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,-x1-x2+x4,+1	{ 2₀₀₁ \| 0 0 1/2 0 }
3	-x1+1/2,x2+1/2,x3+1/2,-x1+x4+3/4,+1	{ m₁₀₀ \| 1/2 1/2 1/2 3/4 }
4	x1+1/2,-x2+1/2,x3,-x2+x4+3/4,+1	{ m₀₁₀ \| 1/2 1/2 0 3/4 }
(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,x3+1/2,-x1-x2+x4+1/2,-1	{ 2'₀₀₁ \| 0 0 1/2 1/2 }
7	-x1+1/2,x2+1/2,x3+1/2,-x1+x4+1/4,-1	{ m'₁₀₀ \| 1/2 1/2 1/2 1/4 }
8	x1+1/2,-x2+1/2,x3,-x2+x4+1/4,-1	{ m'₀₁₀ \| 1/2 1/2 0 1/4 }

N	(x,y,z)	Seitz notation
1	x,y,z,+1	1
2	-x,-y,z,+1	2₀₀₁
3	-x,y,z,+1	m₁₀₀
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	2'₀₀₁
7	-x,y,z,-1	m'₁₀₀
8	x,-y,z,-1	m'₀₁₀

Label	Atom type	x	y	z	Occupancy	Multiplicity
Co1	Co	0.00000	0.50810	0.05754	1.00000	4
Co2	Co	0.17166	0.50000	0.31229	1.00000	4
Co3	Co	0.08655	0.74480	0.81012	1.00000	4
Co4	Co	-0.08238	0.76940	0.31946	1.00000	4

Label	Atom type	x	y	z	Occupancy	Multiplicity
Ca1	Ca	0.67175	0.50531	0.12788	0.93000	4
Sr1	Sr	0.67175	0.50531	0.12788	0.07000	4
Ba1	Ba	0.66545	0.50389	0.50000	1.00000	4
O1	O	0.00023	0.50000	0.74766	1.00000	4
O2	O	0.49251	0.50000	0.77010	1.00000	4
O3	O	0.26092	0.28721	0.21846	1.00000	4
O4	O	0.74336	0.23044	0.79159	1.00000	4
O5	O	0.15218	0.50000	0.49912	1.00000	4
O6	O	0.10899	0.70580	-0.00176	1.00000	4
O7	O	-0.05209	0.76358	0.50407	1.00000	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
Co1	M_xc1	M_yc1	M_zc1	-2.39	0.25	0.0	M_xs1	M_ys1	M_zs1	0.0	-1.3	0.0
Co2	M_xc1	M_yc1	M_zc1	1.53	-1.15	0.0	M_xs1	M_ys1	M_zs1	0.0	0.0	0.0
Co3	M_xc1	M_yc1	M_zc1	1.53	-1.15	0.0	M_xs1	M_ys1	M_zs1	0.0	0.0	0.0
Co4	M_xc1	M_yc1	M_zc1	1.53	-1.15	0.0	M_xs1	M_ys1	M_zs1	0.0	0.0	0.0

Atom	x	y	z
1	0.00000	0.50810	0.05754
2	0.00000	0.49190	0.55754
3	0.50000	0.00810	0.55754
4	0.50000	0.99190	0.05754

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	-2.39000	0.25000	0.0	M_xcos1+M_ysin1	M_ycos1+M_ysin1	M_zcos1+M_ysin1	0.0	-1.30000	0.0
2	1.04958M_xcos1+0.05087M_ysin1	1.04958M_ycos1+0.05087M_ysin1	-1.04958M_zcos1-0.05087M_ysin1	-2.38691	0.18354	0.0	0.94783M_xcos1+0.99871M_ysin1	0.94783M_ycos1+0.99871M_ysin1	-0.94783M_zcos1-0.99871M_ysin1	0.12158	-1.31103	0.0
3	M_xcos1+M_ysin1	-M_ycos1-M_ysin1	-M_zcos1-M_ysin1	0.0	1.30000	0.0	-M_xcos1	M_ycos1	M_zcos1	2.39000	0.25000	0.0
4	0.94783M_xcos1+0.99871M_ysin1	-0.94783M_ycos1-0.99871M_ysin1	0.94783M_zcos1+0.99871M_ysin1	0.12158	1.31103	0.0	-1.04958M_xcos1-0.05087M_ysin1	1.04958M_ycos1+0.05087M_ysin1	-1.04958M_zcos1-0.05087M_ysin1	2.38691	0.18354	0.0

