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+1/2,x4+1/2,+1	{ 2₀₁₀ \| 0 0 1/2 1/2 }
(1/2,1/2,0,0) + set click here to show and hide
3	x1+1/2,x2+1/2,x3,x4,+1	{ 1 \| 1/2 1/2 0 0 }
4	-x1+1/2,x2+1/2,-x3+1/2,x4+1/2,+1	{ 2₀₁₀ \| 1/2 1/2 1/2 1/2 }
(0,0,0,1/2)' + set click here to show and hide
5	x1,x2,x3,x4+1/2,-1	{ 1' \| 0 0 0 1/2 }
6	-x1,x2,-x3+1/2,x4,-1	{ 2'₀₁₀ \| 0 0 1/2 0 }
(1/2,1/2,0,1/2)' + set click here to show and hide
7	x1+1/2,x2+1/2,x3,x4+1/2,-1	{ 1' \| 1/2 1/2 0 1/2 }
8	-x1+1/2,x2+1/2,-x3+1/2,x4,-1	{ 2'₀₁₀ \| 1/2 1/2 1/2 0 }

N	(x,y,z)	Seitz notation
1	x,y,z,+1	1
2	-x,y,-z,+1	2₀₁₀
1' + set click here to show and hide
3	x,y,z,-1	1'
4	-x,y,-z,-1	2'₀₁₀

Label	Atom type	x	y	z	Multiplicity
Na1_1	Na	0	0.3002	0.25	2
Na1_2	Na	0	-0.3002	-0.25	2
Si1_1	Si	0.2905	0.0903	0.2379	4
Si1_2	Si	-0.2905	-0.0903	-0.2379	4
O1_1	O	0.1137	0.0796	0.1384	4
O1_2	O	-0.1137	-0.0796	-0.1384	4
O2_1	O	0.3595	0.2551	0.3041	4
O2_2	O	-0.3595	-0.2551	-0.3041	4
O3_1	O	0.3526	0.0089	0.0105	4
O3_2	O	-0.3526	-0.0089	-0.0105	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
Fe1_1	M_xcos1	0	M_zcos1	2.99	0.0	1.10	M_xsin1	0	M_zsin1	0.0	0.0	-3.13
Fe1_2	M_xcos1	0	M_zcos1	-2.92	0.0	-0.39	M_xsin1	0	M_zsin1	0.65	0.0	3.30

Atom	x	y	z
1	0.00000	0.89940	0.25000
(1/2,1/2,0,0) + set click here to show and hide
2	0.50000	0.39940	0.25000

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	0	M_zcos1	2.99000	0.0	1.10000	M_xsin1	0	M_zsin1	0.0	0.0	-3.13000
(1/2,1/2,0,0) + set click here to show and hide
2	M_xcos1	0	M_zcos1	2.99000	0.0	1.10000	M_xsin1	0	M_zsin1	0.0	0.0	-3.13000

Atom	x	y	z
1	0.00000	0.10060	0.75000
(1/2,1/2,0,0) + set click here to show and hide
2	0.50000	0.60060	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	M_xcos1	0	M_zcos1	-2.92000	0.0	-0.39000	M_xsin1	0	M_zsin1	0.65000	0.0	3.30000
(1/2,1/2,0,0) + set click here to show and hide
2	M_xcos1	0	M_zcos1	-2.92000	0.0	-0.39000	M_xsin1	0	M_zsin1	0.65000	0.0	3.30000

Atom	x	y	z
1	0.00000	0.30020	0.25000
(1/2,1/2,0,0) + set click here to show and hide
2	0.50000	0.80020	0.25000

Atom	x	y	z
1	0.00000	0.69980	0.75000
(1/2,1/2,0,0) + set click here to show and hide
2	0.50000	0.19980	0.75000

Atom	x	y	z
1	0.29050	0.09030	0.23790
2	0.70950	0.09030	0.26210
(1/2,1/2,0,0) + set click here to show and hide
3	0.79050	0.59030	0.23790
4	0.20950	0.59030	0.26210

Atom	x	y	z
1	0.70950	0.90970	0.76210
2	0.29050	0.90970	0.73790
(1/2,1/2,0,0) + set click here to show and hide
3	0.20950	0.40970	0.76210
4	0.79050	0.40970	0.73790

Atom	x	y	z
1	0.11370	0.07960	0.13840
2	0.88630	0.07960	0.36160
(1/2,1/2,0,0) + set click here to show and hide
3	0.61370	0.57960	0.13840
4	0.38630	0.57960	0.36160

