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
Rb1	Rb	0	0	0.5	1
Mo1	Mo	0.333333	0.666667	0.234(3)	1
Mo2	Mo	-0.333333	-0.666667	-0.234(3)	1
O1	O	0.333333	0.666667	0.463(6)	1
O2	O	-0.333333	-0.666667	-0.463(6)	1
O3	O	0.103(4)	-0.218(3)	0.158(4)	3
O4	O	-0.103(4)	0.218(3)	-0.158(4)	3

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	-0.57735M_xsin1	-1.15470M_xsin1	0	-2.25167	-4.50333	0.0	M_xsin1	0	0	3.9(5)	0.0	0.0

Atom	x	y	z
1	0.00000	0.00000	0.00000

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	-2.25167	-4.50333	0.0	M_xsin1	0	0	3.90000	0.0	0.0

Atom	x	y	z
1	0.00000	0.00000	0.50000

Atom	x	y	z
1	0.33333	0.66667	0.23400

Atom	x	y	z
1	0.66667	0.33333	0.76600

Atom	x	y	z
1	0.33333	0.66667	0.46300

Atom	x	y	z
1	0.66667	0.33333	0.53700

Atom	x	y	z
1	0.10300	0.78200	0.15800
2	0.21800	0.32100	0.15800
3	0.67900	0.89700	0.15800

Atom	x	y	z
1	0.89700	0.21800	0.84200
2	0.78200	0.67900	0.84200
3	0.32100	0.10300	0.84200

Reference: M. Kenzelmann, G. Lawes, A.B. Harris, G. Gasparovic, C. Broholm, A.P. Ramirez, G.A. Jorge, M. Jaime, S. Park, Q. Huang, A.Y. Shapiro and L.A. Demianets, Physical Review Letters (2007) 98 267205.
DOI: 10.1103/physrevlett.98.267205
Atomic positions from: ICSD #245666

Parent space group (paramagnetic phase): P-3 (#147)
Propagation vector: k1 (0.333333, 0.333333, 0.458000)

Transition Temperature: 3.8 K
Experiment Temperature: 2 K

Lattice parameters of the basic unit cell:
5.5955(6) 5.5955(6) 7.4377(7) 90 90 120
Transformation from parent structure: (a,b,c;0,0,0)
    [View matrix form]

Magnetic Superspace Group: P31'(1/31/3γ)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	Fe	0	0	0	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	-0.57735M_xsin1	-1.15470M_xsin1	0	-2.25167	-4.50333	0.0	M_xsin1	0	0	3.9(5)	0.0	0.0

Atom	x	y	z
1	0.00000	0.00000	0.00000

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	-2.25167	-4.50333	0.0	M_xsin1	0	0	3.90000	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
mP2mP3	2	4	special	primary	1

Comments:

NSD
Polar point group along z
Multiferroic
Circular spiral along z and 120 degrees configuration on the plane xy are forced by the superspace group symmetry.
x and z 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 y sine amplitude. In orthogonal coordinates, this reduces to quadrature relation between x and y components.
other reference: J. Phys.: Condens. Matter 23 (2011) 446003

Comments (symmetry):

1k incommensurate magnetic structure
There is a higher temperature paramagnetic phase with P-3m symmetry.
The active irrep is a 4-dim physically irreducible one , sum of two complex conjugate irreps.

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

RbFe(MoO₄)₂ (#1.1.2)

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

RbFe(MoO4)2 (#1.1.2)

RbFe(MoO₄)₂ (#1.1.2)