Atom	x	y	z
1	0.17166	0.50000	0.31229
2	0.82834	0.50000	0.81229
3	0.32834	0.00000	0.81229
4	0.67166	0.00000	0.31229

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	1.53000	-1.15000	0.0	M_xcos1+M_ysin1	M_ycos1+M_ysin1	M_zcos1+M_ysin1	0.0	0.0	0.0
2	1.35387M_xcos1+0.88128M_ysin1	1.35387M_ycos1+0.88128M_ysin1	-1.35387M_zcos1-0.88128M_ysin1	0.72306	-0.54348	0.0	-0.40870M_xcos1+0.47259M_ysin1	-0.40870M_ycos1+0.47259M_ysin1	0.40870M_zcos1-0.47259M_ysin1	-1.34836	1.01348	0.0
3	-0.40870M_xcos1+0.47259M_ysin1	0.40870M_ycos1-0.47259M_ysin1	0.40870M_zcos1-0.47259M_ysin1	-1.34836	-1.01348	0.0	-1.35387M_xcos1-0.88128M_ysin1	1.35387M_ycos1+0.88128M_ysin1	1.35387M_zcos1+0.88128M_ysin1	-0.72306	-0.54348	0.0
4	M_xcos1+M_ysin1	-M_ycos1-M_ysin1	M_zcos1+M_ysin1	0.0	0.0	0.0	-M_xcos1	M_ycos1	-M_zcos1	-1.53000	-1.15000	0.0

Atom	x	y	z
1	0.08655	0.74480	0.81012
2	0.91345	0.25520	0.31012
3	0.41345	0.24480	0.31012
4	0.58655	0.75520	0.81012

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	1.53000	-1.15000	0.0	M_xcos1+M_ysin1	M_ycos1+M_ysin1	M_zcos1+M_ysin1	0.0	0.0	0.0
2	0.38302M_xcos1+0.87219M_ysin1	0.38302M_ycos1+0.87219M_ysin1	-0.38302M_zcos1-0.87219M_ysin1	-0.74843	0.56254	0.0	-1.36136M_xcos1-0.48917M_ysin1	-1.36136M_ycos1-0.48917M_ysin1	1.36136M_zcos1+0.48917M_ysin1	-1.33445	1.00302	0.0
3	0.33834M_xcos1+0.85574M_ysin1	-0.33834M_ycos1-0.85574M_ysin1	-0.33834M_zcos1-0.85574M_ysin1	-0.79162	-0.59501	0.0	-1.37314M_xcos1-0.51740M_ysin1	1.37314M_ycos1+0.51740M_ysin1	1.37314M_zcos1+0.51740M_ysin1	-1.30929	-0.98411	0.0
4	-0.96680M_xcos1+0.03267M_ysin1	0.96680M_ycos1-0.03267M_ysin1	-0.96680M_zcos1+0.03267M_ysin1	-1.52918	-1.14939	0.0	-1.03213M_xcos1-0.99947M_ysin1	1.03213M_ycos1+0.99947M_ysin1	-1.03213M_zcos1-0.99947M_ysin1	-0.04998	-0.03757	0.0

Atom	x	y	z
1	0.91762	0.76940	0.31946
2	0.08238	0.23060	0.81946
3	0.58238	0.26940	0.81946
4	0.41762	0.73060	0.31946

