Information of spin space group $I{\phantom{A}}_{\phantom{}}^{\phantom{\text{-}1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\text{-}1}\text{4/}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\text{-}1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\text{-}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$ ( nSSG:69.139.1.1 )

General Positions

The continuously infinite group ^∞1 is omitted.

Coordinates	Seitz symbol
a, b, c | x, y, z	{ 1 ‖ 1 | 0 }
-a, -b, c | x, y, z	{ 1 ‖ 2001 | 0 }
b, a, -c | x, y, z	{ 1 ‖ 2110 | 0 }
-b, -a, -c | x, y, z	{ 1 ‖ 21-10 | 0 }
-a, -b, -c | x, y, z	{ 1 ‖ -1 | 0 }
a, b, -c | x, y, z	{ 1 ‖ m001 | 0 }
-b, -a, c | x, y, z	{ 1 ‖ m110 | 0 }
b, a, c | x, y, z	{ 1 ‖ m1-10 | 0 }
-b, a, c | -x, -y, -z	{ -1 ‖ 4+001 | 0 }
b, -a, c | -x, -y, -z	{ -1 ‖ 4-001 | 0 }
a, -b, -c | -x, -y, -z	{ -1 ‖ 2100 | 0 }
-a, b, -c | -x, -y, -z	{ -1 ‖ 2010 | 0 }
b, -a, -c | -x, -y, -z	{ -1 ‖ -4+001 | 0 }
-b, a, -c | -x, -y, -z	{ -1 ‖ -4-001 | 0 }
-a, b, c | -x, -y, -z	{ -1 ‖ m100 | 0 }
a, -b, c | -x, -y, -z	{ -1 ‖ m010 | 0 }
a+1/2, b+1/2, c+1/2 | x, y, z	{ 1 ‖ 1 | 1/2 1/2 1/2 }
-a+1/2, -b+1/2, c+1/2 | x, y, z	{ 1 ‖ 2001 | 1/2 1/2 1/2 }
b+1/2, a+1/2, -c+1/2 | x, y, z	{ 1 ‖ 2110 | 1/2 1/2 1/2 }
-b+1/2, -a+1/2, -c+1/2 | x, y, z	{ 1 ‖ 21-10 | 1/2 1/2 1/2 }
-a+1/2, -b+1/2, -c+1/2 | x, y, z	{ 1 ‖ -1 | 1/2 1/2 1/2 }
a+1/2, b+1/2, -c+1/2 | x, y, z	{ 1 ‖ m001 | 1/2 1/2 1/2 }
-b+1/2, -a+1/2, c+1/2 | x, y, z	{ 1 ‖ m110 | 1/2 1/2 1/2 }
b+1/2, a+1/2, c+1/2 | x, y, z	{ 1 ‖ m1-10 | 1/2 1/2 1/2 }
-b+1/2, a+1/2, c+1/2 | -x, -y, -z	{ -1 ‖ 4+001 | 1/2 1/2 1/2 }
b+1/2, -a+1/2, c+1/2 | -x, -y, -z	{ -1 ‖ 4-001 | 1/2 1/2 1/2 }
a+1/2, -b+1/2, -c+1/2 | -x, -y, -z	{ -1 ‖ 2100 | 1/2 1/2 1/2 }
-a+1/2, b+1/2, -c+1/2 | -x, -y, -z	{ -1 ‖ 2010 | 1/2 1/2 1/2 }
