MAGNDATA - Collection of Magnetic Structures

Magnetic structure with only magnetic atoms

Reference: L. Canadillas-Delgado, L. Mazzuca, O. Fabelo, J. Rodriguez-Carvajal, V. Petricek, Inorg. Chem. (2020) 59 17896 - 17905
DOI: 10.1021/acs.inorgchem.0c01722
Atomic positions from: same reference

Parent space group (paramagnetic phase): Pnma (#62)
Propagation vector: k1 (0.000000, 0.000000, 0.1426)

Transition Temperature: 34 K
Experiment Temperature: 5(1) K

Wave vectors table:

label	Wave vector	k1 coefficient
1	(0, 0, 0.1426)	1
2	(0, 0, 0.2852)	2

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

Label	Atom type	x	y	z	Multiplicity
O1	O	0.5968(2)	-0.06966(15)	-0.21217(19)	8
O2	O	0.7751(2)	-0.05821(15)	-0.4175(2)	8
O3	O	0.4752(2)	0.15420(16)	-0.12513(19)	8
N1	N	0.9141(2)	0.25	-0.0303(2)	4
C1	C	0.72219(19)	-0.02844(14)	-0.27701(18)	8
C2	C	1.0876(3)	0.25	0.0238(3)	4
C3	C	0.4908(2)	0.25	-0.0529(3)	4
H1	H	0.7919(5)	0.0367(3)	-0.2102(4)	8
H2	H	0.5182(7)	0.25	0.0808(6)	4
H3	H	0.9118(6)	0.25	-0.1579(6)	4
H4	H	1.0923(7)	0.25	0.1570(6)	4
H5	H	0.8524(4)	0.1779(3)	0.0127(4)	8
H6	H	1.1466(4)	0.3262(3)	-0.0227(5)	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
Ni1	M_xcos1	M_ycos1	M_zcos1	0.29(3)	0.02(9)	-0.08(3)	0	0	0	0.0	0.0	0.0

Atom	Displacement vector Fourier Cos coeffs	Displacement vector Fourier Sin coeffs
Symmetry constraints	Numerical values	Symmetry constraints	Numerical values
x	y	z	x	y	z	x	y	z	x	y	z
Ni1	0	0	0	0.0	0.0	0.0	U_xsin1	U_ysin1	U_zsin1	-0.0032(2)	0.02624(16)	0.0004(2)
O1	U_xcos1	U_ycos1	U_zcos1	-0.0026(3)	0.0042(2)	-0.0002(3)	U_xsin1	U_ysin1	U_zsin1	-0.0030(3)	0.0256(2)	0.0009(3)
O2	U_xcos1	U_ycos1	U_zcos1	0.0008(3)	0.0014(2)	0.0033(3)	U_xsin1	U_ysin1	U_zsin1	-0.0026(3)	0.0256(2)	-0.0005(3)
O3	U_xcos1	U_ycos1	U_zcos1	-0.0036(3)	0.0027(2)	-0.0003(3)	U_xsin1	U_ysin1	U_zsin1	-0.0021(3)	0.0262(2)	0.0003(3)
N1	0	U_ycos1	0	0.0	0.00684(19)	0.0	0	U_ysin1	0	0.0	0.02458(18)	0.0
C1	U_xcos1	U_ycos1	U_zcos1	0.0005(3)	0.00143(18)	0.0016(2)	U_xsin1	U_ysin1	U_zsin1	-0.0026(2)	0.02550(19)	0.0002(2)
C2	0	U_ycos1	0	0.0	0.0014(3)	0.0	0	U_ysin1	0	0.0	0.0244(3)	0.0
C3	0	U_ycos1	0	0.0	0.0009(2)	0.0	0	U_ysin1	0	0.0	0.0264(3)	0.0
H1	U_xcos1	U_ycos1	U_zcos1	0.0035(6)	-0.0010(4)	0.0011(6)	U_xsin1	U_ysin1	U_zsin1	-0.0024(6)	0.0254(4)	0.0004(6)
H2	0	U_ycos1	0	0.0	-0.0036(5)	0.0	0	U_ysin1	0	0.0	0.0249(5)	0.0
H3	0	U_ycos1	0	0.0	0.0169(6)	0.0	0	U_ysin1	0	0.0	0.0221(6)	0.0
H4	0	U_ycos1	0	0.0	-0.0102(6)	0.0	0	U_ysin1	0	0.0	0.0241(7)	0.0
H5	U_xcos1	U_ycos1	U_zcos1	-0.0004(5)	0.0044(4)	-0.0072(5)	U_xsin1	U_ysin1	U_zsin1	-0.0009(5)	0.0252(4)	0.0008(5)
H6	U_xcos1	U_ycos1	U_zcos1	0.0006(6)	0.0055(5)	0.0097(6)	U_xsin1	U_ysin1	U_zsin1	0.0007(6)	0.0236(4)	-0.0010(7)

