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 }

N	(x,y,z)	Seitz notation
1	x,y,z,+1	1

Label	Atom type	x	y	z	Multiplicity
O1_1_1	O	0.0956	0.4739	0.25	1
O1_1_2	O	-0.0956	-0.4739	0.75	1
O1_2_1	O	0.4044	-0.0261	0.25	1
O1_2_2	O	-0.4044	0.0261	0.75	1
O2_1_1	O	0.6991	0.298	0.0499	1
O2_1_2	O	-0.6991	-0.298	0.5499	1
O2_2_1	O	0.8009	0.798	0.4501	1
O2_2_2	O	-0.8009	-0.798	0.9501	1
O2_3_1	O	0.3009	0.702	-0.0499	1
O2_3_2	O	-0.3009	-0.702	0.4501	1
O2_4_1	O	0.1991	0.202	0.5499	1
O2_4_2	O	-0.1991	-0.202	1.0499	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
Gd_1_1	M_xcos1	M_ycos1	M_zcos1	0.0	0.0	2.2	M_xsin1	M_ysin1	M_zsin1	4.7	0.0	0.0
Gd_1_2	M_xcos1	M_ycos1	M_zcos1	0.0	0.0	2.2	M_xsin1	M_ysin1	M_zsin1	4.7	0.0	0.0
Gd_2_1	M_xcos1	M_ycos1	M_zcos1	-4.7	0.0	0.0	M_xsin1	M_ysin1	M_zsin1	0.0	0.0	-2.2
Gd_2_2	M_xcos1	M_ycos1	M_zcos1	4.7	0.0	0.0	M_xsin1	M_ysin1	M_zsin1	0.0	0.0	2.2
Cr_1_1	M_xcos1	M_ycos1	M_zcos1	0.0	0.0	0.0	M_xsin1	M_ysin1	M_zsin1	0.0	0.0	0.0
Cr_1_2	M_xcos1	M_ycos1	M_zcos1	0.0	0.0	0.0	M_xsin1	M_ysin1	M_zsin1	0.0	0.0	0.0
Cr_2_1	M_xcos1	M_ycos1	M_zcos1	0.0	0.0	0.0	M_xsin1	M_ysin1	M_zsin1	0.0	0.0	0.0
Cr_2_2	M_xcos1	M_ycos1	M_zcos1	0.0	0.0	0.0	M_xsin1	M_ysin1	M_zsin1	0.0	0.0	0.0

Atom	x	y	z	Symmetry constraints on M	M_0x	M_0y	M_0z
1	0.98500	0.05879	0.25000	m_x,m_y,m_z	0.00000	1.07000	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	M_xcos1	M_ycos1	M_zcos1	0.0	0.0	2.20000	M_xsin1	M_ysin1	M_zsin1	4.70000	0.0	0.0

Atom	x	y	z	Symmetry constraints on M	M_0x	M_0y	M_0z
1	0.01500	0.94121	0.75000	m_x,m_y,m_z	0.00000	1.07000	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	M_xcos1	M_ycos1	M_zcos1	0.0	0.0	2.20000	M_xsin1	M_ysin1	M_zsin1	4.70000	0.0	0.0

Atom	x	y	z	Symmetry constraints on M	M_0x	M_0y	M_0z
1	0.51500	0.55879	0.25000	m_x,m_y,m_z	0.00000	-1.07000	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	M_xcos1	M_ycos1	M_zcos1	-4.70000	0.0	0.0	M_xsin1	M_ysin1	M_zsin1	0.0	0.0	-2.20000

Atom	x	y	z	Symmetry constraints on M	M_0x	M_0y	M_0z
1	0.48500	0.44121	0.75000	m_x,m_y,m_z	0.00000	-1.07000	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	M_xcos1	M_ycos1	M_zcos1	4.70000	0.0	0.0	M_xsin1	M_ysin1	M_zsin1	0.0	0.0	2.20000

Atom	x	y	z	Symmetry constraints on M	M_0x	M_0y	M_0z
1	0.50000	0.00000	0.00000	m_x,m_y,m_z	1.64100	0.00000	1.92000

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	M_zcos1	0.0	0.0	0.0	M_xsin1	M_ysin1	M_zsin1	0.0	0.0	0.0

Atom	x	y	z	Symmetry constraints on M	M_0x	M_0y	M_0z
1	0.50000	0.00000	0.50000	m_x,m_y,m_z	-1.64000	0.00000	-1.92000

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	M_zcos1	0.0	0.0	0.0	M_xsin1	M_ysin1	M_zsin1	0.0	0.0	0.0

Atom	x	y	z	Symmetry constraints on M	M_0x	M_0y	M_0z
1	0.00000	0.50000	0.50000	m_x,m_y,m_z	1.64000	0.00000	1.94000

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	M_zcos1	0.0	0.0	0.0	M_xsin1	M_ysin1	M_zsin1	0.0	0.0	0.0

Atom	x	y	z	Symmetry constraints on M	M_0x	M_0y	M_0z
1	0.00000	0.50000	0.00000	m_x,m_y,m_z	-1.64000	0.00000	-1.92000

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	M_zcos1	0.0	0.0	0.0	M_xsin1	M_ysin1	M_zsin1	0.0	0.0	0.0