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	1.53000	-1.15000	0.0	M_xcos1+M_ysin1	M_ycos1+M_ysin1	M_zcos1+M_ysin1	0.0	0.0	0.0
2	1.30819M_xcos1+0.92272M_ysin1	1.30819M_ycos1+0.92272M_ysin1	-1.30819M_zcos1-0.92272M_ysin1	0.58977	-0.44329	0.0	-0.53725M_xcos1+0.38547M_ysin1	-0.53725M_ycos1+0.38547M_ysin1	0.53725M_zcos1-0.38547M_ysin1	-1.41176	1.06113	0.0
3	1.36381M_xcos1+0.86900M_ysin1	-1.36381M_ycos1-0.86900M_ysin1	-1.36381M_zcos1-0.86900M_ysin1	0.75705	0.56902	0.0	-0.37420M_xcos1+0.49480M_ysin1	0.37420M_ycos1-0.49480M_ysin1	0.37420M_zcos1-0.49480M_ysin1	-1.32958	-0.99936	0.0
4	-1.11417M_xcos1-0.12159M_ysin1	1.11417M_ycos1+0.12159M_ysin1	-1.11417M_zcos1-0.12159M_ysin1	-1.51865	-1.14147	0.0	-0.87099M_xcos1-0.99258M_ysin1	0.87099M_ycos1+0.99258M_ysin1	-0.87099M_zcos1-0.99258M_ysin1	0.18604	0.13983	0.0

Atom	x	y	z
1	0.67175	0.50531	0.12788
2	0.32825	0.49469	0.62788
3	0.82825	0.00531	0.62788
4	0.17175	0.99469	0.12788

Atom	x	y	z
1	0.67175	0.50531	0.12788
2	0.32825	0.49469	0.62788
3	0.82825	0.00531	0.62788
4	0.17175	0.99469	0.12788

Atom	x	y	z
1	0.66545	0.50389	0.50000
2	0.33455	0.49611	0.00000
3	0.83455	0.00389	0.00000
4	0.16545	0.99611	0.50000

Atom	x	y	z
1	0.00023	0.50000	0.74766
2	0.99977	0.50000	0.24766
3	0.49977	0.00000	0.24766
4	0.50023	0.00000	0.74766

Atom	x	y	z
1	0.49251	0.50000	0.77010
2	0.50749	0.50000	0.27010
3	0.00749	0.00000	0.27010
4	0.99251	0.00000	0.77010

Atom	x	y	z
1	0.26092	0.28721	0.21846
2	0.73908	0.71279	0.71846
3	0.23908	0.78721	0.71846
4	0.76092	0.21279	0.21846

Atom	x	y	z
1	0.74336	0.23044	0.79159
2	0.25664	0.76956	0.29159
3	0.75664	0.73044	0.29159
4	0.24336	0.26956	0.79159

Atom	x	y	z
1	0.15218	0.50000	0.49912
2	0.84782	0.50000	0.99912
3	0.34782	0.00000	0.99912
4	0.65218	0.00000	0.49912

Atom	x	y	z
1	0.10899	0.70580	0.99824
2	0.89101	0.29420	0.49824
3	0.39101	0.20580	0.49824
4	0.60899	0.79420	0.99824

Atom	x	y	z
1	0.94791	0.76358	0.50407
2	0.05209	0.23642	0.00407
3	0.55209	0.26358	0.00407
4	0.44791	0.73642	0.50407

Reference: J. Lohr, A.L. Larralde, J. Curiale, R. Sanchez, J. Campo, G.J. Cuello, D. Sheptyakov, L. Keller, M. Kenzelmann and G. Aurelio, Physical Review B (2020) 102 134406.
DOI: 10.1103/physrevb.102.134406
Atomic positions from: same reference

Parent space group (paramagnetic phase): Pna2₁ (#33)
Propagation vector: k1 (0.50000, 0.50000, 0.0197(2))

Transition Temperature: 82 K
Experiment Temperature: 70 K

Lattice parameters of the basic unit cell:
11.03519(3) 6.26586(4) 10.17849(3) 90.00000 90.00000 90.00000
Transformation from parent structure: (a,b,c;0,1/2,0)
    [View matrix form]

Magnetic Superspace Group: Pna2_11'(1/2,1/2,g)qq0s
    [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

     [Show only magnetic atoms]
     [Show all the atoms]

