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,-x2,x3+1/2,x4+1/2,+1	{ 2₀₀₁ \| 0 0 1/2 1/2 }
3	x1,-x2,x3+1/2,x4+1/2,+1	{ m₀₁₀ \| 0 0 1/2 1/2 }
4	-x1,x2,x3,x4,+1	{ m₁₀₀ \| 0 }
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5	x1,x2,x3,x4+1/2,-1	{ 1' \| 0 0 0 1/2 }
6	-x1,-x2,x3+1/2,x4,-1	{ 2'₀₀₁ \| 0 0 1/2 0 }
7	x1,-x2,x3+1/2,x4,-1	{ m'₀₁₀ \| 0 0 1/2 0 }
8	-x1,x2,x3,x4+1/2,-1	{ m'₁₀₀ \| 0 0 0 1/2 }
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9	x1+1/2,x2+1/2,x3,x4,+1	{ 1 \| 1/2 1/2 0 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+1/2,+1	{ m₀₁₀ \| 1/2 1/2 1/2 1/2 }
12	-x1+1/2,x2+1/2,x3,x4,+1	{ m₁₀₀ \| 1/2 1/2 0 0 }
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13	x1+1/2,x2+1/2,x3,x4+1/2,-1	{ 1' \| 1/2 1/2 0 1/2 }
14	-x1+1/2,-x2+1/2,x3+1/2,x4,-1	{ 2'₀₀₁ \| 1/2 1/2 1/2 0 }
15	x1+1/2,-x2+1/2,x3+1/2,x4,-1	{ m'₀₁₀ \| 1/2 1/2 1/2 0 }
16	-x1+1/2,x2+1/2,x3,x4+1/2,-1	{ m'₁₀₀ \| 1/2 1/2 0 1/2 }

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
Rh1_1	Rh	0.718285	0.093905	-0.26139	8
Rh1_2	Rh	-0.5	0.31219	-0.26139	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
Ho1	M_xc1	0	0	6.2(4)	0.0	0.0	M_xs1	0	0	0.9(8)	0.0	0.0
Ho2_1	M_xc1	M_yc1	M_zc1	3.9(3)	3.8(3)	0.0	M_xs1	M_ys1	M_zs1	1.9(2)	1.8(2)	0.0
Ho2_2	M_xc1	0	0	5.4(2)	0.0	0.0	M_xs1	0	0	2.6(3)	0.0	0.0
Ho3_1	M_xc1	M_yc1	M_x_z1	6.0(2)	4.4(3)	0.0	M_xs1	M_ys1	M_x_z1	0.0	0.0	0.0
Ho3_2	M_xc1	0	0	7.5(2)	0.0	0.0	M_xs1	0	0	0.0	0.0	0.0

Atom	x	y	z
1	0.50000	0.16667	0.97899
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2	0.50000	0.83333	0.47899
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3	0.00000	0.66667	0.97899
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4	0.00000	0.33333	0.47899

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	0	6.20000	0.0	0.0	M_xcos1+M_ysin1	0	0	0.90000	0.0	0.0
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2	M_xcos1	0	0	6.20000	0.0	0.0	M_xcos1+M_ysin1	0	0	0.90000	0.0	0.0
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3	M_xcos1	0	0	6.20000	0.0	0.0	M_xcos1+M_ysin1	0	0	0.90000	0.0	0.0
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4	M_xcos1	0	0	6.20000	0.0	0.0	M_xcos1+M_ysin1	0	0	0.90000	0.0	0.0

Atom	x	y	z
1	0.68664	0.43778	0.67560
2	0.31336	0.56222	0.17560
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3	0.68664	0.56222	0.17560
4	0.31336	0.43778	0.67560
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5	0.18664	0.93778	0.67560
6	0.81336	0.06222	0.17560
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7	0.18664	0.06222	0.17560
8	0.81336	0.93778	0.67560

