MAGNDATA - Collection of Magnetic Structures

N	(x,y,z)	Seitz notation
1	x1,x2,x3,x4,+1	{ 1 \| 0 }
2	-x1,-x2,-x3,-x4,-1	{ -1' \| 0 }

N	(x,y,z)	Seitz notation
1	x,y,z,+1	1
2	-x,-y,-z,-1	-1'

Label	Atom type	x	y	z	Occupancy	Multiplicity	Symmetry constraints on M	M_0x	M_0y	M_0z	\|M\|
Nd1_1	Nd	0.31674	0.81674	0	1	2	?,,	1.092	-1.092	0.616	1.66
Nd1_2	Nd	0.81674	0.68326	0	1	2	?,,	-1.092	-1.092	-0.616	1.66

Label	Atom type	x	y	z	Occupancy	Multiplicity
B1_1	B	0	0	0.20394	1.2202	2
B1_2	B	0.5	0.5	0.79606	1.2202	2
B2_1	B	0.08728	0.58728	0.5	1.2098	2
B2_2	B	0.58728	-0.08728	0.5	1.2098	2
B3_1	B	0.17561	0.03865	0.5	1.1756	2
B3_2	B	0.67561	0.46135	0.5	1.1756	2
B3_3	B	0.46135	0.32439	0.5	1.1756	2
B3_4	B	-0.03865	0.17561	0.5	1.1756	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
Nd1_1	M_xcos1	M_ycos1	M_zcos1	0.0	0.0	-0.24	M_xsin1	M_ysin1	M_zsin1	0.0	0.0	0.99
Nd1_2	M_xcos1	M_ycos1	M_zcos1	0.0	0.0	0.0	M_xsin1	M_ysin1	M_zsin1	0.0	0.0	1.02

Atom	x	y	z	Symmetry constraints on M	M_0x	M_0y	M_0z
1	0.31674	0.81674	0.00000	0,0,0	1.09200	-1.09200	0.61600
2	0.68326	0.18326	0.00000	0,0,0	-1.09200	1.09200	-0.61600

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	-0.24000	M_xsin1	M_ysin1	M_zsin1	0.0	0.0	0.99000
2	-M_xcos1	-M_ycos1	-M_zcos1	0.0	0.0	0.24000	M_xsin1	M_ysin1	M_zsin1	0.0	0.0	0.99000

Atom	x	y	z	Symmetry constraints on M	M_0x	M_0y	M_0z
1	0.81674	0.68326	0.00000	0,0,0	-1.09200	-1.09200	-0.61600
2	0.18326	0.31674	0.00000	0,0,0	1.09200	1.09200	0.61600

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_xsin1	M_ysin1	M_zsin1	0.0	0.0	1.02000
2	-M_xcos1	-M_ycos1	-M_zcos1	0.0	0.0	0.0	M_xsin1	M_ysin1	M_zsin1	0.0	0.0	1.02000

Atom	x	y	z
1	0.00000	0.00000	0.20394
2	0.00000	0.00000	0.79606

Atom	x	y	z
1	0.50000	0.50000	0.79606
2	0.50000	0.50000	0.20394

Atom	x	y	z
1	0.08728	0.58728	0.50000
2	0.91272	0.41272	0.50000

Atom	x	y	z
1	0.58728	0.91272	0.50000
2	0.41272	0.08728	0.50000

Atom	x	y	z
1	0.17561	0.03865	0.50000
2	0.82439	0.96135	0.50000

Atom	x	y	z
1	0.67561	0.46135	0.50000
2	0.32439	0.53865	0.50000

Atom	x	y	z
1	0.46135	0.32439	0.50000
2	0.53865	0.67561	0.50000

Atom	x	y	z
1	0.96135	0.17561	0.50000
2	0.03865	0.82439	0.50000

Reference: D.D. Khalyavin, D. Brunt, N. Qureshi, A.R. Wildes, B. Ouladdiaf, R.D. Johnson, G. Balakrishnan, O.A. Petrenko, PHYSICAL REVIEW B (2024) 109 L220411
DOI: 10.1103/PhysRevB.109.L220411
Atomic positions from: same reference

Parent space group (paramagnetic phase): P4/mbm (#127)
Propagation vector: k1 (0.142100, 0.142100, 0.400000)

Transition Temperature: 17.5 K
Experiment Temperature: 5.5 K

Lattice parameters of the basic unit cell:
7.2139 7.2139 4.0977 90 90 90
Transformation from parent structure: (a,b,c;0,0,0)
    [View matrix form]

Magnetic Superspace Group: P-1'(αβγ)0
    [View symmetry operations]

Magnetic Point Group: -1' (2.3.5)
    [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\|
Nd1_1	Nd	0.31674	0.81674	0	2	?,,	1.092	-1.092	0.616	1.66
Nd1_2	Nd	0.81674	0.68326	0	2	?,,	-1.092	-1.092	-0.616	1.66

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
Nd1_1	M_xcos1	M_ycos1	M_zcos1	0.0	0.0	-0.24	M_xsin1	M_ysin1	M_zsin1	0.0	0.0	0.99
Nd1_2	M_xcos1	M_ycos1	M_zcos1	0.0	0.0	0.0	M_xsin1	M_ysin1	M_zsin1	0.0	0.0	1.02

Atom	x	y	z	Symmetry constraints on M	M_0x	M_0y	M_0z
1	0.31674	0.81674	0.00000	0,0,0	1.09200	-1.09200	0.61600
2	0.68326	0.18326	0.00000	0,0,0	-1.09200	1.09200	-0.61600

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	-0.24000	M_xsin1	M_ysin1	M_zsin1	0.0	0.0	0.99000
2	-M_xcos1	-M_ycos1	-M_zcos1	0.0	0.0	0.24000	M_xsin1	M_ysin1	M_zsin1	0.0	0.0	0.99000

Atom	x	y	z	Symmetry constraints on M	M_0x	M_0y	M_0z
1	0.81674	0.68326	0.00000	0,0,0	-1.09200	-1.09200	-0.61600
2	0.18326	0.31674	0.00000	0,0,0	1.09200	1.09200	0.61600

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_xsin1	M_ysin1	M_zsin1	0.0	0.0	1.02000
2	-M_xcos1	-M_ycos1	-M_zcos1	0.0	0.0	0.0	M_xsin1	M_ysin1	M_zsin1	0.0	0.0	1.02000

[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
mGM3-	.	1		primary	1
mGM5-	.	2	general	primary	1
mGM1-	.	1		secondary	1	no
mGM2-	.	1		secondary	1	no
mGM4-	.	1		secondary	1	no
mSM1	.	4	special	secondary	1	no
mSM2	.	4	special	primary	3
mSM3	.	4	special	secondary	4	no
mSM4	.	4	special	secondary	4	no

Comments:

NPD
Position structure from a determination at 25K
Intermediate incommensurate magnetic phase stable in a narrow temperature range

Comments (symmetry):

Only z-component of the Nd moments is modulated.

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

NdB₄ (#1.1.162)

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

NdB4 (#1.1.162)

NdB₄ (#1.1.162)