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	{ 2₀₀₁ \| 0 }
3	x1,-x2,x3,x4+1/2,+1	{ m₀₁₀ \| 0 0 0 1/2 }
4	-x1,x2,x3,-x4+1/2,+1	{ m₁₀₀ \| 0 0 0 1/2 }
5	x1,x2,x3,x4+1/2,-1	{ 1' \| 0 0 0 1/2 }
6	-x1,-x2,x3,-x4+1/2,-1	{ 2'₀₀₁ \| 0 0 0 1/2 }
7	x1,-x2,x3,x4,-1	{ m'₀₁₀ \| 0 }
8	-x1,x2,x3,-x4,-1	{ m'₁₀₀ \| 0 }
9	x1+1/2,x2+1/2,x3+1/2,x4,+1	{ 1 \| 1/2 1/2 1/2 0 }
10	-x1+1/2,-x2+1/2,x3+1/2,-x4,+1	{ 2₀₀₁ \| 1/2 1/2 1/2 0 }
11	x1+1/2,-x2+1/2,x3+1/2,x4+1/2,+1	{ m₀₁₀ \| 1/2 1/2 1/2 1/2 }
12	-x1+1/2,x2+1/2,x3+1/2,-x4+1/2,+1	{ m₁₀₀ \| 1/2 1/2 1/2 1/2 }
13	x1+1/2,x2+1/2,x3+1/2,x4+1/2,-1	{ 1' \| 1/2 1/2 1/2 1/2 }
14	-x1+1/2,-x2+1/2,x3+1/2,-x4+1/2,-1	{ 2'₀₀₁ \| 1/2 1/2 1/2 1/2 }
15	x1+1/2,-x2+1/2,x3+1/2,x4,-1	{ m'₀₁₀ \| 1/2 1/2 1/2 0 }
16	-x1+1/2,x2+1/2,x3+1/2,-x4,-1	{ m'₁₀₀ \| 1/2 1/2 1/2 0 }
(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,-1	{ 2'₀₀₁ \| 0 0 0 1/2 }
19	x1,-x2,x3,x4,-1	{ m'₀₁₀ \| 0 }
20	-x1,x2,x3,-x4,-1	{ m'₁₀₀ \| 0 }
21	x1,x2,x3,x4,+1	{ 1 \| 0 }
22	-x1,-x2,x3,-x4,+1	{ 2₀₀₁ \| 0 }
23	x1,-x2,x3,x4+1/2,+1	{ m₀₁₀ \| 0 0 0 1/2 }
24	-x1,x2,x3,-x4+1/2,+1	{ m₁₀₀ \| 0 0 0 1/2 }
25	x1+1/2,x2+1/2,x3+1/2,x4+1/2,-1	{ 1' \| 1/2 1/2 1/2 1/2 }
26	-x1+1/2,-x2+1/2,x3+1/2,-x4+1/2,-1	{ 2'₀₀₁ \| 1/2 1/2 1/2 1/2 }
27	x1+1/2,-x2+1/2,x3+1/2,x4,-1	{ m'₀₁₀ \| 1/2 1/2 1/2 0 }
28	-x1+1/2,x2+1/2,x3+1/2,-x4,-1	{ m'₁₀₀ \| 1/2 1/2 1/2 0 }
29	x1+1/2,x2+1/2,x3+1/2,x4,+1	{ 1 \| 1/2 1/2 1/2 0 }
30	-x1+1/2,-x2+1/2,x3+1/2,-x4,+1	{ 2₀₀₁ \| 1/2 1/2 1/2 0 }
31	x1+1/2,-x2+1/2,x3+1/2,x4+1/2,+1	{ m₀₁₀ \| 1/2 1/2 1/2 1/2 }
32	-x1+1/2,x2+1/2,x3+1/2,-x4+1/2,+1	{ m₁₀₀ \| 1/2 1/2 1/2 1/2 }

N	(x,y,z)	Seitz notation
1	x,y,z,+1	1
2	-x,-y,z,+1	2₀₀₁
3	x,-y,z,+1	m₀₁₀
4	-x,y,z,+1	m₁₀₀
1' + set click here to show and hide
5	x,y,z,-1	1'
6	-x,-y,z,-1	2'₀₀₁
7	x,-y,z,-1	m'₀₁₀
8	-x,y,z,-1	m'₁₀₀