b+1/2, -a+1/2, -c+1/2 | -x, -y, -z	{ -1 ‖ -4+001 | 1/2 1/2 1/2 }
-b+1/2, a+1/2, -c+1/2 | -x, -y, -z	{ -1 ‖ -4-001 | 1/2 1/2 1/2 }
-a+1/2, b+1/2, c+1/2 | -x, -y, -z	{ -1 ‖ m100 | 1/2 1/2 1/2 }
a+1/2, -b+1/2, c+1/2 | -x, -y, -z	{ -1 ‖ m010 | 1/2 1/2 1/2 }
a, b, c | -x, y, z	{ m ‖ 1 | 0 }
-a, -b, c | -x, y, z	{ m ‖ 2001 | 0 }
b, a, -c | -x, y, z	{ m ‖ 2110 | 0 }
-b, -a, -c | -x, y, z	{ m ‖ 21-10 | 0 }
-a, -b, -c | -x, y, z	{ m ‖ -1 | 0 }
a, b, -c | -x, y, z	{ m ‖ m001 | 0 }
-b, -a, c | -x, y, z	{ m ‖ m110 | 0 }
b, a, c | -x, y, z	{ m ‖ m1-10 | 0 }
-b, a, c | x, -y, -z	{ 2 ‖ 4+001 | 0 }
b, -a, c | x, -y, -z	{ 2 ‖ 4-001 | 0 }
a, -b, -c | x, -y, -z	{ 2 ‖ 2100 | 0 }
-a, b, -c | x, -y, -z	{ 2 ‖ 2010 | 0 }
b, -a, -c | x, -y, -z	{ 2 ‖ -4+001 | 0 }
-b, a, -c | x, -y, -z	{ 2 ‖ -4-001 | 0 }
-a, b, c | x, -y, -z	{ 2 ‖ m100 | 0 }
a, -b, c | x, -y, -z	{ 2 ‖ m010 | 0 }
a+1/2, b+1/2, c+1/2 | -x, y, z	{ m ‖ 1 | 1/2 1/2 1/2 }
-a+1/2, -b+1/2, c+1/2 | -x, y, z	{ m ‖ 2001 | 1/2 1/2 1/2 }
b+1/2, a+1/2, -c+1/2 | -x, y, z	{ m ‖ 2110 | 1/2 1/2 1/2 }
-b+1/2, -a+1/2, -c+1/2 | -x, y, z	{ m ‖ 21-10 | 1/2 1/2 1/2 }
-a+1/2, -b+1/2, -c+1/2 | -x, y, z	{ m ‖ -1 | 1/2 1/2 1/2 }
a+1/2, b+1/2, -c+1/2 | -x, y, z	{ m ‖ m001 | 1/2 1/2 1/2 }
-b+1/2, -a+1/2, c+1/2 | -x, y, z	{ m ‖ m110 | 1/2 1/2 1/2 }
b+1/2, a+1/2, c+1/2 | -x, y, z	{ m ‖ m1-10 | 1/2 1/2 1/2 }
-b+1/2, a+1/2, c+1/2 | x, -y, -z	{ 2 ‖ 4+001 | 1/2 1/2 1/2 }
b+1/2, -a+1/2, c+1/2 | x, -y, -z	{ 2 ‖ 4-001 | 1/2 1/2 1/2 }
a+1/2, -b+1/2, -c+1/2 | x, -y, -z	{ 2 ‖ 2100 | 1/2 1/2 1/2 }
-a+1/2, b+1/2, -c+1/2 | x, -y, -z	{ 2 ‖ 2010 | 1/2 1/2 1/2 }
b+1/2, -a+1/2, -c+1/2 | x, -y, -z	{ 2 ‖ -4+001 | 1/2 1/2 1/2 }
-b+1/2, a+1/2, -c+1/2 | x, -y, -z	{ 2 ‖ -4-001 | 1/2 1/2 1/2 }
-a+1/2, b+1/2, c+1/2 | x, -y, -z	{ 2 ‖ m100 | 1/2 1/2 1/2 }
a+1/2, -b+1/2, c+1/2 | x, -y, -z	{ 2 ‖ m010 | 1/2 1/2 1/2 }

