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,-x4,+1	{ 2₀₀₁ \| 0 }
3	-x1,x2,-x3+1/2,-x4+1/2,+1	{ 2₀₁₀ \| 0 0 1/2 1/2 }
4	x1,-x2,-x3+1/2,x4+1/2,+1	{ 2₁₀₀ \| 0 0 1/2 1/2 }
(1/2,1/2,0,0) + set click here to show and hide
5	x1+1/2,x2+1/2,x3,x4,+1	{ 1 \| 1/2 1/2 0 0 }
6	-x1+1/2,-x2+1/2,x3,-x4,+1	{ 2₀₀₁ \| 1/2 1/2 0 0 }
7	-x1+1/2,x2+1/2,-x3+1/2,-x4+1/2,+1	{ 2₀₁₀ \| 1/2 1/2 1/2 1/2 }
8	x1+1/2,-x2+1/2,-x3+1/2,x4+1/2,+1	{ 2₁₀₀ \| 1/2 1/2 1/2 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,-x4+1/2,-1	{ 2'₀₀₁ \| 0 0 0 1/2 }
11	-x1,x2,-x3+1/2,-x4,-1	{ 2'₀₁₀ \| 0 0 1/2 0 }
12	x1,-x2,-x3+1/2,x4,-1	{ 2'₁₀₀ \| 0 0 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,-x4+1/2,-1	{ 2'₀₀₁ \| 1/2 1/2 0 1/2 }
15	-x1+1/2,x2+1/2,-x3+1/2,-x4,-1	{ 2'₀₁₀ \| 1/2 1/2 1/2 0 }
16	x1+1/2,-x2+1/2,-x3+1/2,x4,-1	{ 2'₁₀₀ \| 1/2 1/2 1/2 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
Li1_1	Li	0	0.5	0.3333	4
Li1_2	Li	0	-0.5	-0.3333	4
Li2_1	Li	0.75	0.25	0.25	4
Li2_2	Li	-0.75	-0.25	-0.25	4
Li3_1	Li	0.75	0.25	0.91667	4
Li3_2	Li	-0.75	-0.25	-0.91667	4
Li4	Li	0.5	0.5	0.5	4
Li5	Li	0.5	0	0	4
O1_1	O	0.77	0.515	0.087	8
O1_2	O	-0.77	-0.515	-0.087	8
O2_1	O	0.72	0.5	0.25	4
O2_2	O	-0.72	-0.5	-0.25	4
O3	O	0	0.262	0	8
O4_1	O	0.49	0.262	0.163	8
O4_2	O	-0.49	-0.262	-0.163	8

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
Ir1_1	0	0	M_zcos1	0.0	0.0	1	M_xsin1	M_ysin1	0	0.65(4)	0.58(1)	0.0
Ir1_2	0	0	M_zcos1	0.0	0.0	1	M_xsin1	M_ysin1	0	-0.65	0.58	0.0
Ir2_1	0	0	M_zcos1	0.0	0.0	1	M_xsin1	M_ysin1	0	-0.65	-0.58	0.0
Ir2_2	0	0	M_zcos1	0.0	0.0	1	M_xsin1	M_ysin1	0	0.65	-0.58	0.0

Atom	x	y	z
1	0.25000	0.25000	0.08360
2	0.75000	0.75000	0.08360
(1/2,1/2,0,0) + set click here to show and hide
3	0.75000	0.25000	0.41640
4	0.25000	0.75000	0.41640

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	1.00000	M_xsin1	M_ysin1	0	0.65000	0.58000	0.0
2	0	0	M_zcos1	0.0	0.0	1.00000	M_xsin1	M_ysin1	0	0.65000	0.58000	0.0
(1/2,1/2,0,0) + set click here to show and hide
3	0	0	M_zcos1	0.0	0.0	1.00000	-M_xsin1	M_ysin1	0	-0.65000	0.58000	0.0
4	0	0	M_zcos1	0.0	0.0	1.00000	-M_xsin1	M_ysin1	0	-0.65000	0.58000	0.0

Atom	x	y	z
1	0.75000	0.75000	0.91640
2	0.25000	0.25000	0.91640
(1/2,1/2,0,0) + set click here to show and hide
3	0.25000	0.75000	0.58360
4	0.75000	0.25000	0.58360

