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	{ m₀₁₀ \| 0 0 1/2 0 }
(0,0,0,1/2)' + set click here to show and hide
3	x1,x2,x3,x4+1/2,-1	{ 1' \| 0 0 0 1/2 }
4	x1,-x2,x3+1/2,x4+1/2,-1	{ m'₀₁₀ \| 0 0 1/2 1/2 }
(1/2,1/2,0,0) + set click here to show and hide
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+1/2,x4,+1	{ m₀₁₀ \| 1/2 1/2 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,-1	{ m'₀₁₀ \| 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	m₀₁₀
1' + set click here to show and hide
3	x,y,z,-1	1'
4	x,-y,z,-1	m'₀₁₀

Label	Atom type	x	y	z	Multiplicity
Na1_1	Na	0.50000	0.80040	0.25000	4
Ge1_1	Ge	0.78810	0.59390	0.22990	4
Ge1_2	Ge	0.21190	0.59390	0.27010	4
O1_1	O	0.60530	0.58070	0.13030	4
O1_2	O	0.39470	0.58070	0.36970	4
O2_1	O	0.85670	0.77150	0.29950	4
O2_2	O	0.14330	0.77150	0.20050	4
O3_1	O	0.86160	0.50700	0.01470	4
O3_2	O	0.13840	0.50700	0.48530	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	M_ycos1	M_zcos1	3.857(8)	0.0	0.0	M_xsin1	M_ysin1	M_zsin1	0.0	0.0	3.857

Atom	x	y	z
1	0.00000	0.90380	0.25000
(0,0,0,1/2)' + set click here to show and hide
2	0.00000	0.09620	0.75000
(1/2,1/2,0,0) + set click here to show and hide
3	0.50000	0.40380	0.25000
(1/2,1/2,0,1/2)' + set click here to show and hide
4	0.50000	0.59620	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	M_ycos1	M_zcos1	3.85700	0.0	0.0	M_xsin1	M_ysin1	M_zsin1	0.0	0.0	3.85700
(0,0,0,1/2)' + set click here to show and hide
2	-M_xcos1	M_ycos1	-M_zcos1	-3.85700	0.0	0.0	-M_xsin1	M_ysin1	-M_zsin1	0.0	0.0	-3.85700
(1/2,1/2,0,0) + set click here to show and hide
3	M_xcos1	M_ycos1	M_zcos1	3.85700	0.0	0.0	M_xsin1	M_ysin1	M_zsin1	0.0	0.0	3.85700
(1/2,1/2,0,1/2)' + set click here to show and hide
4	-M_xcos1	M_ycos1	-M_zcos1	-3.85700	0.0	0.0	-M_xsin1	M_ysin1	-M_zsin1	0.0	0.0	-3.85700

Atom	x	y	z
1	0.50000	0.80040	0.25000
(0,0,0,1/2)' + set click here to show and hide
2	0.50000	0.19960	0.75000
(1/2,1/2,0,0) + set click here to show and hide
3	0.00000	0.30040	0.25000
(1/2,1/2,0,1/2)' + set click here to show and hide
4	0.00000	0.69960	0.75000

Atom	x	y	z
1	0.78810	0.59390	0.22990
(0,0,0,1/2)' + set click here to show and hide
2	0.78810	0.40610	0.72990
(1/2,1/2,0,0) + set click here to show and hide
3	0.28810	0.09390	0.22990
(1/2,1/2,0,1/2)' + set click here to show and hide
4	0.28810	0.90610	0.72990

Atom	x	y	z
1	0.21190	0.59390	0.27010
(0,0,0,1/2)' + set click here to show and hide
2	0.21190	0.40610	0.77010
(1/2,1/2,0,0) + set click here to show and hide
3	0.71190	0.09390	0.27010
(1/2,1/2,0,1/2)' + set click here to show and hide
4	0.71190	0.90610	0.77010

Atom	x	y	z
1	0.60530	0.58070	0.13030
(0,0,0,1/2)' + set click here to show and hide
2	0.60530	0.41930	0.63030
(1/2,1/2,0,0) + set click here to show and hide
3	0.10530	0.08070	0.13030
(1/2,1/2,0,1/2)' + set click here to show and hide
4	0.10530	0.91930	0.63030

Atom	x	y	z
1	0.39470	0.58070	0.36970
(0,0,0,1/2)' + set click here to show and hide
2	0.39470	0.41930	0.86970
(1/2,1/2,0,0) + set click here to show and hide
3	0.89470	0.08070	0.36970
(1/2,1/2,0,1/2)' + set click here to show and hide
4	0.89470	0.91930	0.86970