Wyckoff Positions

WP	Site symmetry	Representative
2a	${\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{4}/{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(0,0,0 | 0,0,0)
2b	${\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{4}/{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(0,0,1/2 | 0,0,0)
4c	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}.{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(0,1/2,0 | 0,0,0)
4d	${\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{-4}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{2}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(0,1/2,1/4 | 0,0,0)
4e	${\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{4}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(0,0,c | 0,0,0)
8f	$..{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{2}/{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(1/4,1/4,1/4 | 0,0,z)
8g	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{2}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}.{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(0,1/2,c | 0,0,0)
8h	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}.{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{2}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(a,a,0 | 0,0,z)
8i	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{2}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}.{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(a,0,0 | 0,0,0)
8j	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{2}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}.{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(a,1/2,0 | 0,0,0)
16k	$..{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{2}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(a,a+1/2,1/4 | 0,0,z)
16l	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}..{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(a,b,0 | 0,0,z)
16m	$..{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(a,a,c | 0,0,z)
16n	$.{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}.{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(0,b,c | 0,0,0)
32o	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{1}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(a,b,c | 0,0,z)

Spin Brillouin Zone & k-little co-groups

Wavevector-k	Little co-group
Γ:(0,0,0)	${\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{4/}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$
M:(1,1,1)	${\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{4/}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$
P:(1/2,1/2,1/2)	${\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{4/}{\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
X:(1/2,1/2,0)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$
N:(1/2,0,1/2)	${\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{2/}{\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$
Λ:(0,0,w)	${\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{4/}{\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
Δ:(u,u,0)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
Q:(1/2,v,1/2)	${\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{2/}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
Σ:(u,0,0)	${\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
W:(1/2,1/2,w)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
Y:(u,1-u,0)	${\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
A:(u,u,w)	${\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{2/}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
B:(u,0,w)	${\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{2/}{\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
C:(u,v,0)	${\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{2/}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
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

4/mmmI

Band Representations (Magnon)

8f

k-vector	k-vector-G↑	Ag↑G(4)
Γ:(0,0,0)	Γ:(0,0,0)	${\Gamma }_1^{S,+}(2)\oplus {\Gamma }_3^{S,+}(2)$
M:(0,0,1)	Z:(0,0,1)	$(M)Z_2^{S,-}(2)\oplus (M)Z_4^{S,-}(2)$
N:(1/2,0,1/2)	L:(1/2,1/2,1/2)	$(N)L_1^{S,+}(2)\oplus (N)L_1^{S,-}(2)$
P:(1/2,1/2,1/2)	H:(0,1,1/2)	$(P)H_1^S(2)\oplus (P)H_3^S(2)$
X:(1/2,1/2,0)	Y:(0,1,0)	$2(X)Y_2^{S,-}(1)\oplus 2(X)Y_4^{S,-}(1)$	Spin Splitting
Δ:(u,u,0)	Δ:(0,2*u,0)	$2{\Delta }_1^S(1)\oplus 2{\Delta }_3^S(1)$	Spin Splitting
Λ:(0,0,w)	Λ:(0,0,w)	${\Lambda }_1^S(2)\oplus {\Lambda }_3^S(2)$
Q:(1/2,v,1/2)	GP:(1/2-v,1/2+v,1/2)	$2(Q)G{P}_1^S(2)$
Σ:(u,0,0)	M:(u,u,0)	$(\Sigma )M_1^S(2)\oplus (\Sigma )M_2^S(2)$
W:(1/2,1/2,w)	H:(0,1,w)	$2(W)H_1^S(1)\oplus 2(W)H_3^S(1)$	Spin Splitting
Y:(u,-u,1)	A:(2*u,0,1)	$2(Y)A_3^S(1)\oplus 2(Y)A_4^S(1)$	Spin Splitting
A:(u,u,w)	E:(0,2*u,w)	$4(A)E_1^S(1)$	Spin Splitting
B:(u,0,w)	GP:(u,u,w)	$2(B)G{P}_1^S(2)$
C:(u,v,0)	M:(u-v,u+v,0)	$2(C)M_1^S(1)\oplus 2(C)M_2^S(1)$	Spin Splitting
GP:(u,v,w)	GP:(u-v,u+v,w)	$4G{P}_1^S(1)$	Spin Splitting

8h

k-vector	k-vector-G↑	A1↑G(4)
Γ:(0,0,0)	Γ:(0,0,0)	${\Gamma }_1^{S,+}(2)\oplus {\Gamma }_4^{S,-}(2)$
M:(0,0,1)	Z:(0,0,1)	$(M)Z_1^{S,+}(2)\oplus (M)Z_4^{S,-}(2)$
N:(1/2,0,1/2)	L:(1/2,1/2,1/2)	$(N)L_1^{S,+}(2)\oplus (N)L_1^{S,-}(2)$
P:(1/2,1/2,1/2)	H:(0,1,1/2)	$(P)H_1^S(2)\oplus (P)H_3^S(2)$
X:(1/2,1/2,0)	Y:(0,1,0)	$2(X)Y_1^{S,+}(1)\oplus 2(X)Y_4^{S,-}(1)$	Spin Splitting
Δ:(u,u,0)	Δ:(0,2*u,0)	$4{\Delta }_1^S(1)$	Spin Splitting
Λ:(0,0,w)	Λ:(0,0,w)	${\Lambda }_1^S(2)\oplus {\Lambda }_3^S(2)$
Q:(1/2,v,1/2)	GP:(1/2-v,1/2+v,1/2)	$2(Q)G{P}_1^S(2)$
Σ:(u,0,0)	M:(u,u,0)	$2(\Sigma )M_1^S(2)$
W:(1/2,1/2,w)	H:(0,1,w)	$2(W)H_1^S(1)\oplus 2(W)H_3^S(1)$	Spin Splitting
Y:(u,-u,1)	A:(2*u,0,1)	$2(Y)A_1^S(1)\oplus 2(Y)A_4^S(1)$	Spin Splitting
A:(u,u,w)	E:(0,2*u,w)	$4(A)E_1^S(1)$	Spin Splitting
B:(u,0,w)	GP:(u,u,w)	$2(B)G{P}_1^S(2)$
C:(u,v,0)	M:(u-v,u+v,0)	$4(C)M_1^S(1)$	Spin Splitting
GP:(u,v,w)	GP:(u-v,u+v,w)	$4G{P}_1^S(1)$	Spin Splitting

