₀₁
18	-y,x-y,-z,+1	-6^-₀₀₁
19	-x+y,y,z,+1	m₁₀₀
20	-x,-x+y,z,+1	m₂₁₀
21	-y,-x,z,+1	m₁₁₀
22	x-y,-y,z,+1	m₁₂₀
23	x,x-y,z,+1	m₀₁₀
24	y,x,z,+1	m_1-10
1' + set click here to show and hide
25	x,y,z,-1	1'
26	x-y,x,z,-1	6'⁺₀₀₁
27	-y,x-y,z,-1	3'⁺₀₀₁
28	-x,-y,z,-1	2'₀₀₁
29	-x+y,-x,z,-1	3'^-₀₀₁
30	y,-x+y,z,-1	6'^-₀₀₁
31	x-y,-y,-z,-1	2'₁₀₀
32	x,x-y,-z,-1	2'₂₁₀
33	y,x,-z,-1	2'₁₁₀
34	-x+y,y,-z,-1	2'₁₂₀
35	-x,-x+y,-z,-1	2'₀₁₀
36	-y,-x,-z,-1	2'_1-10
37	-x,-y,-z,-1	-1'
38	-x+y,-x,-z,-1	-6'⁺₀₀₁
39	y,-x+y,-z,-1	-3'⁺₀₀₁
40	x,y,-z,-1	m'₀₀₁
41	x-y,x,-z,-1	-3'^-₀₀₁
42	-y,x-y,-z,-1	-6'^-₀₀₁
43	-x+y,y,z,-1	m'₁₀₀
44	-x,-x+y,z,-1	m'₂₁₀
45	-y,-x,z,-1	m'₁₁₀
46	x-y,-y,z,-1	m'₁₂₀
47	x,x-y,z,-1	m'₀₁₀
48	y,x,z,-1	m'_1-10

Label	Atom type	x	y	z	Multiplicity
Bi1	Bi	0.25613	0.00000	0.25000	6
Bi2	Bi	0.33333	0.66667	0.00000	4
Ti1	Ti	0.00000	0.00000	0.00000	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
Ce1	0	0	M_zc1	0.0	0.0	-0.50	M_xs1	0	0	-0.50	0.0	0.0

Atom	x	y	z
1	0.61790	0.00000	0.25000
2	0.61790	0.61790	0.75000
3	0.00000	0.61790	0.25000
4	0.38210	0.00000	0.75000
5	0.38210	0.38210	0.25000
6	0.00000	0.38210	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	-0.50000	M_xcos1+M_ysin1	0	0	-0.50000	0.0	0.0
2	0	0	M_zcos1	0.0	0.0	-0.50000	M_xcos1+M_ysin1	M_xcos1+M_ysin1	0	-0.50000	-0.50000	0.0
3	0	0	M_zcos1	0.0	0.0	-0.50000	0	M_xcos1+M_ysin1	0	0.0	-0.50000	0.0
4	0	0	M_zcos1	0.0	0.0	-0.50000	-M_xcos1-M_ysin1	0	0	0.50000	0.0	0.0
5	0	0	M_zcos1	0.0	0.0	-0.50000	-M_xcos1-M_ysin1	-M_xcos1-M_ysin1	0	0.50000	0.50000	0.0
6	0	0	M_zcos1	0.0	0.0	-0.50000	0	-M_xcos1-M_ysin1	0	0.0	0.50000	0.0

Atom	x	y	z
1	0.25613	0.00000	0.25000
2	0.25613	0.25613	0.75000
3	0.00000	0.25613	0.25000
4	0.74387	0.00000	0.75000
5	0.74387	0.74387	0.25000
6	0.00000	0.74387	0.75000

Atom	x	y	z
1	0.33333	0.66667	0.00000
2	0.66666	0.33333	0.50000
3	0.66667	0.33333	0.00000
4	0.33334	0.66667	0.50000

Atom	x	y	z
1	0.00000	0.00000	0.00000
2	0.00000	0.00000	0.50000

Reference: N. Gauthier, R. Sibille, V. Pomjakushin, O.S. Fjellvag, J. Fraser, M. Desmarais, A.D. Bianchi, J.A. Quilliam, PHYSICAL REVIEW B (2024) 109 L140405
DOI: 10.1103/PhysRevB.109.L140405
Atomic positions from: same reference

Parent space group (paramagnetic phase): P6₃/mcm (#193)
Propagation vector: k1 (0.00000, 0.00000, 0.386)

Transition Temperature: 5 K
Experiment Temperature: 1.7 K

Lattice parameters of the basic unit cell:
9.58146 9.58146 6.40091 90.00000 90.00000 120.00000
Transformation from parent structure: (a,b,c;0,0,0)
    [View matrix form]

Magnetic Superspace Group: P6_3/mcm.1'(0,0,g)00sss
    [View symmetry operations]

Magnetic Point Group: 6/mmm.1' (27.2.101)
    [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
Ce1	Ce	0.6179	0.00000	0.25000	6

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
Ce1	0	0	M_zc1	0.0	0.0	-0.50	M_xs1	0	0	-0.50	0.0	0.0

Atom	x	y	z
1	0.61790	0.00000	0.25000
2	0.61790	0.61790	0.75000
3	0.00000	0.61790	0.25000
4	0.38210	0.00000	0.75000
5	0.38210	0.38210	0.25000
6	0.00000	0.38210	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	-0.50000	M_xcos1+M_ysin1	0	0	-0.50000	0.0	0.0
2	0	0	M_zcos1	0.0	0.0	-0.50000	M_xcos1+M_ysin1	M_xcos1+M_ysin1	0	-0.50000	-0.50000	0.0
3	0	0	M_zcos1	0.0	0.0	-0.50000	0	M_xcos1+M_ysin1	0	0.0	-0.50000	0.0
4	0	0	M_zcos1	0.0	0.0	-0.50000	-M_xcos1-M_ysin1	0	0	0.50000	0.0	0.0
5	0	0	M_zcos1	0.0	0.0	-0.50000	-M_xcos1-M_ysin1	-M_xcos1-M_ysin1	0	0.50000	0.50000	0.0
6	0	0	M_zcos1	0.0	0.0	-0.50000	0	-M_xcos1-M_ysin1	0	0.0	0.50000	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
mDT2	1	2	general	primary	2

Comments:

NPD and neutron single crystal diffraction

Comments (symmetry):

1k incommensurate magnetic structure
2-dim (k,-k) irrep along a general direction (global phase is arbitrary. it is fixed by the origin chosen for the MSSG along x4)

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

Ce₃TiBi₅ (#1.1.155)

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

Ce3TiBi5 (#1.1.155)

Ce₃TiBi₅ (#1.1.155)