Information of spin space group $P{\phantom{A}}_{\phantom{}}^{\phantom{\text{-}1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\text{-}1}\text{c}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{c}{\phantom{A}}_{\phantom{}}^{\phantom{\text{-}1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\text{-}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$ ( nSSG:13.49.1.1 )

General Positions

The continuously infinite group ^∞1 is omitted.

Coordinates	Seitz symbol
a, b, c | x, y, z	{ 1 ‖ 1 | 0 }
-a, b, -c+1/2 | x, y, z	{ 1 ‖ 2010 | 0 0 1/2 }
-a, -b, -c | x, y, z	{ 1 ‖ -1 | 0 }
a, -b, c+1/2 | x, y, z	{ 1 ‖ m010 | 0 0 1/2 }
a, -b, -c+1/2 | -x, -y, -z	{ -1 ‖ 2100 | 0 0 1/2 }
-a, -b, c | -x, -y, -z	{ -1 ‖ 2001 | 0 }
-a, b, c+1/2 | -x, -y, -z	{ -1 ‖ m100 | 0 0 1/2 }
a, b, -c | -x, -y, -z	{ -1 ‖ m001 | 0 }
a, b, c | -x, y, z	{ m ‖ 1 | 0 }
-a, b, -c+1/2 | -x, y, z	{ m ‖ 2010 | 0 0 1/2 }
-a, -b, -c | -x, y, z	{ m ‖ -1 | 0 }
a, -b, c+1/2 | -x, y, z	{ m ‖ m010 | 0 0 1/2 }
a, -b, -c+1/2 | x, -y, -z	{ 2 ‖ 2100 | 0 0 1/2 }
-a, -b, c | x, -y, -z	{ 2 ‖ 2001 | 0 }
-a, b, c+1/2 | x, -y, -z	{ 2 ‖ m100 | 0 0 1/2 }
a, b, -c | x, -y, -z	{ 2 ‖ m001 | 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	$..{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{2}/{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(1/2,1/2,0 | 0,0,0)
2c	$..{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{2}/{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(0,1/2,0 | 0,0,0)
2d	$..{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{2}/{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(1/2,0,0 | 0,0,0)
2e	${\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{2}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{2}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{2}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(0,0,1/4 | 0,0,0)
2f	${\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{2}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{2}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{2}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(1/2,0,1/4 | 0,0,0)
2g	${\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{2}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{2}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{2}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(0,1/2,1/4 | 0,0,0)
2h	${\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{2}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{2}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{2}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(1/2,1/2,1/4 | 0,0,0)
4i	${\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{2}..{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(a,0,1/4 | 0,0,0)
4j	${\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{2}..{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(a,1/2,1/4 | 0,0,0)
4k	$.{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{2}.{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(0,b,1/4 | 0,0,z)
4l	$.{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{2}.{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(1/2,b,1/4 | 0,0,z)
4m	$..{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{2}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(0,0,c | 0,0,0)
4n	$..{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{2}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(1/2,1/2,c | 0,0,0)
4o	$..{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{2}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(0,1/2,c | 0,0,0)
4p	$..{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{2}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(1/2,0,c | 0,0,0)
4q	$..{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(a,b,0 | 0,0,0)
8r	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{1}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(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)	${\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
B:(0,v,1/2)	${\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
C:(u,1/2,0)	${\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
D:(1/2,v,0)	${\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
Δ:(0,v,0)	${\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
E:(u,1/2,1/2)	${\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
G:(1/2,0,w)	${\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
H:(0,1/2,w)	${\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
Λ:(0,0,w)	${\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
P:(1/2,v,1/2)	${\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
Q:(1/2,1/2,w)	${\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
Σ:(u,0,0)	${\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
K:(0,v,w)	${\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{2/}{\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
L:(1/2,v,w)	${\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{2/}{\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
M:(u,0,w)	${\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{2/}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
N:(u,1/2,w)	${\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{2/}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
V:(u,v,0)	${\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{2/}{\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
W:(u,v,1/2)	${\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{2/}{\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
GP:(u,v,w)	${\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{-1}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$

Spin Brillouin Zone

Band Representations (Magnon)