Average atomic positions of symmetry independent atoms

Label	Atom type	x	y	z	Multiplicity
Co1	Co	0.00000	0.50810	0.05754	4
Co2	Co	0.17166	0.50000	0.31229	4
Co3	Co	0.08655	0.74480	0.81012	4
Co4	Co	-0.08238	0.76940	0.31946	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
Co1	M_xc1	M_yc1	M_zc1	-2.39	0.25	0.0	M_xs1	M_ys1	M_zs1	0.0	-1.3	0.0
Co2	M_xc1	M_yc1	M_zc1	1.53	-1.15	0.0	M_xs1	M_ys1	M_zs1	0.0	0.0	0.0
Co3	M_xc1	M_yc1	M_zc1	1.53	-1.15	0.0	M_xs1	M_ys1	M_zs1	0.0	0.0	0.0
Co4	M_xc1	M_yc1	M_zc1	1.53	-1.15	0.0	M_xs1	M_ys1	M_zs1	0.0	0.0	0.0

Atom	x	y	z
1	0.00000	0.50810	0.05754
2	0.00000	0.49190	0.55754
3	0.50000	0.00810	0.55754
4	0.50000	0.99190	0.05754

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	-2.39000	0.25000	0.0	M_xcos1+M_ysin1	M_ycos1+M_ysin1	M_zcos1+M_ysin1	0.0	-1.30000	0.0
2	1.04958M_xcos1+0.05087M_ysin1	1.04958M_ycos1+0.05087M_ysin1	-1.04958M_zcos1-0.05087M_ysin1	-2.38691	0.18354	0.0	0.94783M_xcos1+0.99871M_ysin1	0.94783M_ycos1+0.99871M_ysin1	-0.94783M_zcos1-0.99871M_ysin1	0.12158	-1.31103	0.0
3	M_xcos1+M_ysin1	-M_ycos1-M_ysin1	-M_zcos1-M_ysin1	0.0	1.30000	0.0	-M_xcos1	M_ycos1	M_zcos1	2.39000	0.25000	0.0
4	0.94783M_xcos1+0.99871M_ysin1	-0.94783M_ycos1-0.99871M_ysin1	0.94783M_zcos1+0.99871M_ysin1	0.12158	1.31103	0.0	-1.04958M_xcos1-0.05087M_ysin1	1.04958M_ycos1+0.05087M_ysin1	-1.04958M_zcos1-0.05087M_ysin1	2.38691	0.18354	0.0

Atom	x	y	z
1	0.17166	0.50000	0.31229
2	0.82834	0.50000	0.81229
3	0.32834	0.00000	0.81229
4	0.67166	0.00000	0.31229

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	1.53000	-1.15000	0.0	M_xcos1+M_ysin1	M_ycos1+M_ysin1	M_zcos1+M_ysin1	0.0	0.0	0.0
2	1.35387M_xcos1+0.88128M_ysin1	1.35387M_ycos1+0.88128M_ysin1	-1.35387M_zcos1-0.88128M_ysin1	0.72306	-0.54348	0.0	-0.40870M_xcos1+0.47259M_ysin1	-0.40870M_ycos1+0.47259M_ysin1	0.40870M_zcos1-0.47259M_ysin1	-1.34836	1.01348	0.0
3	-0.40870M_xcos1+0.47259M_ysin1	0.40870M_ycos1-0.47259M_ysin1	0.40870M_zcos1-0.47259M_ysin1	-1.34836	-1.01348	0.0	-1.35387M_xcos1-0.88128M_ysin1	1.35387M_ycos1+0.88128M_ysin1	1.35387M_zcos1+0.88128M_ysin1	-0.72306	-0.54348	0.0
4	M_xcos1+M_ysin1	-M_ycos1-M_ysin1	M_zcos1+M_ysin1	0.0	0.0	0.0	-M_xcos1	M_ycos1	-M_zcos1	-1.53000	-1.15000	0.0

Atom	x	y	z
1	0.08655	0.74480	0.81012
2	0.91345	0.25520	0.31012
3	0.41345	0.24480	0.31012
4	0.58655	0.75520	0.81012

