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+1/2,-x3+1/2,-x4,+1	{ 2₀₁₀ \| 0 1/2 1/2 0 }
3	-x1,-x2,-x3,-x4,+1	{ -1 \| 0 }
4	x1,-x2+1/2,x3+1/2,x4,+1	{ m₀₁₀ \| 0 1/2 1/2 0 }
(0,0,0,1/2)' + set click here to show and hide
5	x1,x2,x3,x4+1/2,-1	{ 1' \| 0 0 0 1/2 }
6	-x1,x2+1/2,-x3+1/2,-x4+1/2,-1	{ 2'₀₁₀ \| 0 1/2 1/2 1/2 }
7	-x1,-x2,-x3,-x4+1/2,-1	{ -1' \| 0 0 0 1/2 }
8	x1,-x2+1/2,x3+1/2,x4+1/2,-1	{ m'₀₁₀ \| 0 1/2 1/2 1/2 }

N	(x,y,z)	Seitz notation
1	x,y,z,+1	1
2	-x,y,-z,+1	2₀₁₀
3	-x,-y,-z,+1	-1
4	x,-y,z,+1	m₀₁₀
1' + set click here to show and hide
5	x,y,z,-1	1'
6	-x,y,-z,-1	2'₀₁₀
7	-x,-y,-z,-1	-1'
8	x,-y,z,-1	m'₀₁₀

Label	Atom type	x	y	z	Multiplicity
P1_1	P	0.33340	0.45100	0.09000	4
P1_2	P	0.82980	0.93500	0.08300	4
P2_1	P	0.59150	0.48900	0.38300	4
P2_2	P	0.08880	0.98400	0.36400	4
O1_1	O	0.26740	0.54000	0.08700	4
O1_2	O	0.75280	0.03200	0.07700	4
O2_1	O	0.32220	0.31300	0.20500	4
O2_2	O	0.83510	0.83400	0.19500	4
O3_1	O	0.41320	0.51000	0.13500	4
O3_2	O	0.90100	0.03100	0.12900	4
O4_1	O	0.66310	0.63100	0.05600	4
O4_2	O	0.16880	0.14800	0.06300	4
O5_1	O	0.41880	0.49100	0.46700	4
O5_2	O	0.91380	0.98000	0.46700	4
O6_1	O	0.55090	0.35000	0.33000	4
O6_2	O	0.04540	0.84500	0.33500	4
O7_1	O	0.54950	0.60900	0.29000	4
O7_2	O	0.04660	0.12800	0.28100	4
O8_1	O	0.67900	0.48100	0.33800	4
O8_2	O	0.17140	0.98900	0.35500	4
O9_1	O	0.50820	0.31900	0.02400	4
O9_2	O	0.01330	0.83200	0.03700	4
O10_1	O	0.66800	0.27600	0.14900	4
O10_2	O	0.17570	0.74200	0.13700	4
D1_1	D	0.22440	0.51800	-0.00230	4
D1_2	D	0.72640	0.02600	-0.02300	4
D2_1	D	0.53980	0.39000	-0.02210	4
D2_2	D	0.05480	0.87100	-0.02300	4
D3_1	D	0.48000	0.41300	0.08100	4
D3_2	D	0.99210	0.89100	0.08500	4
D4_1	D	0.70800	0.21400	0.13300	4
D4_2	D	0.22650	0.69100	0.14100	4
D5_1	D	0.68300	0.36200	0.23120	4
D5_2	D	0.18320	0.82100	0.19970	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
Mn1	M_xc1	M_yc1	M_zc1	0.0	0.0	7.0(3)	M_xs1	M_ys1	M_zs1	4.1(2)	0.0	5.2(3)
Mn2_1	M_xc1	M_yc1	M_zc1	0.0	0.0	0.0	M_xs1	M_ys1	M_zs1	1.9(2)	1.3(3)	0.0
Mn2_2	M_xc1	M_yc1	M_zc1	1.3(3)	2.4(1)	3.5(3)	M_xs1	M_ys1	M_zs1	3.9(2)	3.2(4)	-5.1(3)
Mn3_1	M_xc1	M_yc1	M_zc1	2.9(3)	2.2(1)	-2.6(3)	M_xs1	M_ys1	M_zs1	0.0	0.0	-3.6(3)
Mn3_2	M_xc1	M_yc1	M_zc1	0.0	0.0	0.0	M_xs1	M_ys1	M_zs1	0.0	3.0(3)	5.7(3)