4k

k-vector	k-vector-G↑	A↑G(4)
Γ:(0,0,0)	Γ:(0,0,0)	${\Gamma }_1^{S,+}(2)\oplus {\Gamma }_1^{S,-}(2)$
R:(1/2,1/2,1/2)	E:(1/2,1/2,1/2)	$(R)E_1^S(4)$
S:(1/2,1/2,0)	C:(1/2,1/2,0)	$(S)C_1^{S,+}(2)\oplus (S)C_1^{S,-}(2)$
T:(0,1/2,1/2)	D:(0,1/2,1/2)	$(T)D_1^S(4)$
U:(1/2,0,1/2)	A:(1/2,0,1/2)	$(U)A_1^S(4)$
X:(1/2,0,0)	Y:(1/2,0,0)	$(X)Y_1^{S,+}(2)\oplus (X)Y_1^{S,-}(2)$
Y:(0,1/2,0)	Z:(0,1/2,0)	$(Y)Z_1^{S,+}(2)\oplus (Y)Z_1^{S,-}(2)$
Z:(0,0,1/2)	B:(0,0,1/2)	$(Z)B_1^S(4)$
A:(u,0,1/2)	F:(u,0,1/2)	$(A)F_1^S(2)\oplus (A)F_2^S(2)$
B:(0,v,1/2)	V:(0,v,1/2)	$(B)V_1^S{V}_2^S(4)$
C:(u,1/2,0)	G:(u,1/2,0)	$(C)G_1^S(2)\oplus (C)G_2^S(2)$
D:(1/2,v,0)	W:(1/2,v,0)	$2(D)W_1^S(2)$
Δ:(0,v,0)	Λ:(0,v,0)	$2(\Delta ){\Lambda }_1^S(2)$
E:(u,1/2,1/2)	G:(u,1/2,1/2)	$(E)G_1^S(2)\oplus (E)G_2^S(2)$
G:(1/2,0,w)	F:(1/2,0,w)	$(G)F_1^S(2)\oplus (G)F_2^S(2)$
H:(0,1/2,w)	G:(0,1/2,w)	$(H)G_1^S(2)\oplus (H)G_2^S(2)$
Λ:(0,0,w)	F:(0,0,w)	$(\Lambda )F_1^S(2)\oplus (\Lambda )F_2^S(2)$
P:(1/2,v,1/2)	U:(1/2,v,1/2)	$(P)U_1^S{U}_2^S(4)$
Q:(1/2,1/2,w)	G:(1/2,1/2,w)	$(Q)G_1^S(2)\oplus (Q)G_2^S(2)$
Σ:(u,0,0)	F:(u,0,0)	$(\Sigma )F_1^S(2)\oplus (\Sigma )F_2^S(2)$
K:(0,v,w)	GP:(0,v,w)	$2(K)G{P}_1^S(2)$
L:(1/2,v,w)	GP:(1/2,v,w)	$2(L)G{P}_1^S(2)$
M:(u,0,w)	F:(u,0,w)	$2(M)F_1^S(1)\oplus 2(M)F_2^S(1)$	Spin Splitting
N:(u,1/2,w)	G:(u,1/2,w)	$2(N)G_1^S(1)\oplus 2(N)G_2^S(1)$	Spin Splitting
V:(u,v,0)	GP:(u,v,0)	$2(V)G{P}_1^S(2)$
W:(u,v,1/2)	GP:(u,v,1/2)	$2(W)G{P}_1^S(2)$
GP:(u,v,w)	GP:(u,v,w)	$4G{P}_1^S(1)$	Spin Splitting

4l

k-vector	k-vector-G↑	A↑G(4)
Γ:(0,0,0)	Γ:(0,0,0)	${\Gamma }_1^{S,+}(2)\oplus {\Gamma }_1^{S,-}(2)$
R:(1/2,1/2,1/2)	E:(1/2,1/2,1/2)	$(R)E_1^S(4)$
S:(1/2,1/2,0)	C:(1/2,1/2,0)	$(S)C_2^{S,+}(2)\oplus (S)C_2^{S,-}(2)$
T:(0,1/2,1/2)	D:(0,1/2,1/2)	$(T)D_1^S(4)$
U:(1/2,0,1/2)	A:(1/2,0,1/2)	$(U)A_1^S(4)$
X:(1/2,0,0)	Y:(1/2,0,0)	$(X)Y_2^{S,+}(2)\oplus (X)Y_2^{S,-}(2)$
Y:(0,1/2,0)	Z:(0,1/2,0)	$(Y)Z_1^{S,+}(2)\oplus (Y)Z_1^{S,-}(2)$
Z:(0,0,1/2)	B:(0,0,1/2)	$(Z)B_1^S(4)$
A:(u,0,1/2)	F:(u,0,1/2)	$(A)F_1^S(2)\oplus (A)F_2^S(2)$
B:(0,v,1/2)	V:(0,v,1/2)	$(B)V_1^S{V}_2^S(4)$
C:(u,1/2,0)	G:(u,1/2,0)	$(C)G_1^S(2)\oplus (C)G_2^S(2)$
D:(1/2,v,0)	W:(1/2,v,0)	$2(D)W_2^S(2)$
Δ:(0,v,0)	Λ:(0,v,0)	$2(\Delta ){\Lambda }_1^S(2)$
E:(u,1/2,1/2)	G:(u,1/2,1/2)	$(E)G_1^S(2)\oplus (E)G_2^S(2)$
G:(1/2,0,w)	F:(1/2,0,w)	$(G)F_1^S(2)\oplus (G)F_2^S(2)$
H:(0,1/2,w)	G:(0,1/2,w)	$(H)G_1^S(2)\oplus (H)G_2^S(2)$
Λ:(0,0,w)	F:(0,0,w)	$(\Lambda )F_1^S(2)\oplus (\Lambda )F_2^S(2)$
P:(1/2,v,1/2)	U:(1/2,v,1/2)	$(P)U_1^S{U}_2^S(4)$
Q:(1/2,1/2,w)	G:(1/2,1/2,w)	$(Q)G_1^S(2)\oplus (Q)G_2^S(2)$
Σ:(u,0,0)	F:(u,0,0)	$(\Sigma )F_1^S(2)\oplus (\Sigma )F_2^S(2)$
K:(0,v,w)	GP:(0,v,w)	$2(K)G{P}_1^S(2)$
L:(1/2,v,w)	GP:(1/2,v,w)	$2(L)G{P}_1^S(2)$
M:(u,0,w)	F:(u,0,w)	$2(M)F_1^S(1)\oplus 2(M)F_2^S(1)$	Spin Splitting
N:(u,1/2,w)	G:(u,1/2,w)	$2(N)G_1^S(1)\oplus 2(N)G_2^S(1)$	Spin Splitting
V:(u,v,0)	GP:(u,v,0)	$2(V)G{P}_1^S(2)$
W:(u,v,1/2)	GP:(u,v,1/2)	$2(W)G{P}_1^S(2)$
GP:(u,v,w)	GP:(u,v,w)	$4G{P}_1^S(1)$	Spin Splitting

