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,-x2+x4+1/3,+1	{ 3⁺₀₀₁ \| 0 0 0 1/3 }
3	-x1+x2,-x1,x3,-x1+x4+2/3,+1	{ 3^-₀₀₁ \| 0 0 0 2/3 }
(0,0,0,1/2)' + set click here to show and hide
4	x1,x2,x3,x4+1/2,-1	{ 1' \| 0 0 0 1/2 }
5	-x2,x1-x2,x3,-x2+x4+5/6,-1	{ 3'⁺₀₀₁ \| 0 0 0 5/6 }
6	-x1+x2,-x1,x3,-x1+x4+1/6,-1	{ 3'^-₀₀₁ \| 0 0 0 1/6 }

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
1' + set click here to show and hide
4	x,y,z,-1	1'
5	-y,x-y,z,-1	3'⁺₀₀₁
6	-x+y,-x,z,-1	3'^-₀₀₁

Label	Atom type	x	y	z	Multiplicity
Ag1_1	Ag	0.33333	0.66667	0.296(1)	1
Ag1_2	Ag	0.66667	0.33333	0.704	1
K1_1	K	0.00000	0.00000	0.00000	1
V1_1	V	0.33333	0.66667	0.729(1)	1
V1_2	V	0.66667	0.33333	0.27100	1
O1_1	O	0.666(1)	-0.099(1)	0.663(1)	3
O1_2	O	0.33400	0.09900	0.33700	3
O2_1	O	0.33333	0.66667	-0.035(1)	1
O2_2	O	0.66667	0.33333	0.03500	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	-0.57735M_xsin1	-1.15470M_xsin1	0	-1.73205	-3.46410	0.0	M_xsin1	0	0	3.0	0.0	0.0

Atom	x	y	z
1	0.00000	0.00000	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	-0.57735M_xsin1	-1.15470M_xsin1	0	-1.73205	-3.46410	0.0	M_xsin1	0	0	3.00000	0.0	0.0

Atom	x	y	z
1	0.33333	0.66667	0.29600

Atom	x	y	z
1	0.66667	0.33333	0.70400

Atom	x	y	z
1	0.00000	0.00000	0.00000

Atom	x	y	z
1	0.33333	0.66667	0.72900

Atom	x	y	z
1	0.66667	0.33333	0.27100

Atom	x	y	z
1	0.66600	0.90100	0.66300
2	0.09900	0.76500	0.66300
3	0.23500	0.33400	0.66300

Atom	x	y	z
1	0.33400	0.09900	0.33700
2	0.90100	0.23500	0.33700
3	0.76500	0.66600	0.33700

Atom	x	y	z
1	0.33333	0.66667	0.96500

Atom	x	y	z
1	0.66667	0.33333	0.03500

Reference: N. E. Amuneke, J. Tapp, C. R. de la Cruz, A. Moller, Chem. Mater. (2014) 24 5930 - 5935
DOI: 10.1021/cm5025712
Atomic positions from: ICSD #194591

Parent space group (paramagnetic phase): P-3 (#147)
Propagation vector: k1 (0.33333, 0.33333, 0.4035(6))

Transition Temperature: 2.8 K
Experiment Temperature: 1.5 K

Lattice parameters of the basic unit cell:
5.4811(1) 5.4811 7.2119(1) 90.00000 90.00000 120.00000
Transformation from parent structure: (a,b,c;0,0,0)
    [View matrix form]

Magnetic Superspace Group: P31'(1/3,1/3,g)ts
    [View symmetry operations]

Magnetic Point Group: 31' (16.2.61)
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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	0.00000	0.00000	0.50000	1

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	-0.57735M_xsin1	-1.15470M_xsin1	0	-1.73205	-3.46410	0.0	M_xsin1	0	0	3.0	0.0	0.0

Atom	x	y	z
1	0.00000	0.00000	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	-0.57735M_xsin1	-1.15470M_xsin1	0	-1.73205	-3.46410	0.0	M_xsin1	0	0	3.00000	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
mP2P3	2	4	special	primary	1

Comments:

NPD
Polar along c
Multiferroic
The configuration on the plane xy of the layer (0 0 1/2) shown in Fig. 1 of the original reference corresponds to a phase shift of approx. 0.13 of the modulation with respect to the description here. This global modulation phase (i.e. the origin choice along x4) is arbitrary and the form of the symmetry operations of the relevant MSSG does not depend on this choice. Here, this phase origin has been fixed by making arbitrarily zero the y sine amplitude of the Fe moment modulation.
Fe moment magnitude: 3.0

Comments (symmetry):

1k incommensurate magnetic structure
The active primary irrep is a 4-dim physically irreducible representation, sum of two complex conjugate irreps.
The circular spiral along z and the 120 degrees configuration on the plane xy are forced by the MSSG.
The MSSG in the present description is equivalent to the MSSG P31'(1/3,1/3,g)0s (i.e. without phase shift (0,0,0,1/3) for the three fold rotation operation). The MSSG can be transformed to this simpler form through an origin shift (1/2,2/3,0), which is not done here, in order to preserve the origin of the parent structure.
The x and y cosine amplitudes of the moment modulation function are symmetry forced to be -1/(3)^0.5 and -2/(3)^0.5 times the value of the x sine amplitude, respectively. In orthogonal coordinates, this reduces to a quadrature relation between x and y components.
The x and y cosine amplitudes are given with non-significant digits to keep rigorously the symmetry relation with the value of the x sine amplitude.

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

KAg₂Fe(VO₄)₂ (#1.1.99)

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

KAg2Fe(VO4)2 (#1.1.99)

KAg₂Fe(VO₄)₂ (#1.1.99)