Atom	x	y	z
1	0.72720	0.85200	0.74500
2	0.27280	0.35200	0.75500
3	0.27280	0.14800	0.25500
4	0.72720	0.64800	0.24500

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	7.00000	M_xcos1+M_ysin1	M_ycos1+M_ysin1	M_zcos1+M_ysin1	4.10000	0.0	5.20000
2	-M_xcos1	M_ycos1	-M_zcos1	0.0	0.0	-7.00000	M_xcos1+M_ysin1	-M_ycos1-M_ysin1	M_zcos1+M_ysin1	4.10000	0.0	5.20000
3	M_xcos1	M_ycos1	M_zcos1	0.0	0.0	7.00000	-M_xcos1-M_ysin1	-M_ycos1-M_ysin1	-M_zcos1-M_ysin1	-4.10000	0.0	-5.20000
4	-M_xcos1	M_ycos1	-M_zcos1	0.0	0.0	-7.00000	-M_xcos1-M_ysin1	M_ycos1+M_ysin1	-M_zcos1-M_ysin1	-4.10000	0.0	-5.20000

Atom	x	y	z
1	0.42670	0.66200	0.28900
2	0.57330	0.16200	0.21100
3	0.57330	0.33800	0.71100
4	0.42670	0.83800	0.78900

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_xcos1+M_ysin1	M_ycos1+M_ysin1	M_zcos1+M_ysin1	1.90000	1.30000	0.0
2	-M_xcos1	M_ycos1	-M_zcos1	0.0	0.0	0.0	M_xcos1+M_ysin1	-M_ycos1-M_ysin1	M_zcos1+M_ysin1	1.90000	-1.30000	0.0
3	M_xcos1	M_ycos1	M_zcos1	0.0	0.0	0.0	-M_xcos1-M_ysin1	-M_ycos1-M_ysin1	-M_zcos1-M_ysin1	-1.90000	-1.30000	0.0
4	-M_xcos1	M_ycos1	-M_zcos1	0.0	0.0	0.0	-M_xcos1-M_ysin1	M_ycos1+M_ysin1	-M_zcos1-M_ysin1	-1.90000	1.30000	0.0

Atom	x	y	z
1	0.93690	0.13400	0.33700
2	0.06310	0.63400	0.16300
3	0.06310	0.86600	0.66300
4	0.93690	0.36600	0.83700

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	1.30000	2.40000	3.50000	M_xcos1+M_ysin1	M_ycos1+M_ysin1	M_zcos1+M_ysin1	3.90000	3.20000	-5.10000
2	-M_xcos1	M_ycos1	-M_zcos1	-1.30000	2.40000	-3.50000	M_xcos1+M_ysin1	-M_ycos1-M_ysin1	M_zcos1+M_ysin1	3.90000	-3.20000	-5.10000
3	M_xcos1	M_ycos1	M_zcos1	1.30000	2.40000	3.50000	-M_xcos1-M_ysin1	-M_ycos1-M_ysin1	-M_zcos1-M_ysin1	-3.90000	-3.20000	5.10000
4	-M_xcos1	M_ycos1	-M_zcos1	-1.30000	2.40000	-3.50000	-M_xcos1-M_ysin1	M_ycos1+M_ysin1	-M_zcos1-M_ysin1	-3.90000	3.20000	5.10000

Atom	x	y	z
1	0.42800	0.25300	0.37400
2	0.57200	0.75300	0.12600
3	0.57200	0.74700	0.62600
4	0.42800	0.24700	0.87400