16k

k-vector	k-vector-G↑	A↑G(8)
Γ:(0,0,0)	Γ:(0,0,0)	${\Gamma }_1^{S,+}(2)\oplus {\Gamma }_1^{S,-}(2)\oplus {\Gamma }_4^{S,+}(2)\oplus {\Gamma }_4^{S,-}(2)$
M:(0,0,1)	Z:(0,0,1)	$(M)Z_2^{S,+}(2)\oplus (M)Z_2^{S,-}(2)\oplus (M)Z_3^{S,+}(2)\oplus (M)Z_3^{S,-}(2)$
N:(1/2,0,1/2)	L:(1/2,1/2,1/2)	$2(N)L_1^{S,+}(2)\oplus 2(N)L_1^{S,-}(2)$
P:(1/2,1/2,1/2)	H:(0,1,1/2)	$(P)H_1^S(2)\oplus (P)H_2^S(2)\oplus (P)H_3^S(2)\oplus (P)H_4^S(2)$
X:(1/2,1/2,0)	Y:(0,1,0)	$2(X)Y_1^{S,+}(1)\oplus 2(X)Y_1^{S,-}(1)\oplus 2(X)Y_4^{S,+}(1)\oplus 2(X)Y_4^{S,-}(1)$	Spin Splitting
Δ:(u,u,0)	Δ:(0,2*u,0)	$4{\Delta }_1^S(1)\oplus 4{\Delta }_2^S(1)$	Spin Splitting
Λ:(0,0,w)	Λ:(0,0,w)	${\Lambda }_1^S(2)\oplus {\Lambda }_2^S(2)\oplus {\Lambda }_3^S(2)\oplus {\Lambda }_4^S(2)$
Q:(1/2,v,1/2)	GP:(1/2-v,1/2+v,1/2)	$4(Q)G{P}_1^S(2)$
Σ:(u,0,0)	M:(u,u,0)	$2(\Sigma )M_1^S(2)\oplus 2(\Sigma )M_2^S(2)$
W:(1/2,1/2,w)	H:(0,1,w)	$2(W)H_1^S(1)\oplus 2(W)H_2^S(1)\oplus 2(W)H_3^S(1)\oplus 2(W)H_4^S(1)$	Spin Splitting
Y:(u,-u,1)	A:(2*u,0,1)	$2(Y)A_1^S(1)\oplus 2(Y)A_2^S(1)\oplus 2(Y)A_3^S(1)\oplus 2(Y)A_4^S(1)$	Spin Splitting
A:(u,u,w)	E:(0,2*u,w)	$4(A)E_1^S(1)\oplus 4(A)E_2^S(1)$	Spin Splitting
B:(u,0,w)	GP:(u,u,w)	$4(B)G{P}_1^S(2)$
C:(u,v,0)	M:(u-v,u+v,0)	$4(C)M_1^S(1)\oplus 4(C)M_2^S(1)$	Spin Splitting
GP:(u,v,w)	GP:(u-v,u+v,w)	$8G{P}_1^S(1)$	Spin Splitting

