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

Label	Atom type	x	y	z	Multiplicity
Sr1	Sr	0	0	0.5	2
Sr2	Sr	0	0	0.31700	4
O1_1	O	0	0.5	0.0948	4
O1_2	O	0.5	0	0.0948	4
O2	O	0	0	0.19330	4
O3	O	0	0	0	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
Fe1	0	0	M_zcos1	0.0	0.0	3.19	M_xsin1	M_ysin1	0	2.5	-2.5	0.0

Atom	x	y	z
1	0.00000	0.00000	0.09720
2	0.00000	0.00000	0.90280
(1/2,1/2,1/2,1/2) + set click here to show and hide
3	0.50000	0.50000	0.59720
4	0.50000	0.50000	0.40280

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	3.19000	M_xsin1	M_ysin1	0	2.50000	-2.50000	0.0
2	0	0	M_zcos1	0.0	0.0	3.19000	-M_ysin1	-M_xsin1	0	2.50000	-2.50000	0.0
(1/2,1/2,1/2,1/2) + set click here to show and hide
3	0	0	-M_zcos1	0.0	0.0	-3.19000	-M_xsin1	-M_ysin1	0	-2.50000	2.50000	0.0
4	0	0	-M_zcos1	0.0	0.0	-3.19000	M_ysin1	M_xsin1	0	-2.50000	2.50000	0.0

Atom	x	y	z
1	0.00000	0.00000	0.50000
(1/2,1/2,1/2,1/2) + set click here to show and hide
2	0.50000	0.50000	0.00000

Atom	x	y	z
1	0.00000	0.00000	0.31700
2	0.00000	0.00000	0.68300
(1/2,1/2,1/2,1/2) + set click here to show and hide
3	0.50000	0.50000	0.81700
4	0.50000	0.50000	0.18300

Atom	x	y	z
1	0.00000	0.50000	0.09480
2	0.50000	0.00000	0.90520
(1/2,1/2,1/2,1/2) + set click here to show and hide
3	0.50000	0.00000	0.59480
4	0.00000	0.50000	0.40520

Atom	x	y	z
1	0.50000	0.00000	0.09480
2	0.00000	0.50000	0.90520
(1/2,1/2,1/2,1/2) + set click here to show and hide
3	0.00000	0.50000	0.59480
4	0.50000	0.00000	0.40520

Atom	x	y	z
1	0.00000	0.00000	0.19330
2	0.00000	0.00000	0.80670
(1/2,1/2,1/2,1/2) + set click here to show and hide
3	0.50000	0.50000	0.69330
4	0.50000	0.50000	0.30670

Atom	x	y	z
1	0.00000	0.00000	0.00000
(1/2,1/2,1/2,1/2) + set click here to show and hide
2	0.50000	0.50000	0.50000

Reference: J.-H. Kim, A. Jain, M. Reehuis, G. Khaliullin, D. Peets, C. Ulrich, J. Park, E. Faulhaber, A. Hoser, H. Walker, D. Adroja, A. Walters, D. Inosov, A. Maljuk and B. Keimer, Physical Review Letters (2014) 113 147206.
DOI: 10.1103/physrevlett.113.147206
Atomic positions from: ICSD #74422

Parent space group (paramagnetic phase): I4/mmm (#139)
Propagation vector: k1 (0.141600, 0.141600, 0.000000)

Transition Temperature: 115 K
Experiment Temperature: 2 K

Lattice parameters of the basic unit cell:
3.846 3.846 20.234 90 90 90
Transformation from parent structure: (a,b,c;0,0,0)
    [View matrix form]

Magnetic Superspace Group: X2221'(α,α,0)s00s
    [View symmetry operations]

Magnetic Point Group: 2221' (6.2.18)
    [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
Fe1	Fe	0	0	0.09720	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
Fe1	0	0	M_zcos1	0.0	0.0	3.19	M_xsin1	M_ysin1	0	2.5	-2.5	0.0

Atom	x	y	z
1	0.00000	0.00000	0.09720
2	0.00000	0.00000	0.90280
(1/2,1/2,1/2,1/2) + set click here to show and hide
3	0.50000	0.50000	0.59720
4	0.50000	0.50000	0.40280

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	3.19000	M_xsin1	M_ysin1	0	2.50000	-2.50000	0.0
2	0	0	M_zcos1	0.0	0.0	3.19000	-M_ysin1	-M_xsin1	0	2.50000	-2.50000	0.0
(1/2,1/2,1/2,1/2) + set click here to show and hide
3	0	0	-M_zcos1	0.0	0.0	-3.19000	-M_xsin1	-M_ysin1	0	-2.50000	2.50000	0.0
4	0	0	-M_zcos1	0.0	0.0	-3.19000	M_ysin1	M_xsin1	0	-2.50000	2.50000	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
mY3	1	4	primary	1
mY2	1	4	primary	2

Comments:

NPD
atomic positions from icsd 74422 but unit cell parameters from reference

Comments (symmetry):

1k magnetic structure
2 active irreps mY2 and mY3
mY3: (1,-1,0) spin component
mY2: (1,1,0) and (0,0,1) components
Combination of the two irreps in quadrature.
On the ab plane the spin direction (-1,1,0) of the model is not forced by symmetry.
Apparently, simpler models with a single irrep (allowing cycloidal spin modulations) were not tried in the refinement, before trying this spiral model.
X centered model. The original propagation vector is of type (a,a,1). Transformed to (a,a,0) through the additional centering

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

Sr₃Fe₂O₇ (#1.1.22)

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

Sr3Fe2O7 (#1.1.22)

Sr₃Fe₂O₇ (#1.1.22)