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	{ 2₀₀₁ \| 0 0 1/2 1/2 }
3	-x1+1/2,x2+1/2,-x3+1/2,-x4,+1	{ 2₀₁₀ \| 1/2 1/2 1/2 0 }
4	x1+1/2,-x2+1/2,-x3,-x4+1/2,+1	{ 2₁₀₀ \| 1/2 1/2 0 1/2 }
5	-x1,-x2,-x3,-x4,+1	{ -1 \| 0 }
6	x1,x2,-x3+1/2,-x4+1/2,+1	{ m₀₀₁ \| 0 0 1/2 1/2 }
7	x1+1/2,-x2+1/2,x3+1/2,x4,+1	{ m₀₁₀ \| 1/2 1/2 1/2 0 }
8	-x1+1/2,x2+1/2,x3,x4+1/2,+1	{ m₁₀₀ \| 1/2 1/2 0 1/2 }
(0,0,0,1/2)' + set click here to show and hide
9	x1,x2,x3,x4+1/2,-1	{ 1' \| 0 0 0 1/2 }
10	-x1,-x2,x3+1/2,x4,-1	{ 2'₀₀₁ \| 0 0 1/2 0 }
11	-x1+1/2,x2+1/2,-x3+1/2,-x4+1/2,-1	{ 2'₀₁₀ \| 1/2 1/2 1/2 1/2 }
12	x1+1/2,-x2+1/2,-x3,-x4,-1	{ 2'₁₀₀ \| 1/2 1/2 0 0 }
13	-x1,-x2,-x3,-x4+1/2,-1	{ -1' \| 0 0 0 1/2 }
14	x1,x2,-x3+1/2,-x4,-1	{ m'₀₀₁ \| 0 0 1/2 0 }
15	x1+1/2,-x2+1/2,x3+1/2,x4+1/2,-1	{ m'₀₁₀ \| 1/2 1/2 1/2 1/2 }
16	-x1+1/2,x2+1/2,x3,x4,-1	{ m'₁₀₀ \| 1/2 1/2 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
5	-x,-y,-z,+1	-1
6	x,y,-z,+1	m₀₀₁
7	x,-y,z,+1	m₀₁₀
8	-x,y,z,+1	m₁₀₀
1' + set click here to show and hide
9	x,y,z,-1	1'
10	-x,-y,z,-1	2'₀₀₁
11	-x,y,-z,-1	2'₀₁₀
12	x,-y,-z,-1	2'₁₀₀
13	-x,-y,-z,-1	-1'
14	x,y,-z,-1	m'₀₀₁
15	x,-y,z,-1	m'₀₁₀
16	-x,y,z,-1	m'₁₀₀

Label	Atom type	x	y	z	Multiplicity
Ca1	Ca	0.6594	0.7593	0.25	4
O1	O	0.1596	0.2007	0.25	4
O2	O	0.4757	0.1151	0.25	4
O3	O	0.786	0.5285	0.25	4
O4	O	0.4262	0.4177	0.25	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	0	2.88	0.0	0.0	0	0	M_zsin1	0.0	0.0	1.27
Cr2	M_xcos1	M_ycos1	0	-2.88	0.0	0.0	0	0	M_zsin1	0.0	0.0	1.27

Atom	x	y	z
1	0.61240	0.44030	0.25000
2	0.38760	0.55970	0.75000
3	0.88760	0.94030	0.25000
4	0.11240	0.05970	0.75000

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	0	2.88000	0.0	0.0	0	0	M_zsin1	0.0	0.0	1.27000
2	M_xcos1	M_ycos1	0	2.88000	0.0	0.0	0	0	-M_zsin1	0.0	0.0	-1.27000
3	-M_xcos1	M_ycos1	0	-2.88000	0.0	0.0	0	0	M_zsin1	0.0	0.0	1.27000
4	-M_xcos1	M_ycos1	0	-2.88000	0.0	0.0	0	0	-M_zsin1	0.0	0.0	-1.27000

Atom	x	y	z
1	0.10100	0.41690	0.25000
2	0.89900	0.58310	0.75000
3	0.39900	0.91690	0.25000
4	0.60100	0.08310	0.75000

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	0	-2.88000	0.0	0.0	0	0	M_zsin1	0.0	0.0	1.27000
2	M_xcos1	M_ycos1	0	-2.88000	0.0	0.0	0	0	-M_zsin1	0.0	0.0	-1.27000
3	-M_xcos1	M_ycos1	0	2.88000	0.0	0.0	0	0	M_zsin1	0.0	0.0	1.27000
4	-M_xcos1	M_ycos1	0	2.88000	0.0	0.0	0	0	-M_zsin1	0.0	0.0	-1.27000

Atom	x	y	z
1	0.65940	0.75930	0.25000
2	0.34060	0.24070	0.75000
3	0.84060	0.25930	0.25000
4	0.15940	0.74070	0.75000