Atom	x	y	z
1	0.88630	0.92040	0.86160
2	0.11370	0.92040	0.63840
(1/2,1/2,0,0) + set click here to show and hide
3	0.38630	0.42040	0.86160
4	0.61370	0.42040	0.63840

Atom	x	y	z
1	0.35950	0.25510	0.30410
2	0.64050	0.25510	0.19590
(1/2,1/2,0,0) + set click here to show and hide
3	0.85950	0.75510	0.30410
4	0.14050	0.75510	0.19590

Atom	x	y	z
1	0.64050	0.74490	0.69590
2	0.35950	0.74490	0.80410
(1/2,1/2,0,0) + set click here to show and hide
3	0.14050	0.24490	0.69590
4	0.85950	0.24490	0.80410

Atom	x	y	z
1	0.35260	0.00890	0.01050
2	0.64740	0.00890	0.48950
(1/2,1/2,0,0) + set click here to show and hide
3	0.85260	0.50890	0.01050
4	0.14740	0.50890	0.48950

Atom	x	y	z
1	0.64740	0.99110	0.98950
2	0.35260	0.99110	0.51050
(1/2,1/2,0,0) + set click here to show and hide
3	0.14740	0.49110	0.98950
4	0.85260	0.49110	0.51050

Reference: Baum, M et al., PHYSICAL REVIEW B (2015) 91 214415
DOI: 10.1103/PhysRevB.91.214415
Atomic positions from: same reference

Parent space group (paramagnetic phase): C2/c (#15)
Propagation vector: k1 (0.000000, 0.780000, 0.000000)

Transition Temperature: 6 K
Experiment Temperature: 1.9 K

Lattice parameters of the basic unit cell:
9.6618(5) 8.7933(4) 5.2946(2) 90 107.334(3) 90
Transformation from parent structure: (a,b,c;0,0,0)
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Magnetic Superspace Group: C21'(0β0)ss
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Magnetic Point Group: 21' (3.2.7)
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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
Fe1_1	Fe	0	0.8994	0.25	2
Fe1_2	Fe	0	-0.8994	-0.25	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
Fe1_1	M_xcos1	0	M_zcos1	2.99	0.0	1.10	M_xsin1	0	M_zsin1	0.0	0.0	-3.13
Fe1_2	M_xcos1	0	M_zcos1	-2.92	0.0	-0.39	M_xsin1	0	M_zsin1	0.65	0.0	3.30

Atom	x	y	z
1	0.00000	0.89940	0.25000
(1/2,1/2,0,0) + set click here to show and hide
2	0.50000	0.39940	0.25000

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	0	M_zcos1	2.99000	0.0	1.10000	M_xsin1	0	M_zsin1	0.0	0.0	-3.13000
(1/2,1/2,0,0) + set click here to show and hide
2	M_xcos1	0	M_zcos1	2.99000	0.0	1.10000	M_xsin1	0	M_zsin1	0.0	0.0	-3.13000

Atom	x	y	z
1	0.00000	0.10060	0.75000
(1/2,1/2,0,0) + set click here to show and hide
2	0.50000	0.60060	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	M_xcos1	0	M_zcos1	-2.92000	0.0	-0.39000	M_xsin1	0	M_zsin1	0.65000	0.0	3.30000
(1/2,1/2,0,0) + set click here to show and hide
2	M_xcos1	0	M_zcos1	-2.92000	0.0	-0.39000	M_xsin1	0	M_zsin1	0.65000	0.0	3.30000

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

Comments:

NSD
Transverse helical modulation with moment on the ac plane. Another incommensurate phase (transverse collinear) is reported between 6K and 9K (see entry #1.36)
Fourier components of the modulation for the symmetry independent Fe site are only given approximate values that roughly correspond to the parameters reported in the original reference.
Modulation: Mmax: 3.06(3), Mmin: 2.54(4), angle with c axis of major principal axis: 50 degrees, phase shift between modulation of atoms related by inversion: 0.218(2) radians.

Comments (symmetry):

1k magnetic incommensurate structure
MSSG associated with the superposition of two irrep modes for the same irrep.
The Fe site splits into two. Modulations for the two Fe sites are given equal values except for a phase shift. The phase shift indicated in the reference does not seem to correspond to the modulation shown in the figures. 180 degrees have added to conform with the figure.
Chiral structure, polar along b. Space inversion is broken by the magnetic modulation. Type II multiferroic.
The global phase of the modulation is arbitrary and has been fixed here by choosing zero for the amplitude of the sine term of the Mx modulation of Fe1_1.
The structure has seven parameters free. The correlation introduced between the two Fe sites reduces it to four.

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

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