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	1.00000	M_xsin1	M_ysin1	0	-0.65000	0.58000	0.0
2	0	0	M_zcos1	0.0	0.0	1.00000	M_xsin1	M_ysin1	0	-0.65000	0.58000	0.0
(1/2,1/2,0,0) + set click here to show and hide
3	0	0	M_zcos1	0.0	0.0	1.00000	-M_xsin1	M_ysin1	0	0.65000	0.58000	0.0
4	0	0	M_zcos1	0.0	0.0	1.00000	-M_xsin1	M_ysin1	0	0.65000	0.58000	0.0

Atom	x	y	z
1	0.50000	0.50000	0.16700
2	0.50000	0.50000	0.33300
(1/2,1/2,0,0) + set click here to show and hide
3	0.00000	0.00000	0.16700
4	0.00000	0.00000	0.33300

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	1.00000	M_xsin1	M_ysin1	0	-0.65000	-0.58000	0.0
2	0	0	M_zcos1	0.0	0.0	1.00000	-M_xsin1	M_ysin1	0	0.65000	-0.58000	0.0
(1/2,1/2,0,0) + set click here to show and hide
3	0	0	M_zcos1	0.0	0.0	1.00000	M_xsin1	M_ysin1	0	-0.65000	-0.58000	0.0
4	0	0	M_zcos1	0.0	0.0	1.00000	-M_xsin1	M_ysin1	0	0.65000	-0.58000	0.0

Atom	x	y	z
1	0.50000	0.50000	0.83300
2	0.50000	0.50000	0.66700
(1/2,1/2,0,0) + set click here to show and hide
3	0.00000	0.00000	0.83300
4	0.00000	0.00000	0.66700

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	1.00000	M_xsin1	M_ysin1	0	0.65000	-0.58000	0.0
2	0	0	M_zcos1	0.0	0.0	1.00000	-M_xsin1	M_ysin1	0	-0.65000	-0.58000	0.0
(1/2,1/2,0,0) + set click here to show and hide
3	0	0	M_zcos1	0.0	0.0	1.00000	M_xsin1	M_ysin1	0	0.65000	-0.58000	0.0
4	0	0	M_zcos1	0.0	0.0	1.00000	-M_xsin1	M_ysin1	0	-0.65000	-0.58000	0.0

Atom	x	y	z
1	0.00000	0.50000	0.33330
2	0.00000	0.50000	0.16670
(1/2,1/2,0,0) + set click here to show and hide
3	0.50000	0.00000	0.33330
4	0.50000	0.00000	0.16670

Atom	x	y	z
1	0.00000	0.50000	0.66670
2	0.00000	0.50000	0.83330
(1/2,1/2,0,0) + set click here to show and hide
3	0.50000	0.00000	0.66670
4	0.50000	0.00000	0.83330

Atom	x	y	z
1	0.75000	0.25000	0.25000
2	0.25000	0.25000	0.25000
(1/2,1/2,0,0) + set click here to show and hide
3	0.25000	0.75000	0.25000
4	0.75000	0.75000	0.25000

Atom	x	y	z
1	0.25000	0.75000	0.75000
2	0.75000	0.75000	0.75000
(1/2,1/2,0,0) + set click here to show and hide
3	0.75000	0.25000	0.75000
4	0.25000	0.25000	0.75000

Atom	x	y	z
1	0.75000	0.25000	0.91667
2	0.25000	0.25000	0.58333
(1/2,1/2,0,0) + set click here to show and hide
3	0.25000	0.75000	0.91667
4	0.75000	0.75000	0.58333

Atom	x	y	z
1	0.25000	0.75000	0.08333
2	0.75000	0.75000	0.41667
(1/2,1/2,0,0) + set click here to show and hide
3	0.75000	0.25000	0.08333
4	0.25000	0.25000	0.41667

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

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

Atom	x	y	z
1	0.77000	0.51500	0.08700
2	0.23000	0.48500	0.08700
3	0.23000	0.51500	0.41300
4	0.77000	0.48500	0.41300
(1/2,1/2,0,0) + set click here to show and hide
5	0.27000	0.01500	0.08700
6	0.73000	0.98500	0.08700
7	0.73000	0.01500	0.41300
8	0.27000	0.98500	0.41300