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	2.90000	2.20000	-2.60000	M_xcos1+M_ysin1	M_ycos1+M_ysin1	M_zcos1+M_ysin1	0.0	0.0	-3.60000
2	-M_xcos1	M_ycos1	-M_zcos1	-2.90000	2.20000	2.60000	M_xcos1+M_ysin1	-M_ycos1-M_ysin1	M_zcos1+M_ysin1	0.0	0.0	-3.60000
3	M_xcos1	M_ycos1	M_zcos1	2.90000	2.20000	-2.60000	-M_xcos1-M_ysin1	-M_ycos1-M_ysin1	-M_zcos1-M_ysin1	0.0	0.0	3.60000
4	-M_xcos1	M_ycos1	-M_zcos1	-2.90000	2.20000	2.60000	-M_xcos1-M_ysin1	M_ycos1+M_ysin1	-M_zcos1-M_ysin1	0.0	0.0	3.60000

Atom	x	y	z
1	0.91970	0.78800	0.35300
2	0.08030	0.28800	0.14700
3	0.08030	0.21200	0.64700
4	0.91970	0.71200	0.85300

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_xcos1+M_ysin1	M_ycos1+M_ysin1	M_zcos1+M_ysin1	0.0	3.00000	5.70000
2	-M_xcos1	M_ycos1	-M_zcos1	0.0	0.0	0.0	M_xcos1+M_ysin1	-M_ycos1-M_ysin1	M_zcos1+M_ysin1	0.0	-3.00000	5.70000
3	M_xcos1	M_ycos1	M_zcos1	0.0	0.0	0.0	-M_xcos1-M_ysin1	-M_ycos1-M_ysin1	-M_zcos1-M_ysin1	0.0	-3.00000	-5.70000
4	-M_xcos1	M_ycos1	-M_zcos1	0.0	0.0	0.0	-M_xcos1-M_ysin1	M_ycos1+M_ysin1	-M_zcos1-M_ysin1	0.0	3.00000	-5.70000

Atom	x	y	z
1	0.33340	0.45100	0.09000
2	0.66660	0.95100	0.41000
3	0.66660	0.54900	0.91000
4	0.33340	0.04900	0.59000

Atom	x	y	z
1	0.82980	0.93500	0.08300
2	0.17020	0.43500	0.41700
3	0.17020	0.06500	0.91700
4	0.82980	0.56500	0.58300

Atom	x	y	z
1	0.59150	0.48900	0.38300
2	0.40850	0.98900	0.11700
3	0.40850	0.51100	0.61700
4	0.59150	0.01100	0.88300

Atom	x	y	z
1	0.08880	0.98400	0.36400
2	0.91120	0.48400	0.13600
3	0.91120	0.01600	0.63600
4	0.08880	0.51600	0.86400

Atom	x	y	z
1	0.26740	0.54000	0.08700
2	0.73260	0.04000	0.41300
3	0.73260	0.46000	0.91300
4	0.26740	0.96000	0.58700

Atom	x	y	z
1	0.75280	0.03200	0.07700
2	0.24720	0.53200	0.42300
3	0.24720	0.96800	0.92300
4	0.75280	0.46800	0.57700

Atom	x	y	z
1	0.32220	0.31300	0.20500
2	0.67780	0.81300	0.29500
3	0.67780	0.68700	0.79500
4	0.32220	0.18700	0.70500

Atom	x	y	z
1	0.83510	0.83400	0.19500
2	0.16490	0.33400	0.30500
3	0.16490	0.16600	0.80500
4	0.83510	0.66600	0.69500

Atom	x	y	z
1	0.41320	0.51000	0.13500
2	0.58680	0.01000	0.36500
3	0.58680	0.49000	0.86500
4	0.41320	0.99000	0.63500

Atom	x	y	z
1	0.90100	0.03100	0.12900
2	0.09900	0.53100	0.37100
3	0.09900	0.96900	0.87100
4	0.90100	0.46900	0.62900

Atom	x	y	z
1	0.66310	0.63100	0.05600
2	0.33690	0.13100	0.44400
3	0.33690	0.36900	0.94400
4	0.66310	0.86900	0.55600