Atom	x	y	z
1	0.85670	0.77150	0.29950
(0,0,0,1/2)' + set click here to show and hide
2	0.85670	0.22850	0.79950
(1/2,1/2,0,0) + set click here to show and hide
3	0.35670	0.27150	0.29950
(1/2,1/2,0,1/2)' + set click here to show and hide
4	0.35670	0.72850	0.79950

Atom	x	y	z
1	0.14330	0.77150	0.20050
(0,0,0,1/2)' + set click here to show and hide
2	0.14330	0.22850	0.70050
(1/2,1/2,0,0) + set click here to show and hide
3	0.64330	0.27150	0.20050
(1/2,1/2,0,1/2)' + set click here to show and hide
4	0.64330	0.72850	0.70050

Atom	x	y	z
1	0.86160	0.50700	0.01470
(0,0,0,1/2)' + set click here to show and hide
2	0.86160	0.49300	0.51470
(1/2,1/2,0,0) + set click here to show and hide
3	0.36160	0.00700	0.01470
(1/2,1/2,0,1/2)' + set click here to show and hide
4	0.36160	0.99300	0.51470

Atom	x	y	z
1	0.13840	0.50700	0.48530
(0,0,0,1/2)' + set click here to show and hide
2	0.13840	0.49300	0.98530
(1/2,1/2,0,0) + set click here to show and hide
3	0.63840	0.00700	0.48530
(1/2,1/2,0,1/2)' + set click here to show and hide
4	0.63840	0.99300	0.98530

Reference: L. Ding, P. Manuel, D.D. Khalyavin, F. Orlandi and A.A. Tsirlin, Physical Review B (2018) 98 094416.
DOI: 10.1103/physrevb.98.094416
Atomic positions from: ICSD #180310

Parent space group (paramagnetic phase): C2/c (#15)
Propagation vector: k1 (-0.6702(1), 0.00000, 0.08028(5))

Transition Temperature: 11.6 K
Experiment Temperature: 1.5 K

Lattice parameters of the basic unit cell:
9.99290 8.91940 5.51480 90.00000 107.56300 90.00000
Transformation from parent structure: (a,b,c;0,0,0)
    [View matrix form]

Magnetic Superspace Group: Cc1'(a,0,g)0s
    [View symmetry operations]

Magnetic Point Group: m1' (4.2.10)
    [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_1	Fe	0.00000	-0.09620	0.25000	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_1	M_xcos1	M_ycos1	M_zcos1	3.857(8)	0.0	0.0	M_xsin1	M_ysin1	M_zsin1	0.0	0.0	3.857

Atom	x	y	z
1	0.00000	0.90380	0.25000
(0,0,0,1/2)' + set click here to show and hide
2	0.00000	0.09620	0.75000
(1/2,1/2,0,0) + set click here to show and hide
3	0.50000	0.40380	0.25000
(1/2,1/2,0,1/2)' + set click here to show and hide
4	0.50000	0.59620	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	M_ycos1	M_zcos1	3.85700	0.0	0.0	M_xsin1	M_ysin1	M_zsin1	0.0	0.0	3.85700
(0,0,0,1/2)' + set click here to show and hide
2	-M_xcos1	M_ycos1	-M_zcos1	-3.85700	0.0	0.0	-M_xsin1	M_ysin1	-M_zsin1	0.0	0.0	-3.85700
(1/2,1/2,0,0) + set click here to show and hide
3	M_xcos1	M_ycos1	M_zcos1	3.85700	0.0	0.0	M_xsin1	M_ysin1	M_zsin1	0.0	0.0	3.85700
(1/2,1/2,0,1/2)' + set click here to show and hide
4	-M_xcos1	M_ycos1	-M_zcos1	-3.85700	0.0	0.0	-M_xsin1	M_ysin1	-M_zsin1	0.0	0.0	-3.85700

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

Active Irreps:

label	dim. small irrep	dim. full irrep	direction	action
mB1	1	2	general	primary
mB1	1	2	general	primary

Comments:

NPD
Phase called ICM1, observed below 11.6K. Between 11.6K and 13K another incommensurate phase with higher centrosymmetry symmetry exists.
Positional structure retrieved from an icsd entry (180310) for the structure at 2.5K reported by a different work.

Comments (symmetry):

1k incommensurate magnetic structure
This structure requires two distinct order parameters, transforming according to the same irrep mB1, but with a phase shift between the two mB1 modulations. For the reported cycloidal form, this phase shift must be pi/2 (in quadrature).
The MSSG of the structure does not contain any operation transforming k into -k, and therefore, the phase origin of the modulation is not forced by the MSSG setting and can be set arbitrarily. Here it is chosen by setting the component mxs1 to zero.
Polar on the plane ac. Magnetically induced ferroelectricity on the ac plane (multiferroic of type II)

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