Atom	x	y	z
1	0.23000	0.48500	0.91300
2	0.77000	0.51500	0.91300
3	0.77000	0.48500	0.58700
4	0.23000	0.51500	0.58700
(1/2,1/2,0,0) + set click here to show and hide
5	0.73000	0.98500	0.91300
6	0.27000	0.01500	0.91300
7	0.27000	0.98500	0.58700
8	0.73000	0.01500	0.58700

Atom	x	y	z
1	0.72000	0.50000	0.25000
2	0.28000	0.50000	0.25000
(1/2,1/2,0,0) + set click here to show and hide
3	0.22000	0.00000	0.25000
4	0.78000	0.00000	0.25000

Atom	x	y	z
1	0.28000	0.50000	0.75000
2	0.72000	0.50000	0.75000
(1/2,1/2,0,0) + set click here to show and hide
3	0.78000	0.00000	0.75000
4	0.22000	0.00000	0.75000

Atom	x	y	z
1	0.00000	0.26200	0.00000
2	0.00000	0.73800	0.00000
3	0.00000	0.26200	0.50000
4	0.00000	0.73800	0.50000
(1/2,1/2,0,0) + set click here to show and hide
5	0.50000	0.76200	0.00000
6	0.50000	0.23800	0.00000
7	0.50000	0.76200	0.50000
8	0.50000	0.23800	0.50000

Atom	x	y	z
1	0.49000	0.26200	0.16300
2	0.51000	0.73800	0.16300
3	0.51000	0.26200	0.33700
4	0.49000	0.73800	0.33700
(1/2,1/2,0,0) + set click here to show and hide
5	0.99000	0.76200	0.16300
6	0.01000	0.23800	0.16300
7	0.01000	0.76200	0.33700
8	0.99000	0.23800	0.33700

Atom	x	y	z
1	0.51000	0.73800	0.83700
2	0.49000	0.26200	0.83700
3	0.49000	0.73800	0.66300
4	0.51000	0.26200	0.66300
(1/2,1/2,0,0) + set click here to show and hide
5	0.01000	0.23800	0.83700
6	0.99000	0.76200	0.83700
7	0.99000	0.23800	0.66300
8	0.01000	0.76200	0.66300

Reference: A. Biffin, R. Johnson, I. Kimchi, R. Morris, A. Bombardi, J. Analytis, A. Vishwanath and R. Coldea, Physical Review Letters (2014) 113 197201.
DOI: 10.1103/physrevlett.113.197201
Atomic positions from: same reference

Parent space group (paramagnetic phase): Cccm (#66)
Propagation vector: k1 (0.57(1), 0.000000, 0.000000)

Transition Temperature: 39.5 K

Lattice parameters of the basic unit cell:
5.9119 8.4461 17.8363 90 90 90
Transformation from parent structure: (a,b,c;0,0,0)
    [View matrix form]

Magnetic Superspace Group: C2221'(α00)s00s
    [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

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

Average atomic positions of symmetry independent atoms

Label	Atom type	x	y	z	Multiplicity
Ir1_1	Ir	0.25	0.25	0.0836	4
Ir1_2	Ir	-0.25	-0.25	-0.0836	4
Ir2_1	Ir	0.5	0.5	0.167	4
Ir2_2	Ir	-0.5	-0.5	-0.167	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
Ir1_1	0	0	M_zcos1	0.0	0.0	1	M_xsin1	M_ysin1	0	0.65(4)	0.58(1)	0.0
Ir1_2	0	0	M_zcos1	0.0	0.0	1	M_xsin1	M_ysin1	0	-0.65	0.58	0.0
Ir2_1	0	0	M_zcos1	0.0	0.0	1	M_xsin1	M_ysin1	0	-0.65	-0.58	0.0
Ir2_2	0	0	M_zcos1	0.0	0.0	1	M_xsin1	M_ysin1	0	0.65	-0.58	0.0

Atom	x	y	z
1	0.25000	0.25000	0.08360
2	0.75000	0.75000	0.08360
(1/2,1/2,0,0) + set click here to show and hide
3	0.75000	0.25000	0.41640
4	0.25000	0.75000	0.41640

