Information of spin space group $P{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\text{-}1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\text{-}1}\text{a}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$ ( nSSG:25.51.1.1 )

General Positions

The continuously infinite group ^∞1 is omitted.

Coordinates	Seitz symbol
a, b, c | x, y, z	{ 1 ‖ 1 | 0 }
-a+1/2, -b, c | x, y, z	{ 1 ‖ 2001 | 1/2 0 0 }
-a+1/2, b, c | x, y, z	{ 1 ‖ m100 | 1/2 0 0 }
a, -b, c | x, y, z	{ 1 ‖ m010 | 0 }
a+1/2, -b, -c | -x, -y, -z	{ -1 ‖ 2100 | 1/2 0 0 }
-a, b, -c | -x, -y, -z	{ -1 ‖ 2010 | 0 }
-a, -b, -c | -x, -y, -z	{ -1 ‖ -1 | 0 }
a+1/2, b, -c | -x, -y, -z	{ -1 ‖ m001 | 1/2 0 0 }
a, b, c | -x, y, z	{ m ‖ 1 | 0 }
-a+1/2, -b, c | -x, y, z	{ m ‖ 2001 | 1/2 0 0 }
-a+1/2, b, c | -x, y, z	{ m ‖ m100 | 1/2 0 0 }
a, -b, c | -x, y, z	{ m ‖ m010 | 0 }
a+1/2, -b, -c | x, -y, -z	{ 2 ‖ 2100 | 1/2 0 0 }
-a, b, -c | x, -y, -z	{ 2 ‖ 2010 | 0 }
-a, -b, -c | x, -y, -z	{ 2 ‖ -1 | 0 }
a+1/2, b, -c | x, -y, -z	{ 2 ‖ m001 | 1/2 0 0 }

Wyckoff Positions

WP	Site symmetry	Representative
2a	$.{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{2}/{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}.{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(0,0,0 | 0,0,0)
2b	$.{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{2}/{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}.{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(0,1/2,0 | 0,0,0)
2c	$.{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{2}/{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}.{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(0,0,1/2 | 0,0,0)
2d	$.{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{2}/{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}.{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(0,1/2,1/2 | 0,0,0)
2e	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{2}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(1/4,0,c | 0,0,z)
2f	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{2}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(1/4,1/2,c | 0,0,z)
4g	$.{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{2}.{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(0,b,0 | 0,0,0)
4h	$.{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{2}.{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(0,b,1/2 | 0,0,0)
4i	$.{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}.{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(a,0,c | 0,0,z)
4j	$.{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}.{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(a,1/2,c | 0,0,z)
4k	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}..{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(1/4,b,c | 0,0,z)
8l	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{1}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(a,b,c | 0,0,z)

Spin Brillouin Zone & k-little co-groups

Wavevector-k	Little co-group
Γ:(0,0,0)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$
R:(1/2,1/2,1/2)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$
S:(1/2,1/2,0)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$
T:(0,1/2,1/2)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$
U:(1/2,0,1/2)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$
X:(1/2,0,0)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$
Y:(0,1/2,0)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$
Z:(0,0,1/2)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$
A:(u,0,1/2)	${\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
B:(0,v,1/2)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
C:(u,1/2,0)	${\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
D:(1/2,v,0)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
Δ:(0,v,0)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
E:(u,1/2,1/2)	${\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
G:(1/2,0,w)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
H:(0,1/2,w)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
Λ:(0,0,w)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
P:(1/2,v,1/2)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
Q:(1/2,1/2,w)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
Σ:(u,0,0)	${\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
K:(0,v,w)	${\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{2/}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
L:(1/2,v,w)	${\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{2/}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
M:(u,0,w)	${\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{2/}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
N:(u,1/2,w)	${\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{2/}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
V:(u,v,0)	${\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{2/}{\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
W:(u,v,1/2)	${\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{2/}{\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
GP:(u,v,w)	${\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{-1}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$

Spin Brillouin Zone

Band Representations (Magnon)