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	1.53000	-1.15000	0.0	M_xcos1+M_ysin1	M_ycos1+M_ysin1	M_zcos1+M_ysin1	0.0	0.0	0.0
2	0.38302M_xcos1+0.87219M_ysin1	0.38302M_ycos1+0.87219M_ysin1	-0.38302M_zcos1-0.87219M_ysin1	-0.74843	0.56254	0.0	-1.36136M_xcos1-0.48917M_ysin1	-1.36136M_ycos1-0.48917M_ysin1	1.36136M_zcos1+0.48917M_ysin1	-1.33445	1.00302	0.0
3	0.33834M_xcos1+0.85574M_ysin1	-0.33834M_ycos1-0.85574M_ysin1	-0.33834M_zcos1-0.85574M_ysin1	-0.79162	-0.59501	0.0	-1.37314M_xcos1-0.51740M_ysin1	1.37314M_ycos1+0.51740M_ysin1	1.37314M_zcos1+0.51740M_ysin1	-1.30929	-0.98411	0.0
4	-0.96680M_xcos1+0.03267M_ysin1	0.96680M_ycos1-0.03267M_ysin1	-0.96680M_zcos1+0.03267M_ysin1	-1.52918	-1.14939	0.0	-1.03213M_xcos1-0.99947M_ysin1	1.03213M_ycos1+0.99947M_ysin1	-1.03213M_zcos1-0.99947M_ysin1	-0.04998	-0.03757	0.0

Atom	x	y	z
1	0.91762	0.76940	0.31946
2	0.08238	0.23060	0.81946
3	0.58238	0.26940	0.81946
4	0.41762	0.73060	0.31946

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	1.53000	-1.15000	0.0	M_xcos1+M_ysin1	M_ycos1+M_ysin1	M_zcos1+M_ysin1	0.0	0.0	0.0
2	1.30819M_xcos1+0.92272M_ysin1	1.30819M_ycos1+0.92272M_ysin1	-1.30819M_zcos1-0.92272M_ysin1	0.58977	-0.44329	0.0	-0.53725M_xcos1+0.38547M_ysin1	-0.53725M_ycos1+0.38547M_ysin1	0.53725M_zcos1-0.38547M_ysin1	-1.41176	1.06113	0.0
3	1.36381M_xcos1+0.86900M_ysin1	-1.36381M_ycos1-0.86900M_ysin1	-1.36381M_zcos1-0.86900M_ysin1	0.75705	0.56902	0.0	-0.37420M_xcos1+0.49480M_ysin1	0.37420M_ycos1-0.49480M_ysin1	0.37420M_zcos1-0.49480M_ysin1	-1.32958	-0.99936	0.0
4	-1.11417M_xcos1-0.12159M_ysin1	1.11417M_ycos1+0.12159M_ysin1	-1.11417M_zcos1-0.12159M_ysin1	-1.51865	-1.14147	0.0	-0.87099M_xcos1-0.99258M_ysin1	0.87099M_ycos1+0.99258M_ysin1	-0.87099M_zcos1-0.99258M_ysin1	0.18604	0.13983	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
mQ3Q3A	1	2	general	primary	24

Comments:

NPD
The description of this modulated structure includes an origin shift (0 1/2 0) of the reference Pna2_1 basic structure tabulated in the article. This origin shift transforms the relevant magnetic superspace group into a form that is considered by the authors its standard setting.

Comments (symmetry):

1k incommensurate structure
k-maximal magnetic symmetry
2-dim irrep as primary
Spontaneous macroscopic magnetization is not symmetry-allowed.
The label of the irrep associated with the magnetic structure depends on the origin chosen for the description of the parent Pna2_1 structure. The irrep label given here corresponds to its description in Table II of the article, which has an origin shift (0 1/2 0) with respect to the reference basic structure used here.

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

Ca_0.93Sr_0.07BaCo₄O₇ (#1.1.93)

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

Ca0.93Sr0.07BaCo4O7 (#1.1.93)

Ca_0.93Sr_0.07BaCo₄O₇ (#1.1.93)