16l

k-vector	k-vector-G↑	A'↑G(8)
Γ:(0,0,0)	Γ:(0,0,0)	${\Gamma }_1^{S,+}(2)\oplus {\Gamma }_2^{S,+}(2)\oplus {\Gamma }_3^{S,-}(2)\oplus {\Gamma }_4^{S,-}(2)$
M:(0,0,1)	Z:(0,0,1)	$(M)Z_1^{S,+}(2)\oplus (M)Z_2^{S,+}(2)\oplus (M)Z_3^{S,-}(2)\oplus (M)Z_4^{S,-}(2)$
N:(1/2,0,1/2)	L:(1/2,1/2,1/2)	$2(N)L_1^{S,+}(2)\oplus 2(N)L_1^{S,-}(2)$
P:(1/2,1/2,1/2)	H:(0,1,1/2)	$(P)H_1^S(2)\oplus (P)H_2^S(2)\oplus (P)H_3^S(2)\oplus (P)H_4^S(2)$
X:(1/2,1/2,0)	Y:(0,1,0)	$2(X)Y_1^{S,+}(1)\oplus 2(X)Y_2^{S,+}(1)\oplus 2(X)Y_3^{S,-}(1)\oplus 2(X)Y_4^{S,-}(1)$	Spin Splitting
Δ:(u,u,0)	Δ:(0,2*u,0)	$4{\Delta }_1^S(1)\oplus 4{\Delta }_4^S(1)$	Spin Splitting
Λ:(0,0,w)	Λ:(0,0,w)	${\Lambda }_1^S(2)\oplus {\Lambda }_2^S(2)\oplus {\Lambda }_3^S(2)\oplus {\Lambda }_4^S(2)$
Q:(1/2,v,1/2)	GP:(1/2-v,1/2+v,1/2)	$4(Q)G{P}_1^S(2)$
Σ:(u,0,0)	M:(u,u,0)	$4(\Sigma )M_1^S(2)$
W:(1/2,1/2,w)	H:(0,1,w)	$2(W)H_1^S(1)\oplus 2(W)H_2^S(1)\oplus 2(W)H_3^S(1)\oplus 2(W)H_4^S(1)$	Spin Splitting
Y:(u,-u,1)	A:(2*u,0,1)	$4(Y)A_1^S(1)\oplus 4(Y)A_4^S(1)$	Spin Splitting
A:(u,u,w)	E:(0,2*u,w)	$4(A)E_1^S(1)\oplus 4(A)E_2^S(1)$	Spin Splitting
B:(u,0,w)	GP:(u,u,w)	$4(B)G{P}_1^S(2)$
C:(u,v,0)	M:(u-v,u+v,0)	$8(C)M_1^S(1)$	Spin Splitting
GP:(u,v,w)	GP:(u-v,u+v,w)	$8G{P}_1^S(1)$	Spin Splitting

16m

k-vector	k-vector-G↑	A'↑G(8)
Γ:(0,0,0)	Γ:(0,0,0)	${\Gamma }_1^{S,+}(2)\oplus {\Gamma }_2^{S,-}(2)\oplus {\Gamma }_3^{S,+}(2)\oplus {\Gamma }_4^{S,-}(2)$
M:(0,0,1)	Z:(0,0,1)	$(M)Z_1^{S,+}(2)\oplus (M)Z_2^{S,-}(2)\oplus (M)Z_3^{S,+}(2)\oplus (M)Z_4^{S,-}(2)$
N:(1/2,0,1/2)	L:(1/2,1/2,1/2)	$2(N)L_1^{S,+}(2)\oplus 2(N)L_1^{S,-}(2)$
P:(1/2,1/2,1/2)	H:(0,1,1/2)	$2(P)H_1^S(2)\oplus 2(P)H_3^S(2)$
X:(1/2,1/2,0)	Y:(0,1,0)	$2(X)Y_1^{S,+}(1)\oplus 2(X)Y_2^{S,-}(1)\oplus 2(X)Y_3^{S,+}(1)\oplus 2(X)Y_4^{S,-}(1)$	Spin Splitting
Δ:(u,u,0)	Δ:(0,2*u,0)	$4{\Delta }_1^S(1)\oplus 4{\Delta }_3^S(1)$	Spin Splitting
Λ:(0,0,w)	Λ:(0,0,w)	$2{\Lambda }_1^S(2)\oplus 2{\Lambda }_3^S(2)$
Q:(1/2,v,1/2)	GP:(1/2-v,1/2+v,1/2)	$4(Q)G{P}_1^S(2)$
Σ:(u,0,0)	M:(u,u,0)	$2(\Sigma )M_1^S(2)\oplus 2(\Sigma )M_2^S(2)$
W:(1/2,1/2,w)	H:(0,1,w)	$4(W)H_1^S(1)\oplus 4(W)H_3^S(1)$	Spin Splitting
Y:(u,-u,1)	A:(2*u,0,1)	$2(Y)A_1^S(1)\oplus 2(Y)A_2^S(1)\oplus 2(Y)A_3^S(1)\oplus 2(Y)A_4^S(1)$	Spin Splitting
A:(u,u,w)	E:(0,2*u,w)	$8(A)E_1^S(1)$	Spin Splitting
B:(u,0,w)	GP:(u,u,w)	$4(B)G{P}_1^S(2)$
C:(u,v,0)	M:(u-v,u+v,0)	$4(C)M_1^S(1)\oplus 4(C)M_2^S(1)$	Spin Splitting
GP:(u,v,w)	GP:(u-v,u+v,w)	$8G{P}_1^S(1)$	Spin Splitting