2e

k-vector	k-vector-G↑	A1↑G(2)
Γ:(0,0,0)	Γ:(0,0,0)	${\Gamma }_1^S(2)$
R:(1/2,1/2,1/2)	R:(1/2,1/2,1/2)	$R_1^S(2)$
S:(1/2,1/2,0)	S:(1/2,1/2,0)	$S_1^S(2)$
T:(0,1/2,1/2)	T:(0,1/2,1/2)	$T_1^S(2)$
U:(1/2,0,1/2)	U:(1/2,0,1/2)	$U_1^S(2)$
X:(1/2,0,0)	X:(1/2,0,0)	$X_1^S(2)$
Y:(0,1/2,0)	Y:(0,1/2,0)	$Y_1^S(2)$
Z:(0,0,1/2)	Z:(0,0,1/2)	$Z_1^S(2)$
A:(u,0,1/2)	A:(u,0,1/2)	$A_1^S(2)$
B:(0,v,1/2)	B:(0,v,1/2)	$B_1^S(2)$
C:(u,1/2,0)	C:(u,1/2,0)	$C_1^S(2)$
D:(1/2,v,0)	D:(1/2,v,0)	$D_1^S(2)$
Δ:(0,v,0)	Δ:(0,v,0)	${\Delta }_1^S(2)$
E:(u,1/2,1/2)	E:(u,1/2,1/2)	$E_1^S(2)$
G:(1/2,0,w)	G:(1/2,0,w)	$G_1^S(2)$
H:(0,1/2,w)	H:(0,1/2,w)	$H_1^S(2)$
Λ:(0,0,w)	Λ:(0,0,w)	${\Lambda }_1^S(2)$
P:(1/2,v,1/2)	P:(1/2,v,1/2)	$P_1^S(2)$
Q:(1/2,1/2,w)	Q:(1/2,1/2,w)	$Q_1^S(2)$
Σ:(u,0,0)	Σ:(u,0,0)	${\Sigma }_1^S(2)$
K:(0,v,w)	K:(0,v,w)	$K_1^S(2)$
L:(1/2,v,w)	L:(1/2,v,w)	$L_1^S(2)$
M:(u,0,w)	M:(u,0,w)	$M_1^S(2)$
N:(u,1/2,w)	N:(u,1/2,w)	$N_1^S(2)$
V:(u,v,0)	V:(u,v,0)	$V_1^S(2)$
W:(u,v,1/2)	W:(u,v,1/2)	$W_1^S(2)$
GP:(u,v,w)	GP:(u,v,w)	$G{P}_1^S(2)$

2f

k-vector	k-vector-G↑	A1↑G(2)
Γ:(0,0,0)	Γ:(0,0,0)	${\Gamma }_1^S(2)$
R:(1/2,1/2,1/2)	R:(1/2,1/2,1/2)	$R_3^S(2)$
S:(1/2,1/2,0)	S:(1/2,1/2,0)	$S_3^S(2)$
T:(0,1/2,1/2)	T:(0,1/2,1/2)	$T_3^S(2)$
U:(1/2,0,1/2)	U:(1/2,0,1/2)	$U_1^S(2)$
X:(1/2,0,0)	X:(1/2,0,0)	$X_1^S(2)$
Y:(0,1/2,0)	Y:(0,1/2,0)	$Y_3^S(2)$
Z:(0,0,1/2)	Z:(0,0,1/2)	$Z_1^S(2)$
A:(u,0,1/2)	A:(u,0,1/2)	$A_1^S(2)$
B:(0,v,1/2)	B:(0,v,1/2)	$B_1^S(2)$
C:(u,1/2,0)	C:(u,1/2,0)	$C_2^S(2)$
D:(1/2,v,0)	D:(1/2,v,0)	$D_1^S(2)$
Δ:(0,v,0)	Δ:(0,v,0)	${\Delta }_1^S(2)$
E:(u,1/2,1/2)	E:(u,1/2,1/2)	$E_2^S(2)$
G:(1/2,0,w)	G:(1/2,0,w)	$G_1^S(2)$
H:(0,1/2,w)	H:(0,1/2,w)	$H_3^S(2)$
Λ:(0,0,w)	Λ:(0,0,w)	${\Lambda }_1^S(2)$
P:(1/2,v,1/2)	P:(1/2,v,1/2)	$P_1^S(2)$
Q:(1/2,1/2,w)	Q:(1/2,1/2,w)	$Q_3^S(2)$
Σ:(u,0,0)	Σ:(u,0,0)	${\Sigma }_1^S(2)$
K:(0,v,w)	K:(0,v,w)	$K_1^S(2)$
L:(1/2,v,w)	L:(1/2,v,w)	$L_1^S(2)$
M:(u,0,w)	M:(u,0,w)	$M_1^S(2)$
N:(u,1/2,w)	N:(u,1/2,w)	$N_2^S(2)$
V:(u,v,0)	V:(u,v,0)	$V_1^S(2)$
W:(u,v,1/2)	W:(u,v,1/2)	$W_1^S(2)$
GP:(u,v,w)	GP:(u,v,w)	$G{P}_1^S(2)$

