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	{ 2₀₁₀ \| 0 0 1/2 0 }
3	-x1,-x2,-x3,-x4,+1	{ -1 \| 0 }
4	x1,-x2,x3+1/2,x4,+1	{ m₀₁₀ \| 0 0 1/2 0 }
5	x1,x2,x3,x4+1/2,-1	{ 1' \| 0 0 0 1/2 }
6	-x1,x2,-x3+1/2,-x4+1/2,-1	{ 2'₀₁₀ \| 0 0 1/2 1/2 }
7	-x1,-x2,-x3,-x4+1/2,-1	{ -1' \| 0 0 0 1/2 }
8	x1,-x2,x3+1/2,x4+1/2,-1	{ m'₀₁₀ \| 0 0 1/2 1/2 }
9	x1+1/2,x2+1/2,x3,x4,+1	{ 1 \| 1/2 1/2 0 0 }
10	-x1+1/2,x2+1/2,-x3+1/2,-x4,+1	{ 2₀₁₀ \| 1/2 1/2 1/2 0 }
11	-x1+1/2,-x2+1/2,-x3,-x4,+1	{ -1 \| 1/2 1/2 0 0 }
12	x1+1/2,-x2+1/2,x3+1/2,x4,+1	{ m₀₁₀ \| 1/2 1/2 1/2 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+1/2,-x4+1/2,-1	{ 2'₀₁₀ \| 1/2 1/2 1/2 1/2 }
15	-x1+1/2,-x2+1/2,-x3,-x4+1/2,-1	{ -1' \| 1/2 1/2 0 1/2 }
16	x1+1/2,-x2+1/2,x3+1/2,x4+1/2,-1	{ m'₀₁₀ \| 1/2 1/2 1/2 1/2 }
(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+1/2,-x4+1/2,-1	{ 2'₀₁₀ \| 0 0 1/2 1/2 }
19	-x1,-x2,-x3,-x4+1/2,-1	{ -1' \| 0 0 0 1/2 }
20	x1,-x2,x3+1/2,x4+1/2,-1	{ m'₀₁₀ \| 0 0 1/2 1/2 }
21	x1,x2,x3,x4,+1	{ 1 \| 0 }
22	-x1,x2,-x3+1/2,-x4,+1	{ 2₀₁₀ \| 0 0 1/2 0 }
23	-x1,-x2,-x3,-x4,+1	{ -1 \| 0 }
24	x1,-x2,x3+1/2,x4,+1	{ m₀₁₀ \| 0 0 1/2 0 }
25	x1+1/2,x2+1/2,x3,x4+1/2,-1	{ 1' \| 1/2 1/2 0 1/2 }
26	-x1+1/2,x2+1/2,-x3+1/2,-x4+1/2,-1	{ 2'₀₁₀ \| 1/2 1/2 1/2 1/2 }
27	-x1+1/2,-x2+1/2,-x3,-x4+1/2,-1	{ -1' \| 1/2 1/2 0 1/2 }
28	x1+1/2,-x2+1/2,x3+1/2,x4+1/2,-1	{ m'₀₁₀ \| 1/2 1/2 1/2 1/2 }
29	x1+1/2,x2+1/2,x3,x4,+1	{ 1 \| 1/2 1/2 0 0 }
30	-x1+1/2,x2+1/2,-x3+1/2,-x4,+1	{ 2₀₁₀ \| 1/2 1/2 1/2 0 }
31	-x1+1/2,-x2+1/2,-x3,-x4,+1	{ -1 \| 1/2 1/2 0 0 }
32	x1+1/2,-x2+1/2,x3+1/2,x4,+1	{ m₀₁₀ \| 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
3	-x,-y,-z,+1	-1
4	x,-y,z,+1	m₀₁₀
1' + set click here to show and hide
5	x,y,z,-1	1'
6	-x,y,-z,-1	2'₀₁₀
7	-x,-y,-z,-1	-1'
8	x,-y,z,-1	m'₀₁₀

Label	Atom type	x	y	z	Multiplicity
Na1	Na	0	0.3000	0.25	4
Ge1	Ge	0.2881	0.09380	0.2296	8
O1	O	0.1053	0.0803	0.1304	8
O2	O	0.3569	0.27170	0.2997	8
O3	O	0.3615	0.0070	0.0149	8

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	M_ycos1	0	0.0	0.0	0.0	M_xsin1	0	M_zsin1	1.55(2)	0.0	0.0

