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	{ 2₀₀₁ \| 0 0 1/2 0 }
3	x1,-x2,x3+1/2,x4+1/2,+1	{ m₀₁₀ \| 0 0 1/2 1/2 }
4	-x1,x2,x3,-x4+1/2,+1	{ m₁₀₀ \| 0 0 0 1/2 }

N	(x,y,z)	Seitz notation
1	x,y,z,+1	1
2	-x,-y,z,+1	2₀₀₁
3	x,-y,z,+1	m₀₁₀
4	-x,y,z,+1	m₁₀₀

Label	Atom type	x	y	z	Multiplicity
Pb1	Pb	0.7628	0.9746	0.8653	4
Pb2	Pb	0.7462	0.5477	0.5786	4
W1	W	0	0.522	0.8644	2
W2	W	0.5	0.001	0.6117	2
O1	O	0	0.724	0.73	2
O2	O	0	0.311	0.973	2
O3	O	0.5	0.767	0.7103	2
O4	O	0.5	0.222	0.721	2
O5	O	0	0.249	0.7442	2
O6	O	0.5	0.209	0.477	2
O7	O	0.7384	0.0361	0.5956	4
O8	O	0.5	0.294	0.9958	2
O9	O	0.7667	0.52	0.8655	4
O10	O	0	0.786	0.9568	2

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
Mn1	0	M_ycos1	M_zcos1	0.0	-3.26	1.57	M_xsin1	0	0	0.0	0.0	0.0
Mn2	0	M_ycos1	M_zcos1	0.0	5.06	1.57	M_xsin1	0	0	0.0	0.0	0.0

Atom	x	y	z	Symmetry constraints on M	M_0x	M_0y	M_0z
1	0.50000	0.49200	0.86460	m_x,0,0	-2.31000	0.00000	0.00000
2	0.50000	0.50800	0.36460	-m_x,0,0	2.31000	0.00000	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	0	M_ycos1	M_zcos1	0.0	-3.26000	1.57000	M_xsin1	0	0	0.0	0.0	0.0
2	0	-M_ycos1	M_zcos1	0.0	3.26000	1.57000	M_xsin1	0	0	0.0	0.0	0.0

Atom	x	y	z	Symmetry constraints on M	M_0x	M_0y	M_0z
1	0.00000	0.99800	0.10270	m_x,0,0	2.31000	0.00000	0.00000
2	0.00000	0.00200	0.60270	-m_x,0,0	-2.31000	0.00000	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	0	M_ycos1	M_zcos1	0.0	5.06000	1.57000	M_xsin1	0	0	0.0	0.0	0.0
2	0	-M_ycos1	M_zcos1	0.0	-5.06000	1.57000	M_xsin1	0	0	0.0	0.0	0.0

Atom	x	y	z
1	0.76280	0.97460	0.86530
2	0.23720	0.02540	0.36530
3	0.76280	0.02540	0.36530
4	0.23720	0.97460	0.86530

Atom	x	y	z
1	0.74620	0.54770	0.57860
2	0.25380	0.45230	0.07860
3	0.74620	0.45230	0.07860
4	0.25380	0.54770	0.57860

Atom	x	y	z
1	0.00000	0.52200	0.86440
2	0.00000	0.47800	0.36440

Atom	x	y	z
1	0.50000	0.00100	0.61170
2	0.50000	0.99900	0.11170

Atom	x	y	z
1	0.00000	0.72400	0.73000
2	0.00000	0.27600	0.23000

Atom	x	y	z
1	0.00000	0.31100	0.97300
2	0.00000	0.68900	0.47300

Atom	x	y	z
1	0.50000	0.76700	0.71030
2	0.50000	0.23300	0.21030

Atom	x	y	z
1	0.50000	0.22200	0.72100
2	0.50000	0.77800	0.22100

Atom	x	y	z
1	0.00000	0.24900	0.74420
2	0.00000	0.75100	0.24420

Atom	x	y	z
1	0.50000	0.20900	0.47700
2	0.50000	0.79100	0.97700

Atom	x	y	z
1	0.73840	0.03610	0.59560
2	0.26160	0.96390	0.09560
3	0.73840	0.96390	0.09560
4	0.26160	0.03610	0.59560