Atom	x	y	z
1	0.16880	0.14800	0.06300
2	0.83120	0.64800	0.43700
3	0.83120	0.85200	0.93700
4	0.16880	0.35200	0.56300

Atom	x	y	z
1	0.41880	0.49100	0.46700
2	0.58120	0.99100	0.03300
3	0.58120	0.50900	0.53300
4	0.41880	0.00900	0.96700

Atom	x	y	z
1	0.91380	0.98000	0.46700
2	0.08620	0.48000	0.03300
3	0.08620	0.02000	0.53300
4	0.91380	0.52000	0.96700

Atom	x	y	z
1	0.55090	0.35000	0.33000
2	0.44910	0.85000	0.17000
3	0.44910	0.65000	0.67000
4	0.55090	0.15000	0.83000

Atom	x	y	z
1	0.04540	0.84500	0.33500
2	0.95460	0.34500	0.16500
3	0.95460	0.15500	0.66500
4	0.04540	0.65500	0.83500

Atom	x	y	z
1	0.54950	0.60900	0.29000
2	0.45050	0.10900	0.21000
3	0.45050	0.39100	0.71000
4	0.54950	0.89100	0.79000

Atom	x	y	z
1	0.04660	0.12800	0.28100
2	0.95340	0.62800	0.21900
3	0.95340	0.87200	0.71900
4	0.04660	0.37200	0.78100

Atom	x	y	z
1	0.67900	0.48100	0.33800
2	0.32100	0.98100	0.16200
3	0.32100	0.51900	0.66200
4	0.67900	0.01900	0.83800

Atom	x	y	z
1	0.17140	0.98900	0.35500
2	0.82860	0.48900	0.14500
3	0.82860	0.01100	0.64500
4	0.17140	0.51100	0.85500

Atom	x	y	z
1	0.50820	0.31900	0.02400
2	0.49180	0.81900	0.47600
3	0.49180	0.68100	0.97600
4	0.50820	0.18100	0.52400

Atom	x	y	z
1	0.01330	0.83200	0.03700
2	0.98670	0.33200	0.46300
3	0.98670	0.16800	0.96300
4	0.01330	0.66800	0.53700

Atom	x	y	z
1	0.66800	0.27600	0.14900
2	0.33200	0.77600	0.35100
3	0.33200	0.72400	0.85100
4	0.66800	0.22400	0.64900

Atom	x	y	z
1	0.17570	0.74200	0.13700
2	0.82430	0.24200	0.36300
3	0.82430	0.25800	0.86300
4	0.17570	0.75800	0.63700

Atom	x	y	z
1	0.22440	0.51800	0.99770
2	0.77560	0.01800	0.50230
3	0.77560	0.48200	0.00230
4	0.22440	0.98200	0.49770

Atom	x	y	z
1	0.72640	0.02600	0.97700
2	0.27360	0.52600	0.52300
3	0.27360	0.97400	0.02300
4	0.72640	0.47400	0.47700

Atom	x	y	z
1	0.53980	0.39000	0.97790
2	0.46020	0.89000	0.52210
3	0.46020	0.61000	0.02210
4	0.53980	0.11000	0.47790

Reference: S. Park, A. Hartl, D. Sheptyakov, M. Hoelzel, A. Arauzo, Symmetry (2021) 13 1688
DOI: 10.3390/sym13091688
Atomic positions from: same reference

Parent space group (paramagnetic phase): C2/c (#15)
Propagation vector: k1 (0.522(2), 0.00000, 0.055(1))

Transition Temperature: 1.86 K
Experiment Temperature: 1.5 K

Lattice parameters of the basic unit cell:
17.5715(5) 9.1185(3) 9.4931(3) 90.00000 96.391(1) 90.00000
Transformation from parent structure: (a,b,c;0,0,0)
    [View matrix form]

Magnetic Superspace Group: P2_1/c1'(a,0,g)00s
    [View symmetry operations]