Atom	Displacement vector Fourier Cos coeffs	Displacement vector Fourier Sin coeffs
Symmetry constraints	Numerical values	Symmetry constraints	Numerical values
x	y	z	x	y	z	x	y	z	x	y	z
O3	U_xcos2	U_ycos2	U_zcos2	0.0000(5)	-0.0002(2)	-0.0001(4)	U_xsin2	U_ysin2	U_zsin2	0.0001(5)	-0.0001(3)	0.0001(4)
N1	U_xcos2	U_ycos2	U_zcos2	0.0000(5)	-0.0002(2)	-0.0001(4)	U_xsin2	U_ysin2	U_zsin2	0.0001(5)	-0.0001(3)	0.0001(4)
C1	U_xcos2	U_ycos2	U_zcos2	0.0000(5)	-0.0002(2)	-0.0001(4)	U_xsin2	U_ysin2	U_zsin2	0.0001(5)	-0.0001(3)	0.0001(4)
C2	U_xcos2	U_ycos2	U_zcos2	0.0000(5)	-0.0002(2)	-0.0001(4)	U_xsin2	U_ysin2	U_zsin2	0.0001(5)	-0.0001(3)	0.0001(4)
C3	U_xcos2	U_ycos2	U_zcos2	0.0000(5)	-0.0002(2)	-0.0001(4)	U_xsin2	U_ysin2	U_zsin2	0.0001(5)	-0.0001(3)	0.0001(4)
H1	U_xcos2	U_ycos2	U_zcos2	0.0007(11)	-0.0003(4)	0.0002(9)	U_xsin2	U_ysin2	U_zsin2	0.0010(11)	0.0000(5)	-0.0006(9)
H2	U_xcos2	0	U_zcos2	0.0001(16)	0.0	-0.0021(11)	U_xsin2	0	U_zsin2	-0.0003(16)	0.0	-0.0011(12)
H3	U_xcos2	0	U_zcos2	-0.0005(15)	0.0	0.0010(12)	U_xsin2	0	U_zsin2	-0.0019(15)	0.0	0.0005(12)
H4	U_xcos2	0	U_zcos2	-0.0003(17)	0.0	0.0006(13)	U_xsin2	0	U_zsin2	-0.0004(16)	0.0	0.0027(14)
H5	U_xcos2	U_ycos2	U_zcos2	0.0027(10)	0.0003(4)	-0.0007(8)	U_xsin2	U_ysin2	U_zsin2	-0.0021(9)	0.0004(5)	0.0012(8)
H6	U_xcos2	U_ycos2	U_zcos2	0.0007(11)	0.0002(5)	0.0006(10)	U_xsin2	U_ysin2	U_zsin2	0.0001(10)	0.0004(5)	-0.0018(10)

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	0.48000	0.68000	1.97000
2	0.00000	0.00000	0.50000	m_x,m_y,-m_z	0.48000	0.68000	-1.97000
3	0.50000	0.50000	0.00000	-m_x,m_y,-m_z	-0.48000	0.68000	-1.97000
4	0.00000	0.50000	0.50000	-m_x,m_y,m_z	-0.48000	0.68000	1.97000

