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+1/2,-x2+1/2,x3,-x4+1/2,+1	{ 2₀₀₁ \| 1/2 1/2 0 1/2 }
3	-x1,x2+1/2,-x3,x4,+1	{ 2₀₁₀ \| 0 1/2 0 0 }
4	x1+1/2,-x2,-x3,-x4+1/2,+1	{ 2₁₀₀ \| 1/2 0 0 1/2 }
(0,0,0,1/2)' + set click here to show and hide
5	x1,x2,x3,x4+1/2,-1	{ 1' \| 0 0 0 1/2 }
6	-x1+1/2,-x2+1/2,x3,-x4,-1	{ 2'₀₀₁ \| 1/2 1/2 0 0 }
7	-x1,x2+1/2,-x3,x4+1/2,-1	{ 2'₀₁₀ \| 0 1/2 0 1/2 }
8	x1+1/2,-x2,-x3,-x4,-1	{ 2'₁₀₀ \| 1/2 0 0 0 }

N	(x,y,z)	Seitz notation
1	x,y,z,+1	1
2	-x,-y,z,+1	2₀₀₁
3	-x,y,-z,+1	2₀₁₀
4	x,-y,-z,+1	2₁₀₀
1' + set click here to show and hide
5	x,y,z,-1	1'
6	-x,-y,z,-1	2'₀₀₁
7	-x,y,-z,-1	2'₀₁₀
8	x,-y,-z,-1	2'₁₀₀

Label	Atom type	x	y	z	Multiplicity
Ca1	Ca	0.25	0.75	0.1481	2
Ca2	Ca	0.75	0.75	0.4648	2
O1	O	0.594	0.25	0.162	4
O2	O	0.409	0.25	0.821	4
O3_1	O	0.402	0.497	0.33	4
O3_2	O	-0.402	-0.497	-0.33	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
Cr1	M_xcos1	M_ycos1	M_zcos1	0.0	0.0	-1.98(4)	M_xsin1	M_ysin1	M_zsin1	-2.58(3)	0.0	0.0
Cr2	M_xcos1	M_ycos1	M_zcos1	2.58	0.0	0.0	M_xsin1	M_ysin1	M_zsin1	0.0	0.0	-1.98

Atom	x	y	z
1	0.99220	0.25000	0.49420
2	0.50780	0.25000	0.49420
3	0.00780	0.75000	0.50580
4	0.49220	0.75000	0.50580

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	0.0	0.0	-1.98000	M_xsin1	M_ysin1	M_zsin1	-2.58000	0.0	0.0
2	M_xcos1	M_ycos1	-M_zcos1	0.0	0.0	1.98000	-M_xsin1	-M_ysin1	M_zsin1	2.58000	0.0	0.0
3	-M_xcos1	M_ycos1	-M_zcos1	0.0	0.0	1.98000	-M_xsin1	M_ysin1	-M_zsin1	2.58000	0.0	0.0
4	-M_xcos1	M_ycos1	M_zcos1	0.0	0.0	-1.98000	M_xsin1	-M_ysin1	-M_zsin1	-2.58000	0.0	0.0

Atom	x	y
1	0.00000	0.00000
2	0.50000	0.50000
3	0.00000	0.50000
4	0.50000	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	M_xcos1	M_ycos1	M_zcos1	2.58000	0.0	0.0	M_xsin1	M_ysin1	M_zsin1	0.0	0.0	-1.98000
2	M_xcos1	M_ycos1	-M_zcos1	2.58000	0.0	0.0	-M_xsin1	-M_ysin1	M_zsin1	0.0	0.0	-1.98000
3	-M_xcos1	M_ycos1	-M_zcos1	-2.58000	0.0	0.0	-M_xsin1	M_ysin1	-M_zsin1	0.0	0.0	1.98000
4	-M_xcos1	M_ycos1	M_zcos1	-2.58000	0.0	0.0	M_xsin1	-M_ysin1	-M_zsin1	0.0	0.0	1.98000

Atom	x	y	z
1	0.25000	0.75000	0.14810
2	0.75000	0.25000	0.85190

Atom	x	y	z
1	0.75000	0.75000	0.46480
2	0.25000	0.25000	0.53520

Atom	x	y	z
1	0.59400	0.25000	0.16200
2	0.90600	0.25000	0.16200
3	0.40600	0.75000	0.83800
4	0.09400	0.75000	0.83800

Atom	x	y	z
1	0.40900	0.25000	0.82100
2	0.09100	0.25000	0.82100
3	0.59100	0.75000	0.17900
4	0.90900	0.75000	0.17900