Atom	x	y	z
1	0.15960	0.20070	0.25000
2	0.84040	0.79930	0.75000
3	0.34040	0.70070	0.25000
4	0.65960	0.29930	0.75000

Atom	x	y	z
1	0.47570	0.11510	0.25000
2	0.52430	0.88490	0.75000
3	0.02430	0.61510	0.25000
4	0.97570	0.38490	0.75000

Atom	x	y	z
1	0.78600	0.52850	0.25000
2	0.21400	0.47150	0.75000
3	0.71400	0.02850	0.25000
4	0.28600	0.97150	0.75000

Atom	x	y	z
1	0.42620	0.41770	0.25000
2	0.57380	0.58230	0.75000
3	0.07380	0.91770	0.25000
4	0.92620	0.08230	0.75000

Reference: F. Damay, C. Martin, V. Hardy, A. Maignan, G. Andre, K. Knight, S.R. Giblin and L.C. Chapon, Physical Review B (2010) 81 214405.
DOI: 10.1103/physrevb.81.214405
Atomic positions from: ICSD #8288

Parent space group (paramagnetic phase): Pbnm (#62) (non-standard)
Transformation to a standard setting: (b,c,a;0,0,0)
    [View matrix form]
Propagation vector: k1 (0.000000, 0.000000, 0.477000)

Transition Temperature: 21 K
Experiment Temperature: 1.5 K

Lattice parameters of the basic unit cell:
10.639 9.094 2.96 90 90 90
Transformation from parent structure: (a,b,c;0,0,0)
    [View matrix form]

Magnetic Superspace Group: Pbnm1'(00γ)s00s
    [View symmetry operations]

Magnetic Point Group: mmm1' (8.2.25)
    [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

     [Show only magnetic atoms]
     [Show all the atoms]

Average atomic positions of symmetry independent atoms

Label	Atom type	x	y	z	Multiplicity
Cr1	Cr	0.6124	0.4403	0.25	4
Cr2	Cr	0.101	0.4169	0.25	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	0	2.88	0.0	0.0	0	0	M_zsin1	0.0	0.0	1.27
Cr2	M_xcos1	M_ycos1	0	-2.88	0.0	0.0	0	0	M_zsin1	0.0	0.0	1.27

Atom	x	y	z
1	0.61240	0.44030	0.25000
2	0.38760	0.55970	0.75000
3	0.88760	0.94030	0.25000
4	0.11240	0.05970	0.75000

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	0	2.88000	0.0	0.0	0	0	M_zsin1	0.0	0.0	1.27000
2	M_xcos1	M_ycos1	0	2.88000	0.0	0.0	0	0	-M_zsin1	0.0	0.0	-1.27000
3	-M_xcos1	M_ycos1	0	-2.88000	0.0	0.0	0	0	M_zsin1	0.0	0.0	1.27000
4	-M_xcos1	M_ycos1	0	-2.88000	0.0	0.0	0	0	-M_zsin1	0.0	0.0	-1.27000

Atom	x	y	z
1	0.10100	0.41690	0.25000
2	0.89900	0.58310	0.75000
3	0.39900	0.91690	0.25000
4	0.60100	0.08310	0.75000

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	0	-2.88000	0.0	0.0	0	0	M_zsin1	0.0	0.0	1.27000
2	M_xcos1	M_ycos1	0	-2.88000	0.0	0.0	0	0	-M_zsin1	0.0	0.0	-1.27000
3	-M_xcos1	M_ycos1	0	2.88000	0.0	0.0	0	0	M_zsin1	0.0	0.0	1.27000
4	-M_xcos1	M_ycos1	0	2.88000	0.0	0.0	0	0	-M_zsin1	0.0	0.0	-1.27000

[Show all magnetic atoms in unit cell and their moment relations]

Active Irreps:

label	dim. small irrep	dim. full irrep	action	number of modes
mDT3	1	2	primary	6

Comments:

NPD
The four Cr atoms of each Cr orbit have cycloidal modulations on the plane ac with opposite chiralities by pairs. This relation is forced by the MSSG. Non polar global symmetry.
Spin cycloids are symmetry protected.
The system has been incorrectly attributed a polar point group. The actual point group of the reported structure is the centrosymmetric mmm1'.
Non-standard parent setting Pbnm
Nuclear structure taken from icsd_8288 and not from reference.

Comments (symmetry):

1k magnetic structure
k-maximal magnetic symmetry.
One to one correspondence between the MSSG and the active irrep.
A discarded alternative sinusoidal model has lower symmetry.
Symmetry allows an oblique tilt of the plane of spin rotations around the c axis.
Not clear if the experiment could distinguish the absolute chirality of the cycloidal modulations of the symmetry independent sites.

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

CaCr₂O₄ (#1.1.15)

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

CaCr2O4 (#1.1.15)

CaCr₂O₄ (#1.1.15)