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	0.29000	0.02000	-0.08000	0	0	0	0.0	0.0	0.0
2	-M_xcos1	-M_ycos1	M_zcos1	-0.29000	-0.02000	-0.08000	0	0	0	0.0	0.0	0.0
3	M_xcos1	-M_ycos1	M_zcos1	0.29000	-0.02000	-0.08000	0	0	0	0.0	0.0	0.0
4	-M_xcos1	M_ycos1	M_zcos1	-0.29000	0.02000	-0.08000	0	0	0	0.0	0.0	0.0

Atom	x	y	z
1	0.59680	0.93034	0.78783
2	0.90320	0.06966	0.28783
3	0.40320	0.43034	0.21217
4	0.09680	0.56966	0.71217
5	0.40320	0.06966	0.21217
6	0.09680	0.93034	0.71217
7	0.59680	0.56966	0.78783
8	0.90320	0.43034	0.28783

Atom	x	y	z
1	0.77510	0.94179	0.58250
2	0.72490	0.05821	0.08250
3	0.22490	0.44179	0.41750
4	0.27510	0.55821	0.91750
5	0.22490	0.05821	0.41750
6	0.27510	0.94179	0.91750
7	0.77510	0.55821	0.58250
8	0.72490	0.44179	0.08250

Atom	x	y	z
1	0.47520	0.15420	0.87487
2	0.02480	0.84580	0.37487
3	0.52480	0.65420	0.12513
4	0.97520	0.34580	0.62513
5	0.52480	0.84580	0.12513
6	0.97520	0.15420	0.62513
7	0.47520	0.34580	0.87487
8	0.02480	0.65420	0.37487

Atom	x	y	z
1	0.91410	0.25000	0.96970
2	0.58590	0.75000	0.46970
3	0.08590	0.75000	0.03030
4	0.41410	0.25000	0.53030

Atom	x	y	z
1	0.72219	0.97156	0.72299
2	0.77781	0.02844	0.22299
3	0.27781	0.47156	0.27701
4	0.22219	0.52844	0.77701
5	0.27781	0.02844	0.27701
6	0.22219	0.97156	0.77701
7	0.72219	0.52844	0.72299
8	0.77781	0.47156	0.22299

Atom	x	y	z
1	0.08760	0.25000	0.02380
2	0.41240	0.75000	0.52380
3	0.91240	0.75000	0.97620
4	0.58760	0.25000	0.47620

Atom	x	y	z
1	0.49080	0.25000	0.94710
2	0.00920	0.75000	0.44710
3	0.50920	0.75000	0.05290
4	0.99080	0.25000	0.55290

Atom	x	y	z
1	0.79190	0.03670	0.78980
2	0.70810	0.96330	0.28980
3	0.20810	0.53670	0.21020
4	0.29190	0.46330	0.71020
5	0.20810	0.96330	0.21020
6	0.29190	0.03670	0.71020
7	0.79190	0.46330	0.78980
8	0.70810	0.53670	0.28980

Atom	x	y	z
1	0.51820	0.25000	0.08080
2	0.98180	0.75000	0.58080
3	0.48180	0.75000	0.91920
4	0.01820	0.25000	0.41920

Atom	x	y	z
1	0.91180	0.25000	0.84210
2	0.58820	0.75000	0.34210
3	0.08820	0.75000	0.15790
4	0.41180	0.25000	0.65790

Atom	x	y	z
1	0.09230	0.25000	0.15700
2	0.40770	0.75000	0.65700
3	0.90770	0.75000	0.84300
4	0.59230	0.25000	0.34300

Atom	x	y	z
1	0.85240	0.17790	0.01270
2	0.64760	0.82210	0.51270
3	0.14760	0.67790	0.98730
4	0.35240	0.32210	0.48730
5	0.14760	0.82210	0.98730
6	0.35240	0.17790	0.48730
7	0.85240	0.32210	0.01270
8	0.64760	0.67790	0.51270

Atom	x	y	z
1	0.14660	0.32620	0.97730
2	0.35340	0.67380	0.47730
3	0.85340	0.82620	0.02270
4	0.64660	0.17380	0.52270
5	0.85340	0.67380	0.02270
6	0.64660	0.32620	0.52270
7	0.14660	0.17380	0.97730
8	0.35340	0.82620	0.47730

