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	{ 2₁₀₀ \| 1/2 1/2 0 1/2 }
3	x1,x2,-x3+1/2,-x4,+1	{ m₀₀₁ \| 0 0 1/2 0 }
4	x1+1/2,-x2+1/2,x3+1/2,x4+1/2,+1	{ m₀₁₀ \| 1/2 1/2 1/2 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	{ 2'₁₀₀ \| 1/2 1/2 0 0 }
7	x1,x2,-x3+1/2,-x4+1/2,-1	{ m'₀₀₁ \| 0 0 1/2 1/2 }
8	x1+1/2,-x2+1/2,x3+1/2,x4,-1	{ m'₀₁₀ \| 1/2 1/2 1/2 0 }

N	(x,y,z)	Seitz notation
1	x,y,z,+1	1
2	x,-y,-z,+1	2₁₀₀
3	x,y,-z,+1	m₀₀₁
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	2'₁₀₀
7	x,y,-z,-1	m'₀₀₁
8	x,-y,z,-1	m'₀₁₀

Label	Atom type	x	y	z	Multiplicity
Be1_1	Be	-0.06900	0.40600	0.75000	2
Be1_2	Be	0.56900	-0.09400	0.75000	2
O1_1	O	0.27700	0.40700	0.75000	2
O1_2	O	0.22300	-0.09300	0.75000	2
O2_1	O	0.73100	0.06100	0.75000	2
O2_2	O	0.76900	0.56100	0.75000	2
O3_1	O	0.25700	0.16200	0.02200	4
O3_2	O	0.24300	0.66200	0.47800	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_1	M_xc1	M_yc1	M_zc1	1.55	0.0	0.0	M_xs1	M_ys1	M_zs1	0.0	0.0	-1.55
Cr2_1	0	0	M_zc1	0.0	0.0	-2.75	M_xs1	M_ys1	0	-2.75	0.0	0.0
Cr2_2	0	0	M_zc1	0.0	0.0	2.75	M_xs1	M_ys1	0	2.75	0.0	0.0

Atom	x	y	z
1	0.00000	0.00000	0.00000
2	0.50000	0.50000	0.00000
3	0.00000	0.00000	0.50000
4	0.50000	0.50000	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	M_ycos1	M_zcos1	1.55000	0.0	0.0	M_xcos1+M_ysin1	M_ycos1+M_ysin1	M_zcos1+M_ysin1	0.0	0.0	-1.55000
2	-M_xcos1	M_ycos1	M_zcos1	-1.55000	0.0	0.0	M_xcos1+M_ysin1	-M_ycos1-M_ysin1	-M_zcos1-M_ysin1	0.0	0.0	1.55000
3	-M_xcos1	-M_ycos1	M_zcos1	-1.55000	0.0	0.0	M_xcos1+M_ysin1	M_ycos1+M_ysin1	-M_zcos1-M_ysin1	0.0	0.0	1.55000
4	M_xcos1	-M_ycos1	M_zcos1	1.55000	0.0	0.0	M_xcos1+M_ysin1	-M_ycos1-M_ysin1	M_zcos1+M_ysin1	0.0	0.0	-1.55000

Atom	x	y	z
1	0.49500	0.23200	0.75000
2	0.99500	0.26800	0.25000

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	0	M_zcos1	0.0	0.0	-2.75000	M_xcos1+M_ysin1	M_ycos1+M_ysin1	0	-2.75000	0.0	0.0
2	0	0	M_zcos1	0.0	0.0	-2.75000	M_xcos1+M_ysin1	-M_ycos1-M_ysin1	0	-2.75000	0.0	0.0

Atom	x	y	z
1	0.00500	0.73200	0.75000
2	0.50500	0.76800	0.25000

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	0	M_zcos1	0.0	0.0	2.75000	M_xcos1+M_ysin1	M_ycos1+M_ysin1	0	2.75000	0.0	0.0
2	0	0	M_zcos1	0.0	0.0	2.75000	M_xcos1+M_ysin1	-M_ycos1-M_ysin1	0	2.75000	0.0	0.0

Atom	x	y	z
1	0.93100	0.40600	0.75000
2	0.43100	0.09400	0.25000

Atom	x	y	z
1	0.56900	0.90600	0.75000
2	0.06900	0.59400	0.25000

Atom	x	y	z
1	0.27700	0.40700	0.75000
2	0.77700	0.09300	0.25000

Atom	x	y	z
1	0.22300	0.90700	0.75000
2	0.72300	0.59300	0.25000

Atom	x	y	z
1	0.73100	0.06100	0.75000
2	0.23100	0.43900	0.25000

Atom	x	y	z
1	0.76900	0.56100	0.75000
2	0.26900	0.93900	0.25000

Atom	x	y	z
1	0.25700	0.16200	0.02200
2	0.75700	0.33800	0.97800
3	0.25700	0.16200	0.47800
4	0.75700	0.33800	0.52200