Atom	x	y	z
1	0.00000	0.90380	0.25000
2	0.00000	0.09620	0.75000
3	0.50000	0.40380	0.25000
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	0	M_ycos1	0	0.0	0.0	0.0	M_xsin1	0	M_zsin1	1.55000	0.0	0.0
2	0	M_ycos1	0	0.0	0.0	0.0	-M_xsin1	0	-M_zsin1	-1.55000	0.0	0.0
3	0	M_ycos1	0	0.0	0.0	0.0	M_xsin1	0	M_zsin1	1.55000	0.0	0.0
4	0	M_ycos1	0	0.0	0.0	0.0	-M_xsin1	0	-M_zsin1	-1.55000	0.0	0.0

Atom	x	y	z
1	0.00000	0.30000	0.25000
2	0.00000	0.70000	0.75000
3	0.50000	0.80000	0.25000
4	0.50000	0.20000	0.75000

Atom	x	y	z
1	0.28810	0.09380	0.22960
2	0.71190	0.09380	0.27040
3	0.71190	0.90620	0.77040
4	0.28810	0.90620	0.72960
5	0.78810	0.59380	0.22960
6	0.21190	0.59380	0.27040
7	0.21190	0.40620	0.77040
8	0.78810	0.40620	0.72960

Atom	x	y	z
1	0.10530	0.08030	0.13040
2	0.89470	0.08030	0.36960
3	0.89470	0.91970	0.86960
4	0.10530	0.91970	0.63040
5	0.60530	0.58030	0.13040
6	0.39470	0.58030	0.36960
7	0.39470	0.41970	0.86960
8	0.60530	0.41970	0.63040

Atom	x	y	z
1	0.35690	0.27170	0.29970
2	0.64310	0.27170	0.20030
3	0.64310	0.72830	0.70030
4	0.35690	0.72830	0.79970
5	0.85690	0.77170	0.29970
6	0.14310	0.77170	0.20030
7	0.14310	0.22830	0.70030
8	0.85690	0.22830	0.79970

Atom	x	y	z
1	0.36150	0.00700	0.01490
2	0.63850	0.00700	0.48510
3	0.63850	0.99300	0.98510
4	0.36150	0.99300	0.51490
5	0.86150	0.50700	0.01490
6	0.13850	0.50700	0.48510
7	0.13850	0.49300	0.98510
8	0.86150	0.49300	0.51490

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 #180309

Parent space group (paramagnetic phase): C2/c (#15)
Propagation vector: k1 (-0.6999(8), 0.000000, 0.0649(2))

Transition Temperature: 13 K
Experiment Temperature: 12.2 K

Lattice parameters of the basic unit cell:
9.9932 8.9192 5.5145 90 107.5520 90
Transformation from parent structure: (a,b,c;0,0,0)
    [View matrix form]

Magnetic Superspace Group: C2/c1'(a0g)00s
    [View symmetry operations]

Magnetic Point Group: 2/m1' (5.2.13)
    [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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     [Show all the atoms]

Average atomic positions of symmetry independent atoms

Label	Atom type	x	y	z	Multiplicity
Fe1	Fe	0	0.90380	0.25	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	M_ycos1	0	0.0	0.0	0.0	M_xsin1	0	M_zsin1	1.55(2)	0.0	0.0

Atom	x	y	z
1	0.00000	0.90380	0.25000
2	0.00000	0.09620	0.75000
3	0.50000	0.40380	0.25000
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	0	M_ycos1	0	0.0	0.0	0.0	M_xsin1	0	M_zsin1	1.55000	0.0	0.0
2	0	M_ycos1	0	0.0	0.0	0.0	-M_xsin1	0	-M_zsin1	-1.55000	0.0	0.0
3	0	M_ycos1	0	0.0	0.0	0.0	M_xsin1	0	M_zsin1	1.55000	0.0	0.0
4	0	M_ycos1	0	0.0	0.0	0.0	-M_xsin1	0	-M_zsin1	-1.55000	0.0	0.0

[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
mB1	1	2	general	primary	3

Comments:

NPD
Phase called ICM2, observed between 13K and 11.6K. Below 11.6, another incommensurate phase with lower polar symmetry exists.
Positional structure retrieved from an icsd entry (180309) for the structure at 15K

Comments (symmetry):

1k incommensurate magnetic structure
k-maximal symmetry (2 possible)
2-dim irrep primary. The order parameter is two dimensional (amplitude and phase). Its arbitrary phase is chosen here such that the inversion center operation of its magnetic superspace group does not include any phase shift.

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

NaFeGe₂O₆ (#1.1.65)

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

NaFeGe2O6 (#1.1.65)

NaFeGe₂O₆ (#1.1.65)