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	-x2,x1-x2,x3,x4,+1	{ 3⁺₀₀₁ \| 0 }
3	-x1+x2,-x1,x3,x4,+1	{ 3^-₀₀₁ \| 0 }
4	x2,x1,-x3,-x4,+1	{ 2₁₁₀ \| 0 }
5	x1-x2,-x2,-x3,-x4,+1	{ 2₁₀₀ \| 0 }
6	-x1,-x1+x2,-x3,-x4,+1	{ 2₀₁₀ \| 0 }
(0,0,0,1/2)' + set click here to show and hide
7	x1,x2,x3,x4+1/2,-1	{ 1' \| 0 0 0 1/2 }
8	-x2,x1-x2,x3,x4+1/2,-1	{ 3'⁺₀₀₁ \| 0 0 0 1/2 }
9	-x1+x2,-x1,x3,x4+1/2,-1	{ 3'^-₀₀₁ \| 0 0 0 1/2 }
10	x2,x1,-x3,-x4+1/2,-1	{ 2'₁₁₀ \| 0 0 0 1/2 }
11	x1-x2,-x2,-x3,-x4+1/2,-1	{ 2'₁₀₀ \| 0 0 0 1/2 }
12	-x1,-x1+x2,-x3,-x4+1/2,-1	{ 2'₀₁₀ \| 0 0 0 1/2 }

N	(x,y,z)	Seitz notation
1	x,y,z,+1	1
2	-y,x-y,z,+1	3⁺₀₀₁
3	-x+y,-x,z,+1	3^-₀₀₁
4	y,x,-z,+1	2₁₁₀
5	x-y,-y,-z,+1	2₁₀₀
6	-x,-x+y,-z,+1	2₀₁₀
1' + set click here to show and hide
7	x,y,z,-1	1'
8	-y,x-y,z,-1	3'⁺₀₀₁
9	-x+y,-x,z,-1	3'^-₀₀₁
10	y,x,-z,-1	2'₁₁₀
11	x-y,-y,-z,-1	2'₁₀₀
12	-x,-x+y,-z,-1	2'₀₁₀

Label	Atom type	x	y	z	Multiplicity
Ba1	Ba	0.56598(2)	0	0	3
Nb1	Nb	0	0	0	1
Si1	Si	0.666667	0.333333	0.5220(1)	2
O1	O	0.666667	0.333333	0.2162(4)	2
O2	O	0.5259(2)	0.7024(2)	0.3536(3)	6
O3	O	0.7840(2)	0.9002(2)	0.7760(3)	6

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	M_xcos1	0	0	4	0.0	0.0	M_xsin1	2M_xsin1	M_zsin1	-2.31	-4.62	0.0

Atom	x	y	z
1	0.24964	0.00000	0.50000
2	0.00000	0.24964	0.50000
3	0.75036	0.75036	0.50000

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	0	4.00000	0.0	0.0	M_xsin1	2M_xsin1	M_zsin1	-2.31000	-4.62000	0.0
2	0	M_xcos1	0	0.0	4.00000	0.0	-2M_xsin1	-M_xsin1	M_zsin1	4.62000	2.31000	0.0
3	-M_xcos1	-M_xcos1	0	-4.00000	-4.00000	0.0	M_xsin1	-M_xsin1	M_zsin1	-2.31000	2.31000	0.0

Atom	x	y
1	0.56598	0.00000
2	0.00000	0.56598
3	0.43402	0.43402

Atom	x	y	z
1	0.00000	0.00000	0.00000

Atom	x	y	z
1	0.66667	0.33333	0.52200
2	0.33333	0.66667	0.47800

Atom	x	y	z
1	0.66667	0.33333	0.21620
2	0.33333	0.66667	0.78380

Atom	x	y	z
1	0.52590	0.70240	0.35360
2	0.29760	0.82350	0.35360
3	0.17650	0.47410	0.35360
4	0.70240	0.52590	0.64640
5	0.82350	0.29760	0.64640
6	0.47410	0.17650	0.64640

Atom	x	y	z
1	0.78400	0.90020	0.77600
2	0.09980	0.88380	0.77600
3	0.11620	0.21600	0.77600
4	0.90020	0.78400	0.22400
5	0.88380	0.09980	0.22400
6	0.21600	0.11620	0.22400

Reference: K. Marty, V. Simonet, E. Ressouche, R. Ballou, P. Lejay and P. Bordet, Physical Review Letters (2008) 101 247201.
DOI: 10.1103/physrevlett.101.247201
Atomic positions from: ICSD #162894

Parent space group (paramagnetic phase): P321 (#150)
Propagation vector: k1 (0.000000, 0.000000, 0.143000)

Transition Temperature: 27 K
Experiment Temperature: 2 K

Lattice parameters of the basic unit cell:
8.539(1) 8.539(1) 5.2414(1) 90 90 120
Transformation from parent structure: (a,b,c;0,0,0)
    [View matrix form]

Magnetic Superspace Group: P3211'(00γ)000s
    [View symmetry operations]

Magnetic Point Group: 321' (18.2.66)
    [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	0.24964(4)	0	0.5	3

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	M_xcos1	0	0	4	0.0	0.0	M_xsin1	2M_xsin1	M_zsin1	-2.31	-4.62	0.0

Atom	x	y	z
1	0.24964	0.00000	0.50000
2	0.00000	0.24964	0.50000
3	0.75036	0.75036	0.50000

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	0	4.00000	0.0	0.0	M_xsin1	2M_xsin1	M_zsin1	-2.31000	-4.62000	0.0
2	0	M_xcos1	0	0.0	4.00000	0.0	-2M_xsin1	-M_xsin1	M_zsin1	4.62000	2.31000	0.0
3	-M_xcos1	-M_xcos1	0	-4.00000	-4.00000	0.0	M_xsin1	-M_xsin1	M_zsin1	-2.31000	2.31000	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
mDT1	1	2	primary	3

Comments:

NSD and also spin polarized diffraction
circular approximation for the spin helix with Fe spin modulus of 4 Bohr magnetons.
Alternative model in PHYSICAL REVIEW B 88, 104417 (2013). Unfortunately the model in this reference could not be fully interpreted and transformed into an unambiguous description within the superspace formalism, in order to be included in this collection.
This alternative model has an additional modulation component along c, but it does not seem to correspond to a generalization of the model here, and its superspace symmetry would be different, the two models being therefore in contradiction.
Positional structure from room temperature.
Fe1 sine spin modulation components along the (1,2,0) direction given with non significant digits to produce the reported spin modulus of the helix.

Comments (symmetry):

Elliptical spin oblique helix along c with elliptical axes forced by the MSSG to be along (1,0,0) and a variable direction of type (x,2x,z). The model reported implies z=0, restricting the helix plane to the ab plane. The sign of the spin helicity is not forced by symmetry.
2-dim active irrep, which means a one to one correspondence with the MSSG, but less free parameters than in the representation approach, due to the inclusion of the symmetry properties for operations changing k into -k.
Helices of the other Fe atom in the basic unit cell are related by three fold rotation, which means that the 120¼ spin arrangement on the xy plane is forced by the MSSG.
So-called positive triangular chirality among the helices is also forced by the MSSG. The opposite triangular chirality corresponds to a different irrep and MSSG.

Bilbao Crystallographic Server
http://www.cryst.ehu.es

For comments, please mail to
cryst@wm.lc.ehu.es

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

Ba₃NbFe₃Si₂O₁₄ (#1.1.17)

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

Ba3NbFe3Si2O14 (#1.1.17)

Ba₃NbFe₃Si₂O₁₄ (#1.1.17)