Atom	x	y	z
1	0.09560	0.47390	0.25000

Atom	x	y	z
1	0.90440	0.52610	0.75000

Atom	x	y	z
1	0.40440	0.97390	0.25000

Atom	x	y	z
1	0.59560	0.02610	0.75000

Atom	x	y	z
1	0.69910	0.29800	0.04990

Atom	x	y	z
1	0.30090	0.70200	0.54990

Atom	x	y	z
1	0.80090	0.79800	0.45010

Atom	x	y	z
1	0.19910	0.20200	0.95010

Atom	x	y	z
1	0.30090	0.70200	0.95010

Atom	x	y	z
1	0.69910	0.29800	0.45010

Atom	x	y	z
1	0.19910	0.20200	0.54990

Atom	x	y	z
1	0.80090	0.79800	0.04990

Reference: Pascal Manuel, Dmitry Khalyavin, Fabio Orlandi, Laurent Chapon, Wang Xueyun, Sang Wook Cheong, Acta Cryst. B (2025) 81 ? - ?
DOI: 10.1107/S2052520625001921
Atomic positions from: same reference

Parent space group (paramagnetic phase): Pnma (#62)
Propagation vector: k1 (0.080000, 0.320000, 0.000000)

Transition Temperature: 2.4 K
Experiment Temperature: 1.5 K

Lattice parameters of the basic unit cell:
5.3045 5.5203 7.5929 90 90 90
Transformation from parent structure: (c,a,b;0,0,0)
    [View matrix form]

Magnetic Superspace Group: P1.1(abg)0
    [View symmetry operations]

Magnetic Point Group: 1.1 (1.1.1)
    [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 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\|
Gd_1_1	Gd	-0.015	0.05879	0.25	1	M_x,M_y,M_z	0.0	1.07	0.0	1.07
Gd_1_2	Gd	0.015	-0.05879	0.75	1	M_x,M_y,M_z	0.0	1.07	0.0	1.07
Gd_2_1	Gd	0.515	0.55879	0.25	1	M_x,M_y,M_z	0.0	-1.07	0.0	1.07
Gd_2_2	Gd	-0.515	-0.55879	0.75	1	M_x,M_y,M_z	0.0	-1.07	0.0	1.07
Cr_1_1	Cr	0.5	0	0	1	M_x,M_y,M_z	1.641	0.0	1.92	2.53
Cr_1_2	Cr	-0.5	0	0.5	1	M_x,M_y,M_z	-1.64	0.0	-1.92	2.53
Cr_2_1	Cr	0	0.5	0.5	1	M_x,M_y,M_z	1.64	0.0	1.94	2.54
Cr_2_2	Cr	0	-0.5	1	1	M_x,M_y,M_z	-1.64	0.0	-1.92	2.53

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
Gd_1_1	M_xcos1	M_ycos1	M_zcos1	0.0	0.0	2.2	M_xsin1	M_ysin1	M_zsin1	4.7	0.0	0.0
Gd_1_2	M_xcos1	M_ycos1	M_zcos1	0.0	0.0	2.2	M_xsin1	M_ysin1	M_zsin1	4.7	0.0	0.0
Gd_2_1	M_xcos1	M_ycos1	M_zcos1	-4.7	0.0	0.0	M_xsin1	M_ysin1	M_zsin1	0.0	0.0	-2.2
Gd_2_2	M_xcos1	M_ycos1	M_zcos1	4.7	0.0	0.0	M_xsin1	M_ysin1	M_zsin1	0.0	0.0	2.2
Cr_1_1	M_xcos1	M_ycos1	M_zcos1	0.0	0.0	0.0	M_xsin1	M_ysin1	M_zsin1	0.0	0.0	0.0
Cr_1_2	M_xcos1	M_ycos1	M_zcos1	0.0	0.0	0.0	M_xsin1	M_ysin1	M_zsin1	0.0	0.0	0.0
Cr_2_1	M_xcos1	M_ycos1	M_zcos1	0.0	0.0	0.0	M_xsin1	M_ysin1	M_zsin1	0.0	0.0	0.0
Cr_2_2	M_xcos1	M_ycos1	M_zcos1	0.0	0.0	0.0	M_xsin1	M_ysin1	M_zsin1	0.0	0.0	0.0

Atom	x	y	z	Symmetry constraints on M	M_0x	M_0y	M_0z
1	0.98500	0.05879	0.25000	m_x,m_y,m_z	0.00000	1.07000	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	M_xcos1	M_ycos1	M_zcos1	0.0	0.0	2.20000	M_xsin1	M_ysin1	M_zsin1	4.70000	0.0	0.0

Atom	x	y	z	Symmetry constraints on M	M_0x	M_0y	M_0z
1	0.01500	0.94121	0.75000	m_x,m_y,m_z	0.00000	1.07000	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	M_xcos1	M_ycos1	M_zcos1	0.0	0.0	2.20000	M_xsin1	M_ysin1	M_zsin1	4.70000	0.0	0.0

Atom	x	y	z	Symmetry constraints on M	M_0x	M_0y	M_0z
1	0.51500	0.55879	0.25000	m_x,m_y,m_z	0.00000	-1.07000	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	M_xcos1	M_ycos1	M_zcos1	-4.70000	0.0	0.0	M_xsin1	M_ysin1	M_zsin1	0.0	0.0	-2.20000

[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
mGM4+	1	1		primary	3
mGM2+	1	1		primary	3
mM1	2	4	special	primary	6
mM2	2	4	special	primary	6

Comments:

NPD
Transition driven by the Gd ordering with the mM1 and mM2 irreps
The magnetic order parameter induces a ferroelectric distortion as secondary order parameter. The latter transform as the GM4- irrep of the parent Pnma space group.
The combination of all irreps reduce the symmetry to P1.
Only Gd moments are incommensurately modulated
Positional structure from refinement at 20 K using the parent space group
Basic unit cell used is in the Pbnm setting with respect to the parent structures

Comments (symmetry):

1k incommensurate magnetic structure
4 active irreps

Bilbao Crystallographic Server
http://www.cryst.ehu.es

For comments, please mail to
cryst@wm.lc.ehu.es

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

GdCrO₃ (#1.1.159)

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

GdCrO3 (#1.1.159)

GdCrO₃ (#1.1.159)