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+1/2,-x4+1/2,-1	{ 2'₀₀₁ \| 1/2 0 1/2 1/2 }
3	-x1,x2+1/2,-x3,-x4+1/2,+1	{ 2₀₁₀ \| 0 1/2 0 1/2 }
4	x1+1/2,-x2+1/2,-x3+1/2,x4,-1	{ 2'₁₀₀ \| 1/2 1/2 1/2 0 }
5	-x1,-x2,-x3,-x4+1/2,-1	{ -1' \| 0 0 0 1/2 }
6	x1+1/2,x2,-x3+1/2,x4,+1	{ m₀₀₁ \| 1/2 0 1/2 0 }
7	x1,-x2+1/2,x3,x4,-1	{ m'₀₁₀ \| 0 1/2 0 0 }
8	-x1+1/2,x2+1/2,x3+1/2,-x4+1/2,+1	{ m₁₀₀ \| 1/2 1/2 1/2 1/2 }

N	(x,y,z)	Seitz notation
1	x,y,z,+1	1
2	-x,-y,z,-1	2'₀₀₁
3	-x,y,-z,+1	2₀₁₀
4	x,-y,-z,-1	2'₁₀₀
5	-x,-y,-z,-1	-1'
6	x,y,-z,+1	m₀₀₁
7	x,-y,z,-1	m'₀₁₀
8	-x,y,z,+1	m₁₀₀

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
Ho1	M_xcos1	0	M_zcos1	-1.6(2)	0.0	-3.73(16)	M_xsin1	0	M_zsin1	-1.4(3)	0.0	0.8(2)
Ho2	M_xcos1	M_ycos1	M_zcos1	0.48(13)	1.07(16)	-2.02(12)	M_xsin1	M_ysin1	M_zsin1	-0.65(14)	-0.83(18)	-0.11(15)
Co	M_xcos1	0	M_zcos1	-1.0(2)	0.0	-1.02(19)	M_xsin1	0	M_zsin1	-1.1(2)	0.0	0.0(2)

Atom	x	y	z	Symmetry constraints on M	M_0x	M_0z
1	0.02430	0.25000	0.14330	m_x,0,m_z	-1.81000	2.78000
2	0.47570	0.75000	0.64330	m_x,0,-m_z	-1.81000	-2.78000
3	0.97570	0.75000	0.85670	-m_x,0,-m_z	1.81000	-2.78000
4	0.52430	0.25000	0.35670	-m_x,0,m_z	1.81000	2.78000

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	0	M_zcos1	-1.60000	0.0	-3.73000	M_xsin1	0	M_zsin1	-1.40000	0.0	0.80000
2	-M_xcos1	0	M_zcos1	1.60000	0.0	-3.73000	M_xsin1	0	-M_zsin1	-1.40000	0.0	-0.80000
3	M_xcos1	0	M_zcos1	-1.60000	0.0	-3.73000	-M_xsin1	0	-M_zsin1	1.40000	0.0	-0.80000
4	-M_xcos1	0	M_zcos1	1.60000	0.0	-3.73000	-M_xsin1	0	M_zsin1	1.40000	0.0	0.80000

Atom	x	y	z	Symmetry constraints on M	M_0x	M_0y	M_0z
1	0.16780	0.06140	0.67490	m_x,m_y,m_z	1.51000	1.78000	1.39000
2	0.33220	0.93860	0.17490	m_x,m_y,-m_z	1.51000	1.78000	-1.39000
3	0.83220	0.56140	0.32510	-m_x,m_y,-m_z	-1.51000	1.78000	-1.39000
4	0.66780	0.43860	0.82510	-m_x,m_y,m_z	-1.51000	1.78000	1.39000
5	0.83220	0.93860	0.32510	-m_x,-m_y,-m_z	-1.51000	-1.78000	-1.39000
6	0.66780	0.06140	0.82510	-m_x,-m_y,m_z	-1.51000	-1.78000	1.39000
7	0.16780	0.43860	0.67490	m_x,-m_y,m_z	1.51000	-1.78000	1.39000
8	0.33220	0.56140	0.17490	m_x,-m_y,-m_z	1.51000	-1.78000	-1.39000

