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,x2,-x3+1/2,-x4+1/2,+1	{ 2₀₁₀ \| 0 0 1/2 1/2 }
3	-x1,x2,x3,-x4+1/2,+1	{ m₁₀₀ \| 0 0 0 1/2 }
4	x1,x2,-x3+1/2,x4,+1	{ m₀₀₁ \| 0 0 1/2 0 }
(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,x2,-x3+1/2,-x4,-1	{ 2'₀₁₀ \| 0 0 1/2 0 }
7	-x1,x2,x3,-x4,-1	{ m'₁₀₀ \| 0 }
8	x1,x2,-x3+1/2,x4+1/2,-1	{ m'₀₀₁ \| 0 0 1/2 1/2 }
(1/2,1/2,0,0) + set click here to show and hide
9	x1+1/2,x2+1/2,x3,x4,+1	{ 1 \| 1/2 1/2 0 0 }
10	-x1+1/2,x2+1/2,-x3+1/2,-x4+1/2,+1	{ 2₀₁₀ \| 1/2 1/2 1/2 1/2 }
11	-x1+1/2,x2+1/2,x3,-x4+1/2,+1	{ m₁₀₀ \| 1/2 1/2 0 1/2 }
12	x1+1/2,x2+1/2,-x3+1/2,x4,+1	{ m₀₀₁ \| 1/2 1/2 1/2 0 }
(1/2,1/2,0,1/2)' + set click here to show and hide
13	x1+1/2,x2+1/2,x3,x4+1/2,-1	{ 1' \| 1/2 1/2 0 1/2 }
14	-x1+1/2,x2+1/2,-x3+1/2,-x4,-1	{ 2'₀₁₀ \| 1/2 1/2 1/2 0 }
15	-x1+1/2,x2+1/2,x3,-x4,-1	{ m'₁₀₀ \| 1/2 1/2 0 0 }
16	x1+1/2,x2+1/2,-x3+1/2,x4+1/2,-1	{ m'₀₀₁ \| 1/2 1/2 1/2 1/2 }

N	(x,y,z)	Seitz notation
1	x,y,z,+1	1
2	-x,y,-z,+1	2₀₁₀
3	-x,y,z,+1	m₁₀₀
4	x,y,-z,+1	m₀₀₁
1' + set click here to show and hide
5	x,y,z,-1	1'
6	-x,y,-z,-1	2'₀₁₀
7	-x,y,z,-1	m'₁₀₀
8	x,y,-z,-1	m'₀₀₁

Label	Atom type	x	y	z	Multiplicity
P1_1	P	0.00000	0.35030	0.25000	2
P1_2	P	0.00000	0.64970	0.75000	2
O1_1	O	0.00000	0.24590	0.04290	4
O1_2	O	0.00000	0.75410	-0.04290	4
O2_1	O	0.24620	0.47060	0.25000	4
O2_2	O	0.24620	0.52940	0.75000	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	0	M_yc1	M_zc1	0.0	-2.55(10)	0.0	M_xs1	0	0	2.55	0.0	0.0

Atom	x	y	z
1	0.00000	0.00000	0.00000
(0,0,0,1/2)' + set click here to show and hide
2	0.00000	0.00000	0.50000
(1/2,1/2,0,0) + set click here to show and hide
3	0.50000	0.50000	0.00000
(1/2,1/2,0,1/2)' + set click here to show and hide
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	0	M_ycos1	M_zcos1	0.0	-2.55000	0.0	M_xcos1+M_ysin1	0	0	2.55000	0.0	0.0
(0,0,0,1/2)' + set click here to show and hide
2	0	-M_ycos1	M_zcos1	0.0	2.55000	0.0	-M_xcos1-M_ysin1	0	0	-2.55000	0.0	0.0
(1/2,1/2,0,0) + set click here to show and hide
3	0	M_ycos1	M_zcos1	0.0	-2.55000	0.0	M_xcos1+M_ysin1	0	0	2.55000	0.0	0.0
(1/2,1/2,0,1/2)' + set click here to show and hide
4	0	-M_ycos1	M_zcos1	0.0	2.55000	0.0	-M_xcos1-M_ysin1	0	0	-2.55000	0.0	0.0

Atom	x	y	z
1	0.00000	0.35030	0.25000
(0,0,0,1/2)' + set click here to show and hide
2	0.50000	0.85030	0.25000

Atom	x	y	z
1	0.00000	0.64970	0.75000
(0,0,0,1/2)' + set click here to show and hide
2	0.50000	0.14970	0.75000