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	3.90000	3.80000	0.0	M_xcos1+M_ysin1	M_ycos1+M_ysin1	M_zcos1+M_ysin1	1.90000	1.80000	0.0
2	M_xcos1	M_ycos1	-M_zcos1	3.90000	3.80000	0.0	M_xcos1+M_ysin1	M_ycos1+M_ysin1	-M_zcos1-M_ysin1	1.90000	1.80000	0.0
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3	M_xcos1	-M_ycos1	M_zcos1	3.90000	-3.80000	0.0	M_xcos1+M_ysin1	-M_ycos1-M_ysin1	M_zcos1+M_ysin1	1.90000	-1.80000	0.0
4	M_xcos1	-M_ycos1	-M_zcos1	3.90000	-3.80000	0.0	M_xcos1+M_ysin1	-M_ycos1-M_ysin1	-M_zcos1-M_ysin1	1.90000	-1.80000	0.0
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5	M_xcos1	M_ycos1	M_zcos1	3.90000	3.80000	0.0	M_xcos1+M_ysin1	M_ycos1+M_ysin1	M_zcos1+M_ysin1	1.90000	1.80000	0.0
6	M_xcos1	M_ycos1	-M_zcos1	3.90000	3.80000	0.0	M_xcos1+M_ysin1	M_ycos1+M_ysin1	-M_zcos1-M_ysin1	1.90000	1.80000	0.0
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7	M_xcos1	-M_ycos1	M_zcos1	3.90000	-3.80000	0.0	M_xcos1+M_ysin1	-M_ycos1-M_ysin1	M_zcos1+M_ysin1	1.90000	-1.80000	0.0
8	M_xcos1	-M_ycos1	-M_zcos1	3.90000	-3.80000	0.0	M_xcos1+M_ysin1	-M_ycos1-M_ysin1	-M_zcos1-M_ysin1	1.90000	-1.80000	0.0

Atom	x	y	z
1	0.50000	0.62443	0.67560
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2	0.50000	0.37557	0.17560
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3	0.00000	0.12443	0.67560
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4	0.00000	0.87557	0.17560

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	0	5.40000	0.0	0.0	M_xcos1+M_ysin1	0	0	2.60000	0.0	0.0
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2	M_xcos1	0	0	5.40000	0.0	0.0	M_xcos1+M_ysin1	0	0	2.60000	0.0	0.0
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3	M_xcos1	0	0	5.40000	0.0	0.0	M_xcos1+M_ysin1	0	0	2.60000	0.0	0.0
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4	M_xcos1	0	0	5.40000	0.0	0.0	M_xcos1+M_ysin1	0	0	2.60000	0.0	0.0

Atom	x	y	z
1	0.18870	0.27043	0.97287
2	0.81130	0.72957	0.47287
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3	0.18870	0.72957	0.47287
4	0.81130	0.27043	0.97287
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5	0.68870	0.77043	0.97287
6	0.31130	0.22957	0.47287
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7	0.68870	0.22957	0.47287
8	0.31130	0.77043	0.97287

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_xcos1+M_zcos1	6.00000	4.40000	0.0	M_xcos1+M_ysin1	M_ycos1+M_ysin1	M_xcos1+M_zcos1	0.0	0.0	0.0
2	M_xcos1	M_ycos1	-M_xcos1-M_zcos1	6.00000	4.40000	0.0	M_xcos1+M_ysin1	M_ycos1+M_ysin1	-M_xcos1-M_zcos1	0.0	0.0	0.0
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3	M_xcos1	-M_ycos1	M_xcos1+M_zcos1	6.00000	-4.40000	0.0	M_xcos1+M_ysin1	-M_ycos1-M_ysin1	M_xcos1+M_zcos1	0.0	0.0	0.0
4	M_xcos1	-M_ycos1	-M_xcos1-M_zcos1	6.00000	-4.40000	0.0	M_xcos1+M_ysin1	-M_ycos1-M_ysin1	-M_xcos1-M_zcos1	0.0	0.0	0.0
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5	M_xcos1	M_ycos1	M_xcos1+M_zcos1	6.00000	4.40000	0.0	M_xcos1+M_ysin1	M_ycos1+M_ysin1	M_xcos1+M_zcos1	0.0	0.0	0.0
6	M_xcos1	M_ycos1	-M_xcos1-M_zcos1	6.00000	4.40000	0.0	M_xcos1+M_ysin1	M_ycos1+M_ysin1	-M_xcos1-M_zcos1	0.0	0.0	0.0
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7	M_xcos1	-M_ycos1	M_xcos1+M_zcos1	6.00000	-4.40000	0.0	M_xcos1+M_ysin1	-M_ycos1-M_ysin1	M_xcos1+M_zcos1	0.0	0.0	0.0
8	M_xcos1	-M_ycos1	-M_xcos1-M_zcos1	6.00000	-4.40000	0.0	M_xcos1+M_ysin1	-M_ycos1-M_ysin1	-M_xcos1-M_zcos1	0.0	0.0	0.0