32o

k-vector	k-vector-G↑	A↑G(16)
Γ:(0,0,0)	Γ:(0,0,0)	${\Gamma }_1^{S,+}(2)\oplus {\Gamma }_1^{S,-}(2)\oplus {\Gamma }_2^{S,+}(2)\oplus {\Gamma }_2^{S,-}(2)\oplus {\Gamma }_3^{S,+}(2)\oplus {\Gamma }_3^{S,-}(2)\oplus {\Gamma }_4^{S,+}(2)\oplus {\Gamma }_4^{S,-}(2)$
M:(0,0,1)	Z:(0,0,1)	$(M)Z_1^{S,+}(2)\oplus (M)Z_1^{S,-}(2)\oplus (M)Z_2^{S,+}(2)\oplus (M)Z_2^{S,-}(2)\oplus (M)Z_3^{S,+}(2)\oplus (M)Z_3^{S,-}(2)\oplus (M)Z_4^{S,+}(2)\oplus (M)Z_4^{S,-}(2)$
N:(1/2,0,1/2)	L:(1/2,1/2,1/2)	$4(N)L_1^{S,+}(2)\oplus 4(N)L_1^{S,-}(2)$
P:(1/2,1/2,1/2)	H:(0,1,1/2)	$2(P)H_1^S(2)\oplus 2(P)H_2^S(2)\oplus 2(P)H_3^S(2)\oplus 2(P)H_4^S(2)$
X:(1/2,1/2,0)	Y:(0,1,0)	$2(X)Y_1^{S,+}(1)\oplus 2(X)Y_1^{S,-}(1)\oplus 2(X)Y_2^{S,+}(1)\oplus 2(X)Y_2^{S,-}(1)\oplus 2(X)Y_3^{S,+}(1)\oplus 2(X)Y_3^{S,-}(1)\oplus 2(X)Y_4^{S,+}(1)\oplus 2(X)Y_4^{S,-}(1)$	Spin Splitting
Δ:(u,u,0)	Δ:(0,2*u,0)	$4{\Delta }_1^S(1)\oplus 4{\Delta }_2^S(1)\oplus 4{\Delta }_3^S(1)\oplus 4{\Delta }_4^S(1)$	Spin Splitting
Λ:(0,0,w)	Λ:(0,0,w)	$2{\Lambda }_1^S(2)\oplus 2{\Lambda }_2^S(2)\oplus 2{\Lambda }_3^S(2)\oplus 2{\Lambda }_4^S(2)$
Q:(1/2,v,1/2)	GP:(1/2-v,1/2+v,1/2)	$8(Q)G{P}_1^S(2)$
Σ:(u,0,0)	M:(u,u,0)	$4(\Sigma )M_1^S(2)\oplus 4(\Sigma )M_2^S(2)$
W:(1/2,1/2,w)	H:(0,1,w)	$4(W)H_1^S(1)\oplus 4(W)H_2^S(1)\oplus 4(W)H_3^S(1)\oplus 4(W)H_4^S(1)$	Spin Splitting
Y:(u,-u,1)	A:(2*u,0,1)	$4(Y)A_1^S(1)\oplus 4(Y)A_2^S(1)\oplus 4(Y)A_3^S(1)\oplus 4(Y)A_4^S(1)$	Spin Splitting
A:(u,u,w)	E:(0,2*u,w)	$8(A)E_1^S(1)\oplus 8(A)E_2^S(1)$	Spin Splitting
B:(u,0,w)	GP:(u,u,w)	$8(B)G{P}_1^S(2)$
C:(u,v,0)	M:(u-v,u+v,0)	$8(C)M_1^S(1)\oplus 8(C)M_2^S(1)$	Spin Splitting
GP:(u,v,w)	GP:(u-v,u+v,w)	$16G{P}_1^S(1)$	Spin Splitting