Atom	x	y	z
1	0.00000	0.24590	0.04290
(0,0,0,1/2)' + set click here to show and hide
2	0.00000	0.24590	0.45710
(1/2,1/2,0,0) + set click here to show and hide
3	0.50000	0.74590	0.04290
(1/2,1/2,0,1/2)' + set click here to show and hide
4	0.50000	0.74590	0.45710

Atom	x	y	z
1	0.00000	0.75410	0.95710
(0,0,0,1/2)' + set click here to show and hide
2	0.00000	0.75410	0.54290
(1/2,1/2,0,0) + set click here to show and hide
3	0.50000	0.25410	0.95710
(1/2,1/2,0,1/2)' + set click here to show and hide
4	0.50000	0.25410	0.54290

Atom	x	y	z
1	0.24620	0.47060	0.25000
(0,0,0,1/2)' + set click here to show and hide
2	0.75380	0.47060	0.25000
(1/2,1/2,0,0) + set click here to show and hide
3	0.74620	0.97060	0.25000
(1/2,1/2,0,1/2)' + set click here to show and hide
4	0.25380	0.97060	0.25000

Atom	x	y	z
1	0.24620	0.52940	0.75000
(0,0,0,1/2)' + set click here to show and hide
2	0.75380	0.52940	0.75000
(1/2,1/2,0,0) + set click here to show and hide
3	0.74620	0.02940	0.75000
(1/2,1/2,0,1/2)' + set click here to show and hide
4	0.25380	0.02940	0.75000

Reference: J. P. Attfield, P. D. Battle, A. K. Cheetham, JOURNAL OF SOLID STATE CHEMISTRY (1985) 57 357 - 361
DOI: 10.1016/0022-4596(85)90199-9
Atomic positions from: ICSD #62159

Parent space group (paramagnetic phase): 'C (#63)
Propagation vector: k1 (0.326, 0.00000, 0.00000)

Transition Temperature: 37 K
Experiment Temperature: 5 K

Lattice parameters of the basic unit cell:
5.17100 7.75730 6.11830 90.00000 90.00000 90.00000
Transformation from parent structure: (a,b,c;0,0,0)
    [View matrix form]

Magnetic Superspace Group: Cm2m1'(a,0,0)000s
    [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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     [Show all the atoms]

Average atomic positions of symmetry independent atoms

Label	Atom type	x	y	z	Multiplicity
Cr1_1	Cr	0.00000	0.00000	0.00000	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_1	0	M_yc1	M_zc1	0.0	-2.55(10)	0.0	M_xs1	0	0	2.55	0.0	0.0

Atom	x	y	z
1	0.00000	0.00000	0.00000
(0,0,0,1/2)' + set click here to show and hide
2	0.00000	0.00000	0.50000
(1/2,1/2,0,0) + set click here to show and hide
3	0.50000	0.50000	0.00000
(1/2,1/2,0,1/2)' + set click here to show and hide
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	0	M_ycos1	M_zcos1	0.0	-2.55000	0.0	M_xcos1+M_ysin1	0	0	2.55000	0.0	0.0
(0,0,0,1/2)' + set click here to show and hide
2	0	-M_ycos1	M_zcos1	0.0	2.55000	0.0	-M_xcos1-M_ysin1	0	0	-2.55000	0.0	0.0
(1/2,1/2,0,0) + set click here to show and hide
3	0	M_ycos1	M_zcos1	0.0	-2.55000	0.0	M_xcos1+M_ysin1	0	0	2.55000	0.0	0.0
(1/2,1/2,0,1/2)' + set click here to show and hide
4	0	-M_ycos1	M_zcos1	0.0	2.55000	0.0	-M_xcos1-M_ysin1	0	0	-2.55000	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
mSM1	1	2	general	primary	1
mSM4	1	2	special	primary	2

Comments:

NPD
The observed propagation vector is incommensurate with value (0.326,0,0), and the paper fitted the data using a commensurate approximant with k=(1/3,0,0). Here we present the reported model with the actual incommensurate value for the propagation vector and its resulting symmetry, given by a MSSG
Value of the kx component of propagation vector is only approximate (estimatimated from a curve in the paper)
For a better comparison with the initial phase chosen in the paper and the graphical representation therein, the origin along x4 of the MSSG has been shifted with respect to the one that can be considered standard.

Comments (symmetry):

1k incommensurate magnetic structure
two irreps as primary. They are shifted by pi/2 (in quadrature) to produce a cycloidal modulation
The spins rotate circularly on the xy plane, but the MSSG allows a more complex modulation with elliptical orbits their rotation plane being allowed to deviate from the ab plane, while keeping the a direction within the rotation plane.
The structure is polar along b, allowing for magnetically induced ferroelectricity (type II multiferroic)

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

CrPO₄ (#1.1.107)

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

CrPO4 (#1.1.107)

CrPO₄ (#1.1.107)