Atom	x	y	z
1	0.50000	0.95913	0.97287
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2	0.50000	0.04087	0.47287
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3	0.00000	0.45913	0.97287
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4	0.00000	0.54087	0.47287

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	0	7.50000	0.0	0.0	M_xcos1+M_ysin1	0	0	0.0	0.0	0.0
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2	M_xcos1	0	0	7.50000	0.0	0.0	M_xcos1+M_ysin1	0	0	0.0	0.0	0.0
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3	M_xcos1	0	0	7.50000	0.0	0.0	M_xcos1+M_ysin1	0	0	0.0	0.0	0.0
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4	M_xcos1	0	0	7.50000	0.0	0.0	M_xcos1+M_ysin1	0	0	0.0	0.0	0.0

Atom	x	y	z
1	0.71828	0.09391	0.73861
2	0.28172	0.90609	0.23861
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3	0.71828	0.90609	0.23861
4	0.28172	0.09391	0.73861
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5	0.21829	0.59391	0.73861
6	0.78172	0.40610	0.23861
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7	0.21829	0.40610	0.23861
8	0.78172	0.59391	0.73861

Atom	x	y	z
1	0.50000	0.31219	0.73861
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2	0.50000	0.68781	0.23861
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3	0.00000	0.81219	0.73861
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4	0.00000	0.18781	0.23861

Reference: A. F. Gubkin, A. A. Vaulin, T. Tsutaoka, A. F. Prekul, K. P. Skokov, N. V. Baranov, PHYSICAL REVIEW B (2022) 106 134419
DOI: 10.1103/PhysRevB.106.134419
Atomic positions from: same reference

Parent space group (paramagnetic phase): P6₃mc (#186)
Propagation vector: k1 (0.000000, 0.000000, -0.389169)

Transition Temperature: 32 K
Experiment Temperature: 28 K

Lattice parameters of the basic unit cell:
9.6963 16.7945 6.089 90 90 90
Transformation from parent structure: (-b,-2a-b,-c;0,0,1/2)
    [View matrix form]

Magnetic Superspace Group: Cmc21.1'(00g)0sss
    [View symmetry operations]

Magnetic Point Group: mm21' (7.2.21)
    [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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     [Show all the atoms]

Average atomic positions of symmetry independent atoms

Label	Atom type	x	y	z	Multiplicity
Ho1	Ho	0.5	0.166666	-0.02101	4
Ho2_1	Ho	-0.313355	0.437785	-0.3244	8
Ho2_2	Ho	-0.5	-0.37557	-0.3244	4
Ho3_1	Ho	0.188695	0.270435	-0.02713	8
Ho3_2	Ho	-0.5	-0.04087	-0.02713	4

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_xc1	0	0	6.2(4)	0.0	0.0	M_xs1	0	0	0.9(8)	0.0	0.0
Ho2_1	M_xc1	M_yc1	M_zc1	3.9(3)	3.8(3)	0.0	M_xs1	M_ys1	M_zs1	1.9(2)	1.8(2)	0.0
Ho2_2	M_xc1	0	0	5.4(2)	0.0	0.0	M_xs1	0	0	2.6(3)	0.0	0.0
Ho3_1	M_xc1	M_yc1	M_x_z1	6.0(2)	4.4(3)	0.0	M_xs1	M_ys1	M_x_z1	0.0	0.0	0.0
Ho3_2	M_xc1	0	0	7.5(2)	0.0	0.0	M_xs1	0	0	0.0	0.0	0.0

Atom	x	y	z
1	0.50000	0.16667	0.97899
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2	0.50000	0.83333	0.47899
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3	0.00000	0.66667	0.97899
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4	0.00000	0.33333	0.47899