Lattice parameters of the basic unit cell:
8.1724(3) 11.5374(6) 8.0925(3) 90 90 90
Transformation from parent structure: (a,b,c;0,0,0)
    [View matrix form]

Magnetic Superspace Group: Pn'ma'(00g)0s0
    [View symmetry operations]

Magnetic Point Group: m'm'm (8.4.27)
    [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\|
Ni1	Ni	0.5	0	0	4	m_x,m_y,m_z	0.48(3)	0.68(7)	1.97(2)	2.14

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
Ni1	M_xcos1	M_ycos1	M_zcos1	0.29(3)	0.02(9)	-0.08(3)	0	0	0	0.0	0.0	0.0

Displacive modulation parameters of symmetry independent atoms

Wave vector 1

Atom	Displacement vector Fourier Cos coeffs						Displacement vector Fourier Sin coeffs
	Symmetry constraints			Numerical values			Symmetry constraints			Numerical values
	x	y	z	x	y	z	x	y	z	x	y	z
Ni1	0	0	0	0.0	0.0	0.0	U_xsin1	U_ysin1	U_zsin1	-0.0032(2)	0.02624(16)	0.0004(2)

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	0.48000	0.68000	1.97000
2	0.00000	0.00000	0.50000	m_x,m_y,-m_z	0.48000	0.68000	-1.97000
3	0.50000	0.50000	0.00000	-m_x,m_y,-m_z	-0.48000	0.68000	-1.97000
4	0.00000	0.50000	0.50000	-m_x,m_y,m_z	-0.48000	0.68000	1.97000

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	0.29000	0.02000	-0.08000	0	0	0	0.0	0.0	0.0
2	-M_xcos1	-M_ycos1	M_zcos1	-0.29000	-0.02000	-0.08000	0	0	0	0.0	0.0	0.0
3	M_xcos1	-M_ycos1	M_zcos1	0.29000	-0.02000	-0.08000	0	0	0	0.0	0.0	0.0
4	-M_xcos1	M_ycos1	M_zcos1	-0.29000	0.02000	-0.08000	0	0	0	0.0	0.0	0.0

Atom	Displacement vector Fourier Cos coeffs	Displacement vector 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	0	0.0	0.0	0.0	U_xsin1	U_ysin1	U_zsin1	-0.00320	0.02624	0.00040
2	0	0	0	0.0	0.0	0.0	U_xsin1	U_ysin1	-U_zsin1	-0.00320	0.02624	-0.00040
3	0	0	0	0.0	0.0	0.0	-U_xsin1	U_ysin1	-U_zsin1	0.00320	0.02624	-0.00040
4	0	0	0	0.0	0.0	0.0	-U_xsin1	U_ysin1	U_zsin1	0.00320	0.02624	0.00040

[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	presence
LD3	2	2	special	primary
mGM4+	1	1		primary	3
mLD2	1	2	special	secondary	3	yes

Comments:

NSD
structurally modulated below 84K
Magnetic order below 34K

Comments (symmetry):

1k incommensurate magnetic structure
k-maximal magnetic symmetry
Structure with both displacive and magnetic modulations. The primary magnetic ordering is however a k=0 arrangement. The magnetic modulation present in the structure can be considered an induced effect through trilinear coupling with the two primary order parameters, LD3 and mGM4+, corresponding the displacive modulation and the primary k=0 magnetic arrangement, respectively.
The primary magnetic ordering at about 34K, acording to the irrep mGM4+(k=0), takes place on a displacively modulated structure according the irrep LD3, already realized below 84K. The k=0 magnetic order breaks further the system symmetry, allowing as an induced effect the presence of a magnetic modulation according to the mLD2 irrep.

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

(CH₃NH₃)Ni(COOH)₃ (#1.1.98)

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

(CH3NH3)Ni(COOH)3 (#1.1.98)

(CH₃NH₃)Ni(COOH)₃ (#1.1.98)