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	0.48000	1.07000	-2.02000	M_xsin1	M_ysin1	M_zsin1	-0.65000	-0.83000	-0.11000
2	-M_xcos1	-M_ycos1	M_zcos1	-0.48000	-1.07000	-2.02000	M_xsin1	M_ysin1	-M_zsin1	-0.65000	-0.83000	0.11000
3	M_xcos1	-M_ycos1	M_zcos1	0.48000	-1.07000	-2.02000	-M_xsin1	M_ysin1	-M_zsin1	0.65000	-0.83000	0.11000
4	-M_xcos1	M_ycos1	M_zcos1	-0.48000	1.07000	-2.02000	-M_xsin1	M_ysin1	M_zsin1	0.65000	-0.83000	-0.11000
5	M_xcos1	M_ycos1	M_zcos1	0.48000	1.07000	-2.02000	-M_xsin1	-M_ysin1	-M_zsin1	0.65000	0.83000	0.11000
6	-M_xcos1	-M_ycos1	M_zcos1	-0.48000	-1.07000	-2.02000	-M_xsin1	-M_ysin1	M_zsin1	0.65000	0.83000	-0.11000
7	M_xcos1	-M_ycos1	M_zcos1	0.48000	-1.07000	-2.02000	M_xsin1	-M_ysin1	M_zsin1	-0.65000	0.83000	-0.11000
8	-M_xcos1	M_ycos1	M_zcos1	-0.48000	1.07000	-2.02000	M_xsin1	-M_ysin1	-M_zsin1	-0.65000	0.83000	0.11000

Atom	x	y	z	Symmetry constraints on M	M_0x	M_0z
1	0.23700	0.25000	0.05500	m_x,0,m_z	0.24000	0.22000
2	0.26300	0.75000	0.55500	m_x,0,-m_z	0.24000	-0.22000
3	0.76300	0.75000	0.94500	-m_x,0,-m_z	-0.24000	-0.22000
4	0.73700	0.25000	0.44500	-m_x,0,m_z	-0.24000	0.22000

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	0	M_zcos1	-1.00000	0.0	-1.02000	M_xsin1	0	M_zsin1	-1.10000	0.0	0.0
2	-M_xcos1	0	M_zcos1	1.00000	0.0	-1.02000	M_xsin1	0	-M_zsin1	-1.10000	0.0	0.0
3	M_xcos1	0	M_zcos1	-1.00000	0.0	-1.02000	-M_xsin1	0	-M_zsin1	1.10000	0.0	0.0
4	-M_xcos1	0	M_zcos1	1.00000	0.0	-1.02000	-M_xsin1	0	M_zsin1	1.10000	0.0	0.0

Reference: S. Goswami, M. I. Sousa Henriques, V. Petricek, P. D. Babu, PHYSICAL REVIEW B (2024) 109 214417
DOI: 10.1103/PhysRevB.109.214417
Atomic positions from: same reference

Parent space group (paramagnetic phase): Pnma (#62)
Propagation vector: k1 (0.158580, 0.000000, 0.000000)

Transition Temperature: 21 K
Experiment Temperature: 18 K

Lattice parameters of the basic unit cell:
6.9383(11) 9.2451(15) 6.2327(10) 90 90 90
Transformation from parent structure: (a,b,c;0,0,0)
    [View matrix form]

Magnetic Superspace Group: Pnm'a(a00)000
    [View symmetry operations]

Magnetic Point Group: mmm.1' (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 and magnetic moments of symmetry independent atoms

Label	Atom type	x	y	z	Occupancy	Multiplicity	Symmetry constraints on M	M_0x	M_0y	M_0z	\|M\|
Ho1	Ho	0.0243(11)	0.25	0.1433(14)	2	4	m_x,0,m_z	-1.81(8)	0.0	2.78(8)	3.32
Ho2	Ho	0.1678(7)	0.0614(6)	0.6749(9)	2	8	m_x,m_y,m_z	1.51(7)	1.78(4)	1.39(7)	2.72
Co	Co	0.237(3)	0.25	1.055(4)	2	4	m_x,0,m_z	0.24(11)	0.0	0.22(7)	0.33

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
Ho1	M_xcos1	0	M_zcos1	-1.6(2)	0.0	-3.73(16)	M_xsin1	0	M_zsin1	-1.4(3)	0.0	0.8(2)
Ho2	M_xcos1	M_ycos1	M_zcos1	0.48(13)	1.07(16)	-2.02(12)	M_xsin1	M_ysin1	M_zsin1	-0.65(14)	-0.83(18)	-0.11(15)
Co	M_xcos1	0	M_zcos1	-1.0(2)	0.0	-1.02(19)	M_xsin1	0	M_zsin1	-1.1(2)	0.0	0.0(2)

Atom	x	y	z	Symmetry constraints on M	M_0x	M_0z
1	0.02430	0.25000	0.14330	m_x,0,m_z	-1.81000	2.78000
2	0.47570	0.75000	0.64330	m_x,0,-m_z	-1.81000	-2.78000
3	0.97570	0.75000	0.85670	-m_x,0,-m_z	1.81000	-2.78000
4	0.52430	0.25000	0.35670	-m_x,0,m_z	1.81000	2.78000

