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,x3,x4,+1	{ 2₀₀₁ \| 1/2 0 0 0 }
3	x1,-x2,x3,x4+1/2,+1	{ m₀₁₀ \| 0 0 0 1/2 }
4	-x1+1/2,x2,x3,x4+1/2,+1	{ m₁₀₀ \| 1/2 0 0 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,x3,x4+1/2,-1	{ 2'₀₀₁ \| 1/2 0 0 1/2 }
7	x1,-x2,x3,x4,-1	{ m'₀₁₀ \| 0 }
8	-x1+1/2,x2,x3,x4,-1	{ m'₁₀₀ \| 1/2 0 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	m₀₁₀
4	-x,y,z,+1	m₁₀₀
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	m'₀₁₀
8	-x,y,z,-1	m'₁₀₀

Label	Atom type	x	y	z	Multiplicity
Co1_1	Co	0.25	0	0.807	1
Co1_2	Co	-0.25	0	-0.807	1
Al1	Al	0	0	0	2
Al2_1	Al	0.25	0.5	0.037	1
Al2_2	Al	-0.25	-0.5	-0.037	1
Al3_1	Al	0.069	0.5	0.696	2
Al3_2	Al	-0.069	-0.5	-0.696	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
Pr1_1	0	0	M_zcos1	0.0	0.0	2.24	0	0	M_zsin1	0.0	0.0	0.0
Pr1_2	0	0	M_zcos1	0.0	0.0	1.815	0	0	M_zsin1	0.0	0.0	1.31

Atom	x	y	z
1	0.25000	0.00000	0.38600

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	2.24000	0	0	M_zsin1	0.0	0.0	0.0

Atom	x	y	z
1	0.75000	0.00000	0.61400

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	1.81500	0	0	M_zsin1	0.0	0.0	1.31000

Atom	x	y	z
1	0.25000	0.00000	0.80700

Atom	x	y	z
1	0.75000	0.00000	0.19300

Atom	x	y	z
1	0.00000	0.00000	0.00000
2	0.50000	0.00000	0.00000

Atom	x	y	z
1	0.25000	0.50000	0.03700

Atom	x	y	z
1	0.75000	0.50000	0.96300

Atom	x	y	z
1	0.06900	0.50000	0.69600
2	0.43100	0.50000	0.69600

Atom	x	y	z
1	0.93100	0.50000	0.30400
2	0.56900	0.50000	0.30400

Reference: P. Schobinger-Papamantellos, G. Andre, J. Rodriguez-Carvajal, O. Moze, W. Kockelmann, L. Tung and K. Buschow, Journal of Magnetism and Magnetic Materials (2001) 231 162-171.
DOI: 10.1016/s0304-8853(01)00062-2
Atomic positions from: same reference

Parent space group (paramagnetic phase): (#51)
Propagation vector: k1 (0.000000, 0.000000, 0.437000)

Transition Temperature: 17 K
Experiment Temperature: 1.5 K

Lattice parameters of the basic unit cell:
7.644 4.0431 6.8717 90 90 90
Transformation from parent structure: (a,b,c;0,0,0)
    [View matrix form]

Magnetic Superspace Group: Pmm21'(00g)ss0s
    [View symmetry operations]

Magnetic Point Group: mm21' (7.2.21)
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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
Pr1_1	Pr	0.25	0	0.386	1
Pr1_2	Pr	0.75	0	0.614	1

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
Pr1_1	0	0	M_zcos1	0.0	0.0	2.24	0	0	M_zsin1	0.0	0.0	0.0
Pr1_2	0	0	M_zcos1	0.0	0.0	1.815	0	0	M_zsin1	0.0	0.0	1.31

Atom	x	y	z
1	0.25000	0.00000	0.38600

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	2.24000	0	0	M_zsin1	0.0	0.0	0.0

Atom	x	y	z
1	0.75000	0.00000	0.61400

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	1.81500	0	0	M_zsin1	0.0	0.0	1.31000

[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
mLD2	1	2	general	primary	2
mLD2	1	2	general	primary	2

Comments:

NPD
The two Pr atoms related by inversion within the unit cell are modelled as having in phase spin modulations, instead of having modulations related by inversion. This breaks the inversion symmetry of the structure.
As the two atoms have different z coordinates, the parameterization in terms of q.r_i from the superspace formalism, which is used here, requires some specific k-dependent phase shift between the two modulations yielding non-zero amplitudes for both the sine and cosine modulation functions. Amplitudes given with non-significant digit to comply with the reported spin modulation amplitude: 2.24

Comments (symmetry):

1k incommensurate magnetic structure
The proposed spin modulation breaks the centrosymmetry of the structure and yields a polar structure.
It requires the incoherent superposition of two magnetic order parameters for the same irrep.
It seems that the proposed model was chosen ad-ho, and other more symmetric models, with a single order parameter and keeping the point group of the paramagnetic phase, were not explored.
As the MSSG of the structure does not include any operation transforming k into -k, one of the phases of the two independent Pr spin modulations can be fixed arbitrarily (here the sine function has been set to zero), and therefore the spin modulations has only 3 free parameters. The assumption that the two independent spin modulations are in phase reduces these three free parameters to one.
The longitudinal character of the spin modulation is symmetry protected

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

PrCoAl₄ (#1.1.61)

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

PrCoAl4 (#1.1.61)

PrCoAl₄ (#1.1.61)