MAGNDATA - Collection of Magnetic Structures

Magnetic structure with only magnetic atoms

Reference: J.W. Lynn, S. Skanthakumar, Q. Huang, S.K. Sinha, Z. Hossain, L.C. Gupta, R. Nagarajan and C. Godart, Physical Review B (1997) 55 6584-6598.
DOI: 10.1103/physrevb.55.6584
Atomic positions from: ICSD #56651

Parent space group (paramagnetic phase): (#139)
Propagation vector: k1 (0.552600, 0.000000, 0.000000)

Transition Temperature: 6.8 K
Experiment Temperature: 1.5 K

Wave vectors table:

label	Wave vector	k1 coefficient
1	(0.5526, 0, 0)	1
2	(1.1052, 0, 0)	2
3	(1.6578, 0, 0)	3
4	(2.2104, 0, 0)	4
5	(2.763, 0, 0)	5

N	(x,y,z)	Seitz notation
1	x1,x2,x3,x4,+1	{ 1 \| 0 }
2	-x1,-x2,x3,-x4+1/2,+1	{ 2₀₀₁ \| 0 0 0 1/2 }
3	-x1,x2,-x3,-x4,+1	{ 2₀₁₀ \| 0 }
4	x1,-x2,-x3,x4+1/2,+1	{ 2₁₀₀ \| 0 0 0 1/2 }
5	-x1,-x2,-x3,-x4,+1	{ -1 \| 0 }
6	x1,x2,-x3,x4+1/2,+1	{ m₀₀₁ \| 0 0 0 1/2 }
7	x1,-x2,x3,x4,+1	{ m₀₁₀ \| 0 }
8	-x1,x2,x3,-x4+1/2,+1	{ m₁₀₀ \| 0 0 0 1/2 }
(1/2,1/2,1/2,0) + set click here to show and hide
9	x1+1/2,x2+1/2,x3+1/2,x4,+1	{ 1 \| 1/2 1/2 1/2 0 }
10	-x1+1/2,-x2+1/2,x3+1/2,-x4+1/2,+1	{ 2₀₀₁ \| 1/2 1/2 1/2 1/2 }
11	-x1+1/2,x2+1/2,-x3+1/2,-x4,+1	{ 2₀₁₀ \| 1/2 1/2 1/2 0 }
12	x1+1/2,-x2+1/2,-x3+1/2,x4+1/2,+1	{ 2₁₀₀ \| 1/2 1/2 1/2 1/2 }
13	-x1+1/2,-x2+1/2,-x3+1/2,-x4,+1	{ -1 \| 1/2 1/2 1/2 0 }
14	x1+1/2,x2+1/2,-x3+1/2,x4+1/2,+1	{ m₀₀₁ \| 1/2 1/2 1/2 1/2 }
15	x1+1/2,-x2+1/2,x3+1/2,x4,+1	{ m₀₁₀ \| 1/2 1/2 1/2 0 }
16	-x1+1/2,x2+1/2,x3+1/2,-x4+1/2,+1	{ m₁₀₀ \| 1/2 1/2 1/2 1/2 }
(0,0,0,1/2)' + set click here to show and hide
17	x1,x2,x3,x4+1/2,-1	{ 1' \| 0 0 0 1/2 }
18	-x1,-x2,x3,-x4,-1	{ 2'₀₀₁ \| 0 }
19	-x1,x2,-x3,-x4+1/2,-1	{ 2'₀₁₀ \| 0 0 0 1/2 }
20	x1,-x2,-x3,x4,-1	{ 2'₁₀₀ \| 0 }
21	-x1,-x2,-x3,-x4+1/2,-1	{ -1' \| 0 0 0 1/2 }
22	x1,x2,-x3,x4,-1	{ m'₀₀₁ \| 0 }
23	x1,-x2,x3,x4+1/2,-1	{ m'₀₁₀ \| 0 0 0 1/2 }
24	-x1,x2,x3,-x4,-1	{ m'₁₀₀ \| 0 }
(1/2,1/2,1/2,1/2)' + set click here to show and hide
25	x1+1/2,x2+1/2,x3+1/2,x4+1/2,-1	{ 1' \| 1/2 1/2 1/2 1/2 }
26	-x1+1/2,-x2+1/2,x3+1/2,-x4,-1	{ 2'₀₀₁ \| 1/2 1/2 1/2 0 }
27	-x1+1/2,x2+1/2,-x3+1/2,-x4+1/2,-1	{ 2'₀₁₀ \| 1/2 1/2 1/2 1/2 }
28	x1+1/2,-x2+1/2,-x3+1/2,x4,-1	{ 2'₁₀₀ \| 1/2 1/2 1/2 0 }
29	-x1+1/2,-x2+1/2,-x3+1/2,-x4+1/2,-1	{ -1' \| 1/2 1/2 1/2 1/2 }
30	x1+1/2,x2+1/2,-x3+1/2,x4,-1	{ m'₀₀₁ \| 1/2 1/2 1/2 0 }
31	x1+1/2,-x2+1/2,x3+1/2,x4+1/2,-1	{ m'₀₁₀ \| 1/2 1/2 1/2 1/2 }
32	-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	2₀₀₁
3	-x,y,-z,+1	2₀₁₀
4	x,-y,-z,+1	2₁₀₀
5	-x,-y,-z,+1	-1
6	x,y,-z,+1	m₀₀₁
7	x,-y,z,+1	m₀₁₀
8	-x,y,z,+1	m₁₀₀
1' + set click here to show and hide
9	x,y,z,-1	1'
10	-x,-y,z,-1	2'₀₀₁
11	-x,y,-z,-1	2'₀₁₀
12	x,-y,-z,-1	2'₁₀₀
13	-x,-y,-z,-1	-1'
14	x,y,-z,-1	m'₀₀₁
15	x,-y,z,-1	m'₀₁₀
16	-x,y,z,-1	m'₁₀₀