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	0	6.20000	0.0	0.0	M_xcos1+M_ysin1	0	0	0.90000	0.0	0.0
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2	M_xcos1	0	0	6.20000	0.0	0.0	M_xcos1+M_ysin1	0	0	0.90000	0.0	0.0
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3	M_xcos1	0	0	6.20000	0.0	0.0	M_xcos1+M_ysin1	0	0	0.90000	0.0	0.0
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4	M_xcos1	0	0	6.20000	0.0	0.0	M_xcos1+M_ysin1	0	0	0.90000	0.0	0.0

Atom	x	y	z
1	0.68664	0.43778	0.67560
2	0.31336	0.56222	0.17560
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3	0.68664	0.56222	0.17560
4	0.31336	0.43778	0.67560
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5	0.18664	0.93778	0.67560
6	0.81336	0.06222	0.17560
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7	0.18664	0.06222	0.17560
8	0.81336	0.93778	0.67560

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	3.90000	3.80000	0.0	M_xcos1+M_ysin1	M_ycos1+M_ysin1	M_zcos1+M_ysin1	1.90000	1.80000	0.0
2	M_xcos1	M_ycos1	-M_zcos1	3.90000	3.80000	0.0	M_xcos1+M_ysin1	M_ycos1+M_ysin1	-M_zcos1-M_ysin1	1.90000	1.80000	0.0
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3	M_xcos1	-M_ycos1	M_zcos1	3.90000	-3.80000	0.0	M_xcos1+M_ysin1	-M_ycos1-M_ysin1	M_zcos1+M_ysin1	1.90000	-1.80000	0.0
4	M_xcos1	-M_ycos1	-M_zcos1	3.90000	-3.80000	0.0	M_xcos1+M_ysin1	-M_ycos1-M_ysin1	-M_zcos1-M_ysin1	1.90000	-1.80000	0.0
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5	M_xcos1	M_ycos1	M_zcos1	3.90000	3.80000	0.0	M_xcos1+M_ysin1	M_ycos1+M_ysin1	M_zcos1+M_ysin1	1.90000	1.80000	0.0
6	M_xcos1	M_ycos1	-M_zcos1	3.90000	3.80000	0.0	M_xcos1+M_ysin1	M_ycos1+M_ysin1	-M_zcos1-M_ysin1	1.90000	1.80000	0.0
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7	M_xcos1	-M_ycos1	M_zcos1	3.90000	-3.80000	0.0	M_xcos1+M_ysin1	-M_ycos1-M_ysin1	M_zcos1+M_ysin1	1.90000	-1.80000	0.0
8	M_xcos1	-M_ycos1	-M_zcos1	3.90000	-3.80000	0.0	M_xcos1+M_ysin1	-M_ycos1-M_ysin1	-M_zcos1-M_ysin1	1.90000	-1.80000	0.0

Atom	x	y	z
1	0.50000	0.62443	0.67560
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2	0.50000	0.37557	0.17560
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3	0.00000	0.12443	0.67560
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4	0.00000	0.87557	0.17560

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	0	5.40000	0.0	0.0	M_xcos1+M_ysin1	0	0	2.60000	0.0	0.0
(0,0,0,1/2)' + set click here to show and hide
2	M_xcos1	0	0	5.40000	0.0	0.0	M_xcos1+M_ysin1	0	0	2.60000	0.0	0.0
(1/2,1/2,0,0) + set click here to show and hide
3	M_xcos1	0	0	5.40000	0.0	0.0	M_xcos1+M_ysin1	0	0	2.60000	0.0	0.0
(1/2,1/2,0,1/2)' + set click here to show and hide
4	M_xcos1	0	0	5.40000	0.0	0.0	M_xcos1+M_ysin1	0	0	2.60000	0.0	0.0

Atom	x	y	z
1	0.18870	0.27043	0.97287
2	0.81130	0.72957	0.47287
(0,0,0,1/2)' + set click here to show and hide
3	0.18870	0.72957	0.47287
4	0.81130	0.27043	0.97287
(1/2,1/2,0,0) + set click here to show and hide
5	0.68870	0.77043	0.97287
6	0.31130	0.22957	0.47287
(1/2,1/2,0,1/2)' + set click here to show and hide
7	0.68870	0.22957	0.47287
8	0.31130	0.77043	0.97287