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	0	M_zcos1	-1.60000	0.0	-3.73000	M_xsin1	0	M_zsin1	-1.40000	0.0	0.80000
2	-M_xcos1	0	M_zcos1	1.60000	0.0	-3.73000	M_xsin1	0	-M_zsin1	-1.40000	0.0	-0.80000
3	M_xcos1	0	M_zcos1	-1.60000	0.0	-3.73000	-M_xsin1	0	-M_zsin1	1.40000	0.0	-0.80000
4	-M_xcos1	0	M_zcos1	1.60000	0.0	-3.73000	-M_xsin1	0	M_zsin1	1.40000	0.0	0.80000

Atom	x	y	z	Symmetry constraints on M	M_0x	M_0y	M_0z
1	0.16780	0.06140	0.67490	m_x,m_y,m_z	1.51000	1.78000	1.39000
2	0.33220	0.93860	0.17490	m_x,m_y,-m_z	1.51000	1.78000	-1.39000
3	0.83220	0.56140	0.32510	-m_x,m_y,-m_z	-1.51000	1.78000	-1.39000
4	0.66780	0.43860	0.82510	-m_x,m_y,m_z	-1.51000	1.78000	1.39000
5	0.83220	0.93860	0.32510	-m_x,-m_y,-m_z	-1.51000	-1.78000	-1.39000
6	0.66780	0.06140	0.82510	-m_x,-m_y,m_z	-1.51000	-1.78000	1.39000
7	0.16780	0.43860	0.67490	m_x,-m_y,m_z	1.51000	-1.78000	1.39000
8	0.33220	0.56140	0.17490	m_x,-m_y,-m_z	1.51000	-1.78000	-1.39000

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	0.48000	1.07000	-2.02000	M_xsin1	M_ysin1	M_zsin1	-0.65000	-0.83000	-0.11000
2	-M_xcos1	-M_ycos1	M_zcos1	-0.48000	-1.07000	-2.02000	M_xsin1	M_ysin1	-M_zsin1	-0.65000	-0.83000	0.11000
3	M_xcos1	-M_ycos1	M_zcos1	0.48000	-1.07000	-2.02000	-M_xsin1	M_ysin1	-M_zsin1	0.65000	-0.83000	0.11000
4	-M_xcos1	M_ycos1	M_zcos1	-0.48000	1.07000	-2.02000	-M_xsin1	M_ysin1	M_zsin1	0.65000	-0.83000	-0.11000
5	M_xcos1	M_ycos1	M_zcos1	0.48000	1.07000	-2.02000	-M_xsin1	-M_ysin1	-M_zsin1	0.65000	0.83000	0.11000
6	-M_xcos1	-M_ycos1	M_zcos1	-0.48000	-1.07000	-2.02000	-M_xsin1	-M_ysin1	M_zsin1	0.65000	0.83000	-0.11000
7	M_xcos1	-M_ycos1	M_zcos1	0.48000	-1.07000	-2.02000	M_xsin1	-M_ysin1	M_zsin1	-0.65000	0.83000	-0.11000
8	-M_xcos1	M_ycos1	M_zcos1	-0.48000	1.07000	-2.02000	M_xsin1	-M_ysin1	-M_zsin1	-0.65000	0.83000	0.11000

Atom	x	y	z	Symmetry constraints on M	M_0x	M_0z
1	0.23700	0.25000	0.05500	m_x,0,m_z	0.24000	0.22000
2	0.26300	0.75000	0.55500	m_x,0,-m_z	0.24000	-0.22000
3	0.76300	0.75000	0.94500	-m_x,0,-m_z	-0.24000	-0.22000
4	0.73700	0.25000	0.44500	-m_x,0,m_z	-0.24000	0.22000

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	0	M_zcos1	-1.00000	0.0	-1.02000	M_xsin1	0	M_zsin1	-1.10000	0.0	0.0
2	-M_xcos1	0	M_zcos1	1.00000	0.0	-1.02000	M_xsin1	0	-M_zsin1	-1.10000	0.0	0.0
3	M_xcos1	0	M_zcos1	-1.00000	0.0	-1.02000	-M_xsin1	0	-M_zsin1	1.10000	0.0	0.0
4	-M_xcos1	0	M_zcos1	1.00000	0.0	-1.02000	-M_xsin1	0	M_zsin1	1.10000	0.0	0.0

[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
mSM4	1	2	general	primary	14
mGM4	1	1		primary	7

Comments:

Comments (symmetry):

1k incommemsurate magnetic structure
k-maximal symmetry
Two irreps as primary irreps: one incommensurate 2-dim (k,-k) and one at k=0
The arbitrary global phase of the modulation is fixed by the choice of origin along x4 in the MSSG operations.

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

Ho₃Co (#1.1.156)

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

Ho3Co (#1.1.156)

Ho₃Co (#1.1.156)