Label	Atom type	x	y	z	Multiplicity
Ni1	Ni	0.5	0	0.25	4
B1	B	0	0	0.3597	4
C1	C	0.5	0.5	0	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
Er1	0	M_ycos1	0	0.0	9.15(12)	0.0	0	0	0	0.0	0.0	0.0

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
Er1	0	0	0	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0

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
Er1	0	M_ycos3	0	0.0	-2.77(30)	0.0	0	0	0	0.0	0.0	0.0

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
Er1	0	0	0	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0

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
Er1	0	M_ycos5	0	0.0	1.53(40)	0.0	0	0	0	0.0	0.0	0.0

Atom	x	y	z
1	0.00000	0.00000	0.00000
(1/2,1/2,1/2,0) + set click here to show and hide
2	0.50000	0.50000	0.50000

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	0	0.0	9.15000	0.0	0	0	0	0.0	0.0	0.0
(1/2,1/2,1/2,0) + set click here to show and hide
2	0	M_ycos1	0	0.0	9.15000	0.0	0	0	0	0.0	0.0	0.0

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	0	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0
(1/2,1/2,1/2,0) + set click here to show and hide
2	0	0	0	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0

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_ycos3	0	0.0	-2.77000	0.0	0	0	0	0.0	0.0	0.0
(1/2,1/2,1/2,0) + set click here to show and hide
2	0	M_ycos3	0	0.0	-2.77000	0.0	0	0	0	0.0	0.0	0.0

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	0	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0
(1/2,1/2,1/2,0) + set click here to show and hide
2	0	0	0	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0

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_ycos5	0	0.0	1.53000	0.0	0	0	0	0.0	0.0	0.0
(1/2,1/2,1/2,0) + set click here to show and hide
2	0	M_ycos5	0	0.0	1.53000	0.0	0	0	0	0.0	0.0	0.0

Atom	x	y	z
1	0.50000	0.00000	0.25000
2	0.50000	0.00000	0.75000
(1/2,1/2,1/2,0) + set click here to show and hide
3	0.00000	0.50000	0.75000
4	0.00000	0.50000	0.25000