Atom	x	y	z
1	0.40200	0.49700	0.33000
2	0.09800	0.00300	0.33000
3	0.59800	0.99700	0.67000
4	0.90200	0.50300	0.67000

Atom	x	y	z
1	0.59800	0.50300	0.67000
2	0.90200	0.99700	0.67000
3	0.40200	0.00300	0.33000
4	0.09800	0.49700	0.33000

Reference: S. Toth, B. Lake, S.A.J. Kimber, O. Pieper, M. Reehuis, A.T.M.N. Islam, O. Zaharko, C. Ritter, A.H. Hill, H. Ryll, K. Kiefer, D.N. Argyriou and A.J. Williams, Physical Review B (2011) 84 054452.
DOI: 10.1103/physrevb.84.054452
Atomic positions from: ICSD #6131

Parent space group (paramagnetic phase): Pmmn (#59)
Propagation vector: k1 (0.000000, 0.333(5), 0.000000)

Transition Temperature: 43 K
Experiment Temperature: 6 K

Lattice parameters of the basic unit cell:
11.059 5.836 5.114 90 90 90
Transformation from parent structure: (a,b,c;0,0,0)
    [View matrix form]

Magnetic Superspace Group: P2_12_121'(0b0)000s
    [View symmetry operations]

Magnetic Point Group: 2221' (6.2.18)
    [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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Average atomic positions of symmetry independent atoms

Label	Atom type	x	y	z	Multiplicity
Cr1	Cr	-0.00780	0.25000	0.49420	4
Cr2	Cr	0	0	0	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
Cr1	M_xcos1	M_ycos1	M_zcos1	0.0	0.0	-1.98(4)	M_xsin1	M_ysin1	M_zsin1	-2.58(3)	0.0	0.0
Cr2	M_xcos1	M_ycos1	M_zcos1	2.58	0.0	0.0	M_xsin1	M_ysin1	M_zsin1	0.0	0.0	-1.98

Atom	x	y	z
1	0.99220	0.25000	0.49420
2	0.50780	0.25000	0.49420
3	0.00780	0.75000	0.50580
4	0.49220	0.75000	0.50580

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	0.0	0.0	-1.98000	M_xsin1	M_ysin1	M_zsin1	-2.58000	0.0	0.0
2	M_xcos1	M_ycos1	-M_zcos1	0.0	0.0	1.98000	-M_xsin1	-M_ysin1	M_zsin1	2.58000	0.0	0.0
3	-M_xcos1	M_ycos1	-M_zcos1	0.0	0.0	1.98000	-M_xsin1	M_ysin1	-M_zsin1	2.58000	0.0	0.0
4	-M_xcos1	M_ycos1	M_zcos1	0.0	0.0	-1.98000	M_xsin1	-M_ysin1	-M_zsin1	-2.58000	0.0	0.0

Atom	x	y
1	0.00000	0.00000
2	0.50000	0.50000
3	0.00000	0.50000
4	0.50000	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	M_xcos1	M_ycos1	M_zcos1	2.58000	0.0	0.0	M_xsin1	M_ysin1	M_zsin1	0.0	0.0	-1.98000
2	M_xcos1	M_ycos1	-M_zcos1	2.58000	0.0	0.0	-M_xsin1	-M_ysin1	M_zsin1	0.0	0.0	-1.98000
3	-M_xcos1	M_ycos1	-M_zcos1	-2.58000	0.0	0.0	-M_xsin1	M_ysin1	-M_zsin1	0.0	0.0	1.98000
4	-M_xcos1	M_ycos1	M_zcos1	-2.58000	0.0	0.0	M_xsin1	-M_ysin1	-M_zsin1	0.0	0.0	1.98000

[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	6
mDT2	1	2	primary	6

Comments:

NPD
Position structure from a room temperature model retrieved from ICSD
polymorph (alpha)
See also (Chapon et al., Phys. Rev B 83, 024409 (2011)) (#1.1.86) for a similar model, but with circular spirals instead of elliptical, and with opposite chirality of the spin spirals, corresponding to an equivalent inversion-related domain.

Comments (symmetry):

1k incommensurate magnetic structure
two irreps involved as primary. The two irrep modulations are superposed in quadrature
The spin modulation breaks the inversion symmetry but the resulting point group is non-polar. No magnetically induced ferroelectricity is possible.

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

CaCr₂O₄ (#1.1.87)

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

CaCr2O4 (#1.1.87)

CaCr₂O₄ (#1.1.87)