4i

k-vector	k-vector-G↑	A'↑G(4)
Γ:(0,0,0)	Γ:(0,0,0)	${\Gamma }_1^S(2)\oplus {\Gamma }_4^S(2)$
R:(1/2,1/2,1/2)	R:(1/2,1/2,1/2)	$R_1^S(2)\oplus R_4^S(2)$
S:(1/2,1/2,0)	S:(1/2,1/2,0)	$S_1^S(2)\oplus S_4^S(2)$
T:(0,1/2,1/2)	T:(0,1/2,1/2)	$T_1^S(2)\oplus T_4^S(2)$
U:(1/2,0,1/2)	U:(1/2,0,1/2)	$U_1^S(2)\oplus U_4^S(2)$
X:(1/2,0,0)	X:(1/2,0,0)	$X_1^S(2)\oplus X_4^S(2)$
Y:(0,1/2,0)	Y:(0,1/2,0)	$Y_1^S(2)\oplus Y_4^S(2)$
Z:(0,0,1/2)	Z:(0,0,1/2)	$Z_1^S(2)\oplus Z_4^S(2)$
A:(u,0,1/2)	A:(u,0,1/2)	$2A_1^S(2)$
B:(0,v,1/2)	B:(0,v,1/2)	$B_1^S(2)\oplus B_2^S(2)$
C:(u,1/2,0)	C:(u,1/2,0)	$2C_1^S(2)$
D:(1/2,v,0)	D:(1/2,v,0)	$D_1^S(2)\oplus D_2^S(2)$
Δ:(0,v,0)	Δ:(0,v,0)	${\Delta }_1^S(2)\oplus {\Delta }_2^S(2)$
E:(u,1/2,1/2)	E:(u,1/2,1/2)	$2E_1^S(2)$
G:(1/2,0,w)	G:(1/2,0,w)	$G_1^S(2)\oplus G_4^S(2)$
H:(0,1/2,w)	H:(0,1/2,w)	$H_1^S(2)\oplus H_4^S(2)$
Λ:(0,0,w)	Λ:(0,0,w)	${\Lambda }_1^S(2)\oplus {\Lambda }_4^S(2)$
P:(1/2,v,1/2)	P:(1/2,v,1/2)	$P_1^S(2)\oplus P_2^S(2)$
Q:(1/2,1/2,w)	Q:(1/2,1/2,w)	$Q_1^S(2)\oplus Q_4^S(2)$
Σ:(u,0,0)	Σ:(u,0,0)	$2{\Sigma }_1^S(2)$
K:(0,v,w)	K:(0,v,w)	$K_1^S(2)\oplus K_2^S(2)$
L:(1/2,v,w)	L:(1/2,v,w)	$L_1^S(2)\oplus L_2^S(2)$
M:(u,0,w)	M:(u,0,w)	$2M_1^S(2)$
N:(u,1/2,w)	N:(u,1/2,w)	$2N_1^S(2)$
V:(u,v,0)	V:(u,v,0)	$2V_1^S(2)$
W:(u,v,1/2)	W:(u,v,1/2)	$2W_1^S(2)$
GP:(u,v,w)	GP:(u,v,w)	$2G{P}_1^S(2)$