8r

k-vector	k-vector-G↑	A↑G(8)
Γ:(0,0,0)	Γ:(0,0,0)	${\Gamma }_1^{S,+}(2)\oplus {\Gamma }_1^{S,-}(2)\oplus {\Gamma }_2^{S,+}(2)\oplus {\Gamma }_2^{S,-}(2)$
R:(1/2,1/2,1/2)	E:(1/2,1/2,1/2)	$2(R)E_1^S(4)$
S:(1/2,1/2,0)	C:(1/2,1/2,0)	$(S)C_1^{S,+}(2)\oplus (S)C_1^{S,-}(2)\oplus (S)C_2^{S,+}(2)\oplus (S)C_2^{S,-}(2)$
T:(0,1/2,1/2)	D:(0,1/2,1/2)	$2(T)D_1^S(4)$
U:(1/2,0,1/2)	A:(1/2,0,1/2)	$2(U)A_1^S(4)$
X:(1/2,0,0)	Y:(1/2,0,0)	$(X)Y_1^{S,+}(2)\oplus (X)Y_1^{S,-}(2)\oplus (X)Y_2^{S,+}(2)\oplus (X)Y_2^{S,-}(2)$
Y:(0,1/2,0)	Z:(0,1/2,0)	$(Y)Z_1^{S,+}(2)\oplus (Y)Z_1^{S,-}(2)\oplus (Y)Z_2^{S,+}(2)\oplus (Y)Z_2^{S,-}(2)$
Z:(0,0,1/2)	B:(0,0,1/2)	$2(Z)B_1^S(4)$
A:(u,0,1/2)	F:(u,0,1/2)	$2(A)F_1^S(2)\oplus 2(A)F_2^S(2)$
B:(0,v,1/2)	V:(0,v,1/2)	$2(B)V_1^S{V}_2^S(4)$
C:(u,1/2,0)	G:(u,1/2,0)	$2(C)G_1^S(2)\oplus 2(C)G_2^S(2)$
D:(1/2,v,0)	W:(1/2,v,0)	$2(D)W_1^S(2)\oplus 2(D)W_2^S(2)$
Δ:(0,v,0)	Λ:(0,v,0)	$2(\Delta ){\Lambda }_1^S(2)\oplus 2(\Delta ){\Lambda }_2^S(2)$
E:(u,1/2,1/2)	G:(u,1/2,1/2)	$2(E)G_1^S(2)\oplus 2(E)G_2^S(2)$
G:(1/2,0,w)	F:(1/2,0,w)	$2(G)F_1^S(2)\oplus 2(G)F_2^S(2)$
H:(0,1/2,w)	G:(0,1/2,w)	$2(H)G_1^S(2)\oplus 2(H)G_2^S(2)$
Λ:(0,0,w)	F:(0,0,w)	$2(\Lambda )F_1^S(2)\oplus 2(\Lambda )F_2^S(2)$
P:(1/2,v,1/2)	U:(1/2,v,1/2)	$2(P)U_1^S{U}_2^S(4)$
Q:(1/2,1/2,w)	G:(1/2,1/2,w)	$2(Q)G_1^S(2)\oplus 2(Q)G_2^S(2)$
Σ:(u,0,0)	F:(u,0,0)	$2(\Sigma )F_1^S(2)\oplus 2(\Sigma )F_2^S(2)$
K:(0,v,w)	GP:(0,v,w)	$4(K)G{P}_1^S(2)$
L:(1/2,v,w)	GP:(1/2,v,w)	$4(L)G{P}_1^S(2)$
M:(u,0,w)	F:(u,0,w)	$4(M)F_1^S(1)\oplus 4(M)F_2^S(1)$	Spin Splitting
N:(u,1/2,w)	G:(u,1/2,w)	$4(N)G_1^S(1)\oplus 4(N)G_2^S(1)$	Spin Splitting
V:(u,v,0)	GP:(u,v,0)	$4(V)G{P}_1^S(2)$
W:(u,v,1/2)	GP:(u,v,1/2)	$4(W)G{P}_1^S(2)$
GP:(u,v,w)	GP:(u,v,w)	$8G{P}_1^S(1)$	Spin Splitting