Magnetic Point Group: 2/m1' (5.2.13)
    [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
Mn1	Mn	0.72720	0.85200	0.74500	4
Mn2_1	Mn	0.42670	0.66200	0.28900	4
Mn2_2	Mn	0.93690	0.134	0.33700	4
Mn3_1	Mn	0.42800	0.25300	0.37400	4
Mn3_2	Mn	0.91970	0.78800	0.35300	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
Mn1	M_xc1	M_yc1	M_zc1	0.0	0.0	7.0(3)	M_xs1	M_ys1	M_zs1	4.1(2)	0.0	5.2(3)
Mn2_1	M_xc1	M_yc1	M_zc1	0.0	0.0	0.0	M_xs1	M_ys1	M_zs1	1.9(2)	1.3(3)	0.0
Mn2_2	M_xc1	M_yc1	M_zc1	1.3(3)	2.4(1)	3.5(3)	M_xs1	M_ys1	M_zs1	3.9(2)	3.2(4)	-5.1(3)
Mn3_1	M_xc1	M_yc1	M_zc1	2.9(3)	2.2(1)	-2.6(3)	M_xs1	M_ys1	M_zs1	0.0	0.0	-3.6(3)
Mn3_2	M_xc1	M_yc1	M_zc1	0.0	0.0	0.0	M_xs1	M_ys1	M_zs1	0.0	3.0(3)	5.7(3)

[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
mB1(k1)	1	2	general	primary	15
Y2-(k2)	1	1		primary	58
mB1(k1+k2)	1	2	special	secondary	15

Comments:

NPD
Fully deuterated material
Between 6.17K and 1.86K the system is ferrimagnetic with MSG C2'/c' (see other entries in this database), with C2/c being the parent space group. The C centering of the parent phase is argued in the paper to be broken in the MSSG of the magnetic structure by the presence of the incommensurate spin modulation reducing the average space group of the modulated structure to P2_1/c, but this is not correct: the C centering is always mantained in the MSSGS by a spin modulation according to the reported propagation vector. The structural modulation breaking the C centering of the parent phase, which is present in the proposed magnetic structure, cannot therefore be justified as an induced effect of the magnetic ordering, as pretended in the paper. This structural distortion, if present, must be due to some additional independent mechanism.
The figure of the structure in the paper is not consistent with the reported propagation vector.
Range of moment magnitudes in the Mn moment modulations:
Mn1: 3.38-4.46; Mn2_1: 1.19-2.24; Mn2_2: 4.31-5.51; Mn3_1: 3.25-2.96; Mn3_2: 0.00-3.96

Comments (symmetry):

1k incommensurate magnetic structure
The model includes an independent structural distortion according to the irrep Y2- with wave vector (1,0,0), reducing the average space group to P2_1/c, from the ferrimagnetic structure that is reported at 3.4K, with MSG C2'/c'.
The MSSG allows a secondary irrep according to a wave vector k1+k2, where k1 is the wave vector of the primary modulation and k2 that of the structural modulation. Both wave vectors, k1 and k1+k2, become equivalent under the MSSG description, and the relative weight of the second one is not specified in this description.

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Atom	x	y	z
1	0.70800	0.21400	0.13300
2	0.29200	0.71400	0.36700
3	0.29200	0.78600	0.86700
4	0.70800	0.28600	0.63300

Atom	x	y	z
1	0.22650	0.69100	0.14100
2	0.77350	0.19100	0.35900
3	0.77350	0.30900	0.85900
4	0.22650	0.80900	0.64100

Atom	x	y	z
1	0.68300	0.36200	0.23120
2	0.31700	0.86200	0.26880
3	0.31700	0.63800	0.76880
4	0.68300	0.13800	0.73120

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

Mn₅(PO₄)₂(PO₃(OH))₂(HOH)₄ (#1.1.134)

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

Mn5(PO4)2(PO3(OH))2(HOH)4 (#1.1.134)

Mn₅(PO₄)₂(PO₃(OH))₂(HOH)₄ (#1.1.134)