4j

k-vector	k-vector-G↑	A'↑G(4)
Γ:(0,0,0)	Γ:(0,0,0)	${\Gamma }_1^S(2)\oplus {\Gamma }_4^S(2)$
R:(1/2,1/2,1/2)	R:(1/2,1/2,1/2)	$R_2^S(2)\oplus R_3^S(2)$
S:(1/2,1/2,0)	S:(1/2,1/2,0)	$S_2^S(2)\oplus S_3^S(2)$
T:(0,1/2,1/2)	T:(0,1/2,1/2)	$T_2^S(2)\oplus T_3^S(2)$
U:(1/2,0,1/2)	U:(1/2,0,1/2)	$U_1^S(2)\oplus U_4^S(2)$
X:(1/2,0,0)	X:(1/2,0,0)	$X_1^S(2)\oplus X_4^S(2)$
Y:(0,1/2,0)	Y:(0,1/2,0)	$Y_2^S(2)\oplus Y_3^S(2)$
Z:(0,0,1/2)	Z:(0,0,1/2)	$Z_1^S(2)\oplus Z_4^S(2)$
A:(u,0,1/2)	A:(u,0,1/2)	$2A_1^S(2)$
B:(0,v,1/2)	B:(0,v,1/2)	$B_1^S(2)\oplus B_2^S(2)$
C:(u,1/2,0)	C:(u,1/2,0)	$2C_2^S(2)$
D:(1/2,v,0)	D:(1/2,v,0)	$D_1^S(2)\oplus D_2^S(2)$
Δ:(0,v,0)	Δ:(0,v,0)	${\Delta }_1^S(2)\oplus {\Delta }_2^S(2)$
E:(u,1/2,1/2)	E:(u,1/2,1/2)	$2E_2^S(2)$
G:(1/2,0,w)	G:(1/2,0,w)	$G_1^S(2)\oplus G_4^S(2)$
H:(0,1/2,w)	H:(0,1/2,w)	$H_2^S(2)\oplus H_3^S(2)$
Λ:(0,0,w)	Λ:(0,0,w)	${\Lambda }_1^S(2)\oplus {\Lambda }_4^S(2)$
P:(1/2,v,1/2)	P:(1/2,v,1/2)	$P_1^S(2)\oplus P_2^S(2)$
Q:(1/2,1/2,w)	Q:(1/2,1/2,w)	$Q_2^S(2)\oplus Q_3^S(2)$
Σ:(u,0,0)	Σ:(u,0,0)	$2{\Sigma }_1^S(2)$
K:(0,v,w)	K:(0,v,w)	$K_1^S(2)\oplus K_2^S(2)$
L:(1/2,v,w)	L:(1/2,v,w)	$L_1^S(2)\oplus L_2^S(2)$
M:(u,0,w)	M:(u,0,w)	$2M_1^S(2)$
N:(u,1/2,w)	N:(u,1/2,w)	$2N_2^S(2)$
V:(u,v,0)	V:(u,v,0)	$2V_1^S(2)$
W:(u,v,1/2)	W:(u,v,1/2)	$2W_1^S(2)$
GP:(u,v,w)	GP:(u,v,w)	$2G{P}_1^S(2)$

4k

k-vector	k-vector-G↑	A'↑G(4)
Γ:(0,0,0)	Γ:(0,0,0)	${\Gamma }_1^S(2)\oplus {\Gamma }_3^S(2)$
R:(1/2,1/2,1/2)	R:(1/2,1/2,1/2)	$R_1^S(2)\oplus R_3^S(2)$
S:(1/2,1/2,0)	S:(1/2,1/2,0)	$S_1^S(2)\oplus S_3^S(2)$
T:(0,1/2,1/2)	T:(0,1/2,1/2)	$T_1^S(2)\oplus T_3^S(2)$
U:(1/2,0,1/2)	U:(1/2,0,1/2)	$U_1^S(2)\oplus U_3^S(2)$
X:(1/2,0,0)	X:(1/2,0,0)	$X_1^S(2)\oplus X_3^S(2)$
Y:(0,1/2,0)	Y:(0,1/2,0)	$Y_1^S(2)\oplus Y_3^S(2)$
Z:(0,0,1/2)	Z:(0,0,1/2)	$Z_1^S(2)\oplus Z_3^S(2)$
A:(u,0,1/2)	A:(u,0,1/2)	$A_1^S(2)\oplus A_2^S(2)$
B:(0,v,1/2)	B:(0,v,1/2)	$2B_1^S(2)$
C:(u,1/2,0)	C:(u,1/2,0)	$C_1^S(2)\oplus C_2^S(2)$
D:(1/2,v,0)	D:(1/2,v,0)	$2D_1^S(2)$
Δ:(0,v,0)	Δ:(0,v,0)	$2{\Delta }_1^S(2)$
E:(u,1/2,1/2)	E:(u,1/2,1/2)	$E_1^S(2)\oplus E_2^S(2)$
G:(1/2,0,w)	G:(1/2,0,w)	$G_1^S(2)\oplus G_3^S(2)$
H:(0,1/2,w)	H:(0,1/2,w)	$H_1^S(2)\oplus H_3^S(2)$
Λ:(0,0,w)	Λ:(0,0,w)	${\Lambda }_1^S(2)\oplus {\Lambda }_3^S(2)$
P:(1/2,v,1/2)	P:(1/2,v,1/2)	$2P_1^S(2)$
Q:(1/2,1/2,w)	Q:(1/2,1/2,w)	$Q_1^S(2)\oplus Q_3^S(2)$
Σ:(u,0,0)	Σ:(u,0,0)	${\Sigma }_1^S(2)\oplus {\Sigma }_2^S(2)$
K:(0,v,w)	K:(0,v,w)	$2K_1^S(2)$
L:(1/2,v,w)	L:(1/2,v,w)	$2L_1^S(2)$
M:(u,0,w)	M:(u,0,w)	$M_1^S(2)\oplus M_2^S(2)$
N:(u,1/2,w)	N:(u,1/2,w)	$N_1^S(2)\oplus N_2^S(2)$
V:(u,v,0)	V:(u,v,0)	$2V_1^S(2)$
W:(u,v,1/2)	W:(u,v,1/2)	$2W_1^S(2)$
GP:(u,v,w)	GP:(u,v,w)	$2G{P}_1^S(2)$