Atom	x	y	z
1	0.24300	0.66200	0.47800
2	0.74300	0.83800	0.52200
3	0.24300	0.66200	0.02200
4	0.74300	0.83800	0.97800

Reference: D. E. Cox, B. C. Frazer, R. E. Newnham, R. P. Santoro, JOURNAL OF APPLIED PHYSICS (1969) 40 1124 - 1125
DOI: 10.1063/1.1657557
Atomic positions from: ICSD #164258

Parent space group (paramagnetic phase): Pbnm (#62)
Propagation vector: k1 (0.00000, 0.00000, 0.087)

Transition Temperature: 28 K
Experiment Temperature: 4.2 K

Lattice parameters of the basic unit cell:
4.55500 9.79200 5.66300 90.00000 90.00000 90.00000
Transformation from parent structure: (a,b,c;0,0,0)
    [View matrix form]

Magnetic Superspace Group: P2_1nm1'(0,0,g)0s0s
    [View symmetry operations]

Magnetic Point Group: mm21' (7.2.21)
    [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_1	Cr	0.00000	0.00000	0.00000	4
Cr2_1	Cr	0.49500	0.23200	0.75000	2
Cr2_2	Cr	0.00500	0.73200	0.75000	2

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_1	M_xc1	M_yc1	M_zc1	1.55	0.0	0.0	M_xs1	M_ys1	M_zs1	0.0	0.0	-1.55
Cr2_1	0	0	M_zc1	0.0	0.0	-2.75	M_xs1	M_ys1	0	-2.75	0.0	0.0
Cr2_2	0	0	M_zc1	0.0	0.0	2.75	M_xs1	M_ys1	0	2.75	0.0	0.0

Atom	x	y	z
1	0.00000	0.00000	0.00000
2	0.50000	0.50000	0.00000
3	0.00000	0.00000	0.50000
4	0.50000	0.50000	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	M_ycos1	M_zcos1	1.55000	0.0	0.0	M_xcos1+M_ysin1	M_ycos1+M_ysin1	M_zcos1+M_ysin1	0.0	0.0	-1.55000
2	-M_xcos1	M_ycos1	M_zcos1	-1.55000	0.0	0.0	M_xcos1+M_ysin1	-M_ycos1-M_ysin1	-M_zcos1-M_ysin1	0.0	0.0	1.55000
3	-M_xcos1	-M_ycos1	M_zcos1	-1.55000	0.0	0.0	M_xcos1+M_ysin1	M_ycos1+M_ysin1	-M_zcos1-M_ysin1	0.0	0.0	1.55000
4	M_xcos1	-M_ycos1	M_zcos1	1.55000	0.0	0.0	M_xcos1+M_ysin1	-M_ycos1-M_ysin1	M_zcos1+M_ysin1	0.0	0.0	-1.55000

Atom	x	y	z
1	0.49500	0.23200	0.75000
2	0.99500	0.26800	0.25000

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	0	M_zcos1	0.0	0.0	-2.75000	M_xcos1+M_ysin1	M_ycos1+M_ysin1	0	-2.75000	0.0	0.0
2	0	0	M_zcos1	0.0	0.0	-2.75000	M_xcos1+M_ysin1	-M_ycos1-M_ysin1	0	-2.75000	0.0	0.0

Atom	x	y	z
1	0.00500	0.73200	0.75000
2	0.50500	0.76800	0.25000

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	0	M_zcos1	0.0	0.0	2.75000	M_xcos1+M_ysin1	M_ycos1+M_ysin1	0	2.75000	0.0	0.0
2	0	0	M_zcos1	0.0	0.0	2.75000	M_xcos1+M_ysin1	-M_ycos1-M_ysin1	0	2.75000	0.0	0.0

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Active Irreps:

label	dim. small irrep	dim. full irrep	direction	action	number of modes
mDT2	1	2	general	primary	6
mDT4	1	2	special	primary	6

Comments:

NPD
Position structure from a determination at 150K
Non-standard Pbnm parent setting
Polar along a (setting Pbnm). Possible magnetically induced ferroelectricity (type II multiferroic).
The wavelength of the cycloidal modulation in the graphical representation of the paper is inconsistent with the value given in the text. The value in the text has been assumed correct.

Comments (symmetry):

1k incommensurate magnetic structure
The MSSG is used here with an origin shift along x4 with respect to what could be a standard choice, which minimize the translations along x4 of the symmetry operations
Two irreps as primary. Their modulations superposed in quadrature.
Not clear if all possible degrees of freedom allowed by the magnetic symmetry of the model were checked.

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

Cr₂BeO₄ (#1.1.108)

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

Cr2BeO4 (#1.1.108)

Cr₂BeO₄ (#1.1.108)