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_xcos1+M_zcos1	6.00000	4.40000	0.0	M_xcos1+M_ysin1	M_ycos1+M_ysin1	M_xcos1+M_zcos1	0.0	0.0	0.0
2	M_xcos1	M_ycos1	-M_xcos1-M_zcos1	6.00000	4.40000	0.0	M_xcos1+M_ysin1	M_ycos1+M_ysin1	-M_xcos1-M_zcos1	0.0	0.0	0.0
(0,0,0,1/2)' + set click here to show and hide
3	M_xcos1	-M_ycos1	M_xcos1+M_zcos1	6.00000	-4.40000	0.0	M_xcos1+M_ysin1	-M_ycos1-M_ysin1	M_xcos1+M_zcos1	0.0	0.0	0.0
4	M_xcos1	-M_ycos1	-M_xcos1-M_zcos1	6.00000	-4.40000	0.0	M_xcos1+M_ysin1	-M_ycos1-M_ysin1	-M_xcos1-M_zcos1	0.0	0.0	0.0
(1/2,1/2,0,0) + set click here to show and hide
5	M_xcos1	M_ycos1	M_xcos1+M_zcos1	6.00000	4.40000	0.0	M_xcos1+M_ysin1	M_ycos1+M_ysin1	M_xcos1+M_zcos1	0.0	0.0	0.0
6	M_xcos1	M_ycos1	-M_xcos1-M_zcos1	6.00000	4.40000	0.0	M_xcos1+M_ysin1	M_ycos1+M_ysin1	-M_xcos1-M_zcos1	0.0	0.0	0.0
(1/2,1/2,0,1/2)' + set click here to show and hide
7	M_xcos1	-M_ycos1	M_xcos1+M_zcos1	6.00000	-4.40000	0.0	M_xcos1+M_ysin1	-M_ycos1-M_ysin1	M_xcos1+M_zcos1	0.0	0.0	0.0
8	M_xcos1	-M_ycos1	-M_xcos1-M_zcos1	6.00000	-4.40000	0.0	M_xcos1+M_ysin1	-M_ycos1-M_ysin1	-M_xcos1-M_zcos1	0.0	0.0	0.0

Atom	x	y	z
1	0.50000	0.95913	0.97287
(0,0,0,1/2)' + set click here to show and hide
2	0.50000	0.04087	0.47287
(1/2,1/2,0,0) + set click here to show and hide
3	0.00000	0.45913	0.97287
(1/2,1/2,0,1/2)' + set click here to show and hide
4	0.00000	0.54087	0.47287

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	0	7.50000	0.0	0.0	M_xcos1+M_ysin1	0	0	0.0	0.0	0.0
(0,0,0,1/2)' + set click here to show and hide
2	M_xcos1	0	0	7.50000	0.0	0.0	M_xcos1+M_ysin1	0	0	0.0	0.0	0.0
(1/2,1/2,0,0) + set click here to show and hide
3	M_xcos1	0	0	7.50000	0.0	0.0	M_xcos1+M_ysin1	0	0	0.0	0.0	0.0
(1/2,1/2,0,1/2)' + set click here to show and hide
4	M_xcos1	0	0	7.50000	0.0	0.0	M_xcos1+M_ysin1	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	direction	action	number of modes
mDT6U6	2	4	special	primary	14
mDT4U4	1	2	general	secondary	4

Comments:

NPD
Structure described in a standard setting of the basic space group Cmc2_1 of the MSSG. Transformation from the P6_3mc basis of the parent structure described in the article: (-b,-2a-b,-c;0,0,1/2), with the incommensurate vector defined as (0,0,-0.389).
Two other incommensurate phases are observed at lower temperatures.

Comments (symmetry):

1k incommensurate structure
4-dim physically irreducible irrep along a special direction as primary
2-dim physically irreducible irrep along a special direction is symmetry allowed as secondary. The structure has been refined under the MSSG. Therefore, this secondary irrep component may be present in the model.

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

Ho₇Rh₃ (#1.1.146)

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

Ho7Rh3 (#1.1.146)

Ho₇Rh₃ (#1.1.146)