Atom	x	y	z
1	0.00000	0.00000	0.35970
2	0.00000	0.00000	0.64030
(1/2,1/2,1/2,0) + set click here to show and hide
3	0.50000	0.50000	0.85970
4	0.50000	0.50000	0.14030

Atom	x	y	z
1	0.50000	0.50000	0.00000
(1/2,1/2,1/2,0) + set click here to show and hide
2	0.00000	0.00000	0.50000

Lattice parameters of the basic unit cell:
3.5019 3.5019 10.5580 90 90 90
Transformation from parent structure: (a,b,c;0,0,0)
    [View matrix form]

Magnetic Superspace Group: Immm1'(a00)00ss
    [View symmetry operations]

Magnetic Point Group: mmm1' (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 of symmetry independent atoms

Label	Atom type	x	y	z	Multiplicity
Er1	Er	0	0	0	2

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
Er1	0	M_ycos1	0	0.0	9.15(12)	0.0	0	0	0	0.0	0.0	0.0

Wave vector 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
Er1	0	0	0	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0

Wave vector 3

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
Er1	0	M_ycos3	0	0.0	-2.77(30)	0.0	0	0	0	0.0	0.0	0.0

Wave vector 4

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
Er1	0	0	0	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0

Wave vector 5

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
Er1	0	M_ycos5	0	0.0	1.53(40)	0.0	0	0	0	0.0	0.0	0.0

Atom	x	y	z
1	0.00000	0.00000	0.00000
(1/2,1/2,1/2,0) + set click here to show and hide
2	0.50000	0.50000	0.50000

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	0	0.0	9.15000	0.0	0	0	0	0.0	0.0	0.0
(1/2,1/2,1/2,0) + set click here to show and hide
2	0	M_ycos1	0	0.0	9.15000	0.0	0	0	0	0.0	0.0	0.0

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	0	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0
(1/2,1/2,1/2,0) + set click here to show and hide
2	0	0	0	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0

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_ycos3	0	0.0	-2.77000	0.0	0	0	0	0.0	0.0	0.0
(1/2,1/2,1/2,0) + set click here to show and hide
2	0	M_ycos3	0	0.0	-2.77000	0.0	0	0	0	0.0	0.0	0.0

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	0	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0
(1/2,1/2,1/2,0) + set click here to show and hide
2	0	0	0	0.0	0.0	0.0	0	0	0	0.0	0.0	0.0

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_ycos5	0	0.0	1.53000	0.0	0	0	0	0.0	0.0	0.0
(1/2,1/2,1/2,0) + set click here to show and hide
2	0	M_ycos5	0	0.0	1.53000	0.0	0	0	0	0.0	0.0	0.0

[Show all magnetic atoms in unit cell and their moment relations]

Active Irreps:

label	dim. small irrep	dim. full irrep	action	number of modes	is present?
mSM3(k1)	1	4	primary	2	.
mSM3(3k1)	1	4	secondary	2	yes
mSM3(5k1)	1	4	secondary	2	yes

Comments:

NPD
Positional structure from a room temperature model
The weak magnetic modulation of Ni atoms proposed in a previous publication (see entry #1.1.57) is not confirmed in this reference, no evidence for any magnetic ordering of Ni is found.
The spin modulation is significantly squared-up, much more than the mentioned previous model (entry #1.1.57).
Estimated modulus of the ideal square modulation:7.19

Comments (symmetry):

1k incommensurate magnetic structure
k-maximal magnetic symmetry (4 possible)
1-dim small irrep as primary irrep
Third and fifth harmonic spin modulations. They correspond to secondary irreps of the same type allowed for odd harmonics.
The sign of the amplitude of the third harmonic cosine function is not consistent with the â€œsquaring-upâ€ of the modulation, mentioned in the text. Here it is given a minus sign to be be effectively a squaring-up harmonic.

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

ErNi₂B₂C (#1.1.58)

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

ErNi2B2C (#1.1.58)

ErNi₂B₂C (#1.1.58)