Atom	x	y	z
1	0.50000	0.29400	0.99580
2	0.50000	0.70600	0.49580

Atom	x	y	z
1	0.76670	0.52000	0.86550
2	0.23330	0.48000	0.36550
3	0.76670	0.48000	0.36550
4	0.23330	0.52000	0.86550

Atom	x	y	z
1	0.00000	0.78600	0.95680
2	0.00000	0.21400	0.45680

Reference: F. Orlandi, L. Righi, C. Ritter, C. Pernechele, M. Solzi, R. Cabassi, F. Bolzoni and G. Calestani, J. Mater. Chem. C (2014) 2 9215-9223.
DOI: 10.1039/c4tc01450b
Atomic positions from: same reference

Parent space group (paramagnetic phase): Pmc2₁ (#26)
Propagation vector: k1 (0.250000, 0.000000, 0.000000)

Transition Temperature: 7 K
Experiment Temperature: 2 K

Lattice parameters of the basic unit cell:
8.01620(10) 5.78220(10) 11.63490(10) 90 90 90
Transformation from parent structure: (a,b,c;0,0,0)
    [View matrix form]

Magnetic Superspace Group: Pmc21(a00)0s0
    [View symmetry operations]

Magnetic Point Group: mm2 (7.1.20)
    [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 and magnetic moments of symmetry independent atoms

Label	Atom type	x	y	z	Multiplicity	Symmetry constraints on M	M_0x	M_0y	M_0z	\|M\|
Mn1	Mn	0.5	0.492	0.8646	2	m_x,0,0	-2.31	0.0	0.0	2.31
Mn2	Mn	0	0.998	0.1027	2	m_x,0,0	2.31	0.0	0.0	2.31

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
Mn1	0	M_ycos1	M_zcos1	0.0	-3.26	1.57	M_xsin1	0	0	0.0	0.0	0.0
Mn2	0	M_ycos1	M_zcos1	0.0	5.06	1.57	M_xsin1	0	0	0.0	0.0	0.0

Atom	x	y	z	Symmetry constraints on M	M_0x	M_0y	M_0z
1	0.50000	0.49200	0.86460	m_x,0,0	-2.31000	0.00000	0.00000
2	0.50000	0.50800	0.36460	-m_x,0,0	2.31000	0.00000	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	0	M_ycos1	M_zcos1	0.0	-3.26000	1.57000	M_xsin1	0	0	0.0	0.0	0.0
2	0	-M_ycos1	M_zcos1	0.0	3.26000	1.57000	M_xsin1	0	0	0.0	0.0	0.0

Atom	x	y	z	Symmetry constraints on M	M_0x	M_0y	M_0z
1	0.00000	0.99800	0.10270	m_x,0,0	2.31000	0.00000	0.00000
2	0.00000	0.00200	0.60270	-m_x,0,0	-2.31000	0.00000	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	0	M_ycos1	M_zcos1	0.0	5.06000	1.57000	M_xsin1	0	0	0.0	0.0	0.0
2	0	-M_ycos1	M_zcos1	0.0	-5.06000	1.57000	M_xsin1	0	0	0.0	0.0	0.0

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Active Irreps:

label	dim. small irrep	dim. full irrep	direction	action	number of modes	presence
mSM2	1	2	general	primary	6
mGM1	1	1		primary	2
mX4	1	1		secondary	3	no

Comments:

NPD
Between about 9K to 7K a preceding incommensurate structure is observed
Commensurate structure refined as a modulated structure using the superspace formalism under a magnetic superspace group (MSSG) with k=(0.25,0,0).
The initial phase to define the commensurate structure could not be determined, but the value t=0.125 or equivalent (special direction for the 2-dim mSM2 order parameter) is proposed as the most plausible.
The resulting commensurate structure described under a MSG can be seen in #2.38 (a shift of the origin along x is required for its description in the standard setting of its MSG).
The modulation includes a single harmonic (restricted to the y and z moment components) plus a symmetry-allowed homogeneous k=0 term of the x component.
The MSSG also allows a sine modulation of the x component which yielded negligible values in the refinement and was fixed to zero.

Comments (symmetry):

2k magnetic structure
k-maximal magnetic symmetry
two irreps with different k-vectors as primary.
Harmonic with k=(1/2,0,0) (irrep mX4) is symmetry allowed but it is not present

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

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