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	1.00000	M_xsin1	M_ysin1	0	0.65000	0.58000	0.0
2	0	0	M_zcos1	0.0	0.0	1.00000	M_xsin1	M_ysin1	0	0.65000	0.58000	0.0
(1/2,1/2,0,0) + set click here to show and hide
3	0	0	M_zcos1	0.0	0.0	1.00000	-M_xsin1	M_ysin1	0	-0.65000	0.58000	0.0
4	0	0	M_zcos1	0.0	0.0	1.00000	-M_xsin1	M_ysin1	0	-0.65000	0.58000	0.0

Atom	x	y	z
1	0.75000	0.75000	0.91640
2	0.25000	0.25000	0.91640
(1/2,1/2,0,0) + set click here to show and hide
3	0.25000	0.75000	0.58360
4	0.75000	0.25000	0.58360

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	1.00000	M_xsin1	M_ysin1	0	-0.65000	0.58000	0.0
2	0	0	M_zcos1	0.0	0.0	1.00000	M_xsin1	M_ysin1	0	-0.65000	0.58000	0.0
(1/2,1/2,0,0) + set click here to show and hide
3	0	0	M_zcos1	0.0	0.0	1.00000	-M_xsin1	M_ysin1	0	0.65000	0.58000	0.0
4	0	0	M_zcos1	0.0	0.0	1.00000	-M_xsin1	M_ysin1	0	0.65000	0.58000	0.0

Atom	x	y	z
1	0.50000	0.50000	0.16700
2	0.50000	0.50000	0.33300
(1/2,1/2,0,0) + set click here to show and hide
3	0.00000	0.00000	0.16700
4	0.00000	0.00000	0.33300

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	1.00000	M_xsin1	M_ysin1	0	-0.65000	-0.58000	0.0
2	0	0	M_zcos1	0.0	0.0	1.00000	-M_xsin1	M_ysin1	0	0.65000	-0.58000	0.0
(1/2,1/2,0,0) + set click here to show and hide
3	0	0	M_zcos1	0.0	0.0	1.00000	M_xsin1	M_ysin1	0	-0.65000	-0.58000	0.0
4	0	0	M_zcos1	0.0	0.0	1.00000	-M_xsin1	M_ysin1	0	0.65000	-0.58000	0.0

Atom	x	y	z
1	0.50000	0.50000	0.83300
2	0.50000	0.50000	0.66700
(1/2,1/2,0,0) + set click here to show and hide
3	0.00000	0.00000	0.83300
4	0.00000	0.00000	0.66700

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	1.00000	M_xsin1	M_ysin1	0	0.65000	-0.58000	0.0
2	0	0	M_zcos1	0.0	0.0	1.00000	-M_xsin1	M_ysin1	0	-0.65000	-0.58000	0.0
(1/2,1/2,0,0) + set click here to show and hide
3	0	0	M_zcos1	0.0	0.0	1.00000	M_xsin1	M_ysin1	0	0.65000	-0.58000	0.0
4	0	0	M_zcos1	0.0	0.0	1.00000	-M_xsin1	M_ysin1	0	-0.65000	-0.58000	0.0

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

Active Irreps:

label	dim. small irrep	dim. full irrep	action	number of modes
mSM3	1	2	primary	6
mSM4	1	2	primary	6

Comments:

MRXD
arbitrary moment scale. Absolute moments unknown.
gamma polymorph.
model has three free parameters instead of the 12 allowed by the symmetry.
Positional structure with Cccm space group from a 300K measurement.

Comments (symmetry):

1k magnetic structure.
The MSSG is the result of the superposition of two active irrep distortions in quadrature.
Non centrosymmetric, non-polar symmetry.
The symmetry reduction splits most of the atomic positions (space group of the average structure for the MSSG: C222).
Elliptical counter-rotating spin modulations are protected by the MSSG, but four symmetry independent modulations with different components are allowed. These differences are taken as negligible, reducing the number of free spin parameters from 12 to 3.

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

Li₂IrO₃ (#1.1.21)

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

Li2IrO3 (#1.1.21)

Li₂IrO₃ (#1.1.21)