8l

k-vector	k-vector-G↑	A↑G(8)
Γ:(0,0,0)	Γ:(0,0,0)	${\Gamma }_1^S(2)\oplus {\Gamma }_2^S(2)\oplus {\Gamma }_3^S(2)\oplus {\Gamma }_4^S(2)$
R:(1/2,1/2,1/2)	R:(1/2,1/2,1/2)	$R_1^S(2)\oplus R_2^S(2)\oplus R_3^S(2)\oplus R_4^S(2)$
S:(1/2,1/2,0)	S:(1/2,1/2,0)	$S_1^S(2)\oplus S_2^S(2)\oplus S_3^S(2)\oplus S_4^S(2)$
T:(0,1/2,1/2)	T:(0,1/2,1/2)	$T_1^S(2)\oplus T_2^S(2)\oplus T_3^S(2)\oplus T_4^S(2)$
U:(1/2,0,1/2)	U:(1/2,0,1/2)	$U_1^S(2)\oplus U_2^S(2)\oplus U_3^S(2)\oplus U_4^S(2)$
X:(1/2,0,0)	X:(1/2,0,0)	$X_1^S(2)\oplus X_2^S(2)\oplus X_3^S(2)\oplus X_4^S(2)$
Y:(0,1/2,0)	Y:(0,1/2,0)	$Y_1^S(2)\oplus Y_2^S(2)\oplus Y_3^S(2)\oplus Y_4^S(2)$
Z:(0,0,1/2)	Z:(0,0,1/2)	$Z_1^S(2)\oplus Z_2^S(2)\oplus Z_3^S(2)\oplus Z_4^S(2)$
A:(u,0,1/2)	A:(u,0,1/2)	$2A_1^S(2)\oplus 2A_2^S(2)$
B:(0,v,1/2)	B:(0,v,1/2)	$2B_1^S(2)\oplus 2B_2^S(2)$
C:(u,1/2,0)	C:(u,1/2,0)	$2C_1^S(2)\oplus 2C_2^S(2)$
D:(1/2,v,0)	D:(1/2,v,0)	$2D_1^S(2)\oplus 2D_2^S(2)$
Δ:(0,v,0)	Δ:(0,v,0)	$2{\Delta }_1^S(2)\oplus 2{\Delta }_2^S(2)$
E:(u,1/2,1/2)	E:(u,1/2,1/2)	$2E_1^S(2)\oplus 2E_2^S(2)$
G:(1/2,0,w)	G:(1/2,0,w)	$G_1^S(2)\oplus G_2^S(2)\oplus G_3^S(2)\oplus G_4^S(2)$
H:(0,1/2,w)	H:(0,1/2,w)	$H_1^S(2)\oplus H_2^S(2)\oplus H_3^S(2)\oplus H_4^S(2)$
Λ:(0,0,w)	Λ:(0,0,w)	${\Lambda }_1^S(2)\oplus {\Lambda }_2^S(2)\oplus {\Lambda }_3^S(2)\oplus {\Lambda }_4^S(2)$
P:(1/2,v,1/2)	P:(1/2,v,1/2)	$2P_1^S(2)\oplus 2P_2^S(2)$
Q:(1/2,1/2,w)	Q:(1/2,1/2,w)	$Q_1^S(2)\oplus Q_2^S(2)\oplus Q_3^S(2)\oplus Q_4^S(2)$
Σ:(u,0,0)	Σ:(u,0,0)	$2{\Sigma }_1^S(2)\oplus 2{\Sigma }_2^S(2)$
K:(0,v,w)	K:(0,v,w)	$2K_1^S(2)\oplus 2K_2^S(2)$
L:(1/2,v,w)	L:(1/2,v,w)	$2L_1^S(2)\oplus 2L_2^S(2)$
M:(u,0,w)	M:(u,0,w)	$2M_1^S(2)\oplus 2M_2^S(2)$
N:(u,1/2,w)	N:(u,1/2,w)	$2N_1^S(2)\oplus 2N_2^S(2)$
V:(u,v,0)	V:(u,v,0)	$4V_1^S(2)$
W:(u,v,1/2)	W:(u,v,1/2)	$4W_1^S(2)$
GP:(u,v,w)	GP:(u,v,w)	$4G{P}_1^S(2)$