Label	Atom type	y	z	Multiplicity
Al1_1	Al	0	0.18	2
Al1_2	Al	0.5	0.43	2
Ge1_1	Ge	0	0.01	2
Ge1_2	Ge	0.5	0.26	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_1	0	0	M_zcos1	0.0	0.0	-0.30(8)	M_xsin1	0	0	0.64(1)	0.0	0.0
Ce1_2	0	0	M_zcos1	0.0	0.0	0.4(1)	M_xsin1	0	0	1.45(2)	0.0	0.0

Atom	x	y	z
1	0.00000	0.00000	0.59000
2	0.50000	0.50000	0.09000

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	-0.30000	M_xsin1	0	0	0.64000	0.0	0.0
2	0	0	M_zcos1	0.0	0.0	-0.30000	M_xsin1	0	0	0.64000	0.0	0.0

Atom	x	y	z
1	0.00000	0.50000	0.84000
2	0.50000	0.00000	0.34000

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	0.40000	M_xsin1	0	0	1.45000	0.0	0.0
2	0	0	M_zcos1	0.0	0.0	0.40000	M_xsin1	0	0	1.45000	0.0	0.0

Atom	x	y	z
1	0.00000	0.00000	0.18000
2	0.50000	0.50000	0.68000

Atom	x	y	z
1	0.00000	0.50000	0.43000
2	0.50000	0.00000	0.93000

Atom	x	y	z
1	0.00000	0.00000	0.01000
2	0.50000	0.50000	0.51000

Atom	x	y	z
1	0.00000	0.50000	0.26000
2	0.50000	0.00000	0.76000

Reference: P. Puphal, V. Pomjakushin, N. Kanazawa, V. Ukleev, D.J. Gawryluk, J. Ma, M. Naamneh, N.C. Plumb, L. Keller, R. Cubitt, E. Pomjakushina and J.S. White, Physical Review Letters (2020) 124 017202.
DOI: 10.1103/physrevlett.124.017202
Atomic positions from: same reference

Parent space group (paramagnetic phase): I4₁md (#109)
Propagation vector: k1 (0.066000, 0.000000, 0.000000)

Transition Temperature: 4.4 K
Experiment Temperature: 1.5 K

Lattice parameters of the basic unit cell:
4.2572 4.2572 14.6452 90 90 90
Transformation from parent structure: (a,b,c;0,0,0)
    [View matrix form]

Magnetic Superspace Group: Imm21'(α00)0s0s
    [View symmetry operations]

Magnetic Point Group: mm21' (7.2.21)
    [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_1	Ce	0	0	0.59	2
Ce1_2	Ce	0	0.5	0.84	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
Ce1_1	0	0	M_zcos1	0.0	0.0	-0.30(8)	M_xsin1	0	0	0.64(1)	0.0	0.0
Ce1_2	0	0	M_zcos1	0.0	0.0	0.4(1)	M_xsin1	0	0	1.45(2)	0.0	0.0

Atom	x	y	z
1	0.00000	0.00000	0.59000
2	0.50000	0.50000	0.09000

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	-0.30000	M_xsin1	0	0	0.64000	0.0	0.0
2	0	0	M_zcos1	0.0	0.0	-0.30000	M_xsin1	0	0	0.64000	0.0	0.0

Atom	x	y	z
1	0.00000	0.50000	0.84000
2	0.50000	0.00000	0.34000

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	0.40000	M_xsin1	0	0	1.45000	0.0	0.0
2	0	0	M_zcos1	0.0	0.0	0.40000	M_xsin1	0	0	1.45000	0.0	0.0

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

Active Irreps:

label	dim. small irrep	dim. full irrep	action	number of modes
mSM2	1	4	primary	4

Comments:

Comments (symmetry):

1k incommensurate magnetic structure
k-maximal magnetic superspace symmetry
A 2k incommensurate model equally fits the data. The 2k model of higher symmetry is prioritized in the reference.
1-dim small irrep and 2-dim irrep for the 1k structure as primary irrep. General direction of the OP within this 2-dim irrep (restricted to a single k).

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

CeAlGe (#1.1.68)