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,x3-x4+1/2,+1	{ 2₀₀₁ \| 0 0 0 1/2 }
3	x2,x1,-x3,-x3+x4,+1	{ 2₁₁₀ \| 0 }
4	-x2,-x1,-x3,-x4+1/2,+1	{ 2_1-10 \| 0 0 0 1/2 }
5	-x1+1/2,-x2+1/2,-x3,-x4,+1	{ -1 \| 1/2 1/2 0 0 }
6	x1+1/2,x2+1/2,-x3,-x3+x4+1/2,+1	{ m₀₀₁ \| 1/2 1/2 0 1/2 }
7	-x2+1/2,-x1+1/2,x3,x3-x4,+1	{ m₁₁₀ \| 1/2 1/2 0 0 }
8	x2+1/2,x1+1/2,x3,x4+1/2,+1	{ m_1-10 \| 1/2 1/2 0 1/2 }
(0,0,0,1/2)' + set click here to show and hide
9	x1,x2,x3,x4+1/2,-1	{ 1' \| 0 0 0 1/2 }
10	-x1,-x2,x3,x3-x4,-1	{ 2'₀₀₁ \| 0 }
11	x2,x1,-x3,-x3+x4+1/2,-1	{ 2'₁₁₀ \| 0 0 0 1/2 }
12	-x2,-x1,-x3,-x4,-1	{ 2'_1-10 \| 0 }
13	-x1+1/2,-x2+1/2,-x3,-x4+1/2,-1	{ -1' \| 1/2 1/2 0 1/2 }
14	x1+1/2,x2+1/2,-x3,-x3+x4,-1	{ m'₀₀₁ \| 1/2 1/2 0 0 }
15	-x2+1/2,-x1+1/2,x3,x3-x4+1/2,-1	{ m'₁₁₀ \| 1/2 1/2 0 1/2 }
16	x2+1/2,x1+1/2,x3,x4,-1	{ m'_1-10 \| 1/2 1/2 0 0 }

N	(x,y,z)	Seitz notation
1	x,y,z,+1	1
2	-x,-y,z,+1	2₀₀₁
3	y,x,-z,+1	2₁₁₀
4	-y,-x,-z,+1	2_1-10
5	-x,-y,-z,+1	-1
6	x,y,-z,+1	m₀₀₁
7	-y,-x,z,+1	m₁₁₀
8	y,x,z,+1	m_1-10
1' + set click here to show and hide
9	x,y,z,-1	1'
10	-x,-y,z,-1	2'₀₀₁
11	y,x,-z,-1	2'₁₁₀
12	-y,-x,-z,-1	2'_1-10
13	-x,-y,-z,-1	-1'
14	x,y,-z,-1	m'₀₀₁
15	-y,-x,z,-1	m'₁₁₀
16	y,x,z,-1	m'_1-10

Label	Atom type	x	y	z	Multiplicity
Au	Au	-0.5	0.5	0.5	2
Sb1	Sb	0	0	0	2
Sb2	Sb	0	0.5	0.331921	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
Ce	M_xcos1	M_xcos1	M_zcos1	0.0	0.0	0.47(2)	-1.03049M_xcos1	-1.03049M_xcos1	0.97041M_zcos1	0.0	0.0	0.46(2)

Atom	x	y	z
1	0.00000	0.50000	0.74522
2	0.50000	0.00000	0.25478

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	M_xcos1	M_xcos1	M_zcos1	0.0	0.0	0.47000	-1.03049M_xcos1	-1.03049M_xcos1	0.97041M_zcos1	0.0	0.0	0.46000
2	1.00000M_xcos1	1.00000M_xcos1	1.00000M_zcos1	0.0	0.0	0.47391	1.03049M_xcos1	1.03049M_xcos1	-0.97041M_zcos1	0.0	0.0	-0.45597

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

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

Atom	x	y	z
1	0.00000	0.50000	0.33192
2	0.50000	0.00000	0.66808

Reference: R. Waite, F. Orlandi, D. A. Sokolov, R. A. Ribeiro, P. C. Canfield, P. Manuel, D. D. Khalyavin, C. W. Hicks, S. M. Hayden, PHYSICAL REVIEW B (2022) 106 224415
DOI: 10.1103/PhysRevB.106.224415
Atomic positions from: same reference

Parent space group (paramagnetic phase): P4/nmm (#129)
Propagation vector: k1 (0.137000, 0.137000, 0.500000)

Transition Temperature: 6.5 K
Experiment Temperature: 1.7 K

Lattice parameters of the basic unit cell:
4.3976(3) 4.3976(3) 10.30644(9) 90 90 90
Transformation from parent structure: (a,b,c;0,0,0)
    [View matrix form]

Magnetic Superspace Group: Cmmc1'(0,b,1/2)s0ss
    [View symmetry operations]

Magnetic Point Group: mmm1' (8.2.25)
    [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

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Average atomic positions of symmetry independent atoms

Label	Atom type	x	y	z	Multiplicity
Ce	Ce	0	0.5	0.74522	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
Ce	M_xcos1	M_xcos1	M_zcos1	0.0	0.0	0.47(2)	-1.03049M_xcos1	-1.03049M_xcos1	0.97041M_zcos1	0.0	0.0	0.46(2)

Atom	x	y	z
1	0.00000	0.50000	0.74522
2	0.50000	0.00000	0.25478

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	M_xcos1	M_xcos1	M_zcos1	0.0	0.0	0.47000	-1.03049M_xcos1	-1.03049M_xcos1	0.97041M_zcos1	0.0	0.0	0.46000
2	1.00000M_xcos1	1.00000M_xcos1	1.00000M_zcos1	0.0	0.0	0.47391	1.03049M_xcos1	1.03049M_xcos1	-0.97041M_zcos1	0.0	0.0	-0.45597

[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
mS4	1	4	general	primary	2

Comments:

NSD
Non-standard parent setting P4/nmm (N. 129), with origin 1 choice.
So-called phase A observed at zero stress. At non-zero (0,1,0) stress a commensurate phase is reported.
The atomic positions in the mcif file provided as supplemental material of the article differ from those given in the article for the same temperature. Here, the positions in this mcif file have been assumed to be correct.
The MSSG label refers to a basis (a-b,a+b,c;1/4,1/4,0) with respect to the basic unit cell and origin used here
The data could be equally well fitted with an alternative model according to irrep mS2, with the next nearest neighbors spins along z being AFM oriented, instead of FM oriented.

Comments (symmetry):

1k incommensurate magnetic structure
4-dim irrep with 4 k-vectors in its star. The spin arrangement involves a pair (k,-k) of this star, with the OP along a general direction (arbitrary phase). This arbitrary phase is however fixed by the choice of origin along x4 done by the form chosen for the MSSG operations transforming x4 into -x4.

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

CeAuSb₂ (#1.1.145)

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

CeAuSb2 (#1.1.145)

CeAuSb₂ (#1.1.145)