Information of spin space group $P{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{-}\text{3}{\phantom{A}}_{\phantom{}}^{\phantom{\text{-}1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\text{-}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$ ( nSSG:200.221.1.1 )

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 ‖ 2100 | 0 }
-a, b, -c | x, y, z	{ 1 ‖ 2010 | 0 }
-a, -b, c | x, y, z	{ 1 ‖ 2001 | 0 }
c, a, b | x, y, z	{ 1 ‖ 3+111 | 0 }
b, c, a | x, y, z	{ 1 ‖ 3-111 | 0 }
-b, c, -a | x, y, z	{ 1 ‖ 3-1-1-1 | 0 }
-c, -a, b | x, y, z	{ 1 ‖ 3+1-1-1 | 0 }
-b, -c, a | x, y, z	{ 1 ‖ 3--11-1 | 0 }
c, -a, -b | x, y, z	{ 1 ‖ 3+-11-1 | 0 }
b, -c, -a | x, y, z	{ 1 ‖ 3--1-11 | 0 }
-c, a, -b | x, y, z	{ 1 ‖ 3+-1-11 | 0 }
-a, -b, -c | x, y, z	{ 1 ‖ -1 | 0 }
-a, b, c | x, y, z	{ 1 ‖ m100 | 0 }
a, -b, c | x, y, z	{ 1 ‖ m010 | 0 }
a, b, -c | x, y, z	{ 1 ‖ m001 | 0 }
-c, -a, -b | x, y, z	{ 1 ‖ -3+111 | 0 }
-b, -c, -a | x, y, z	{ 1 ‖ -3-111 | 0 }
b, -c, a | x, y, z	{ 1 ‖ -3-1-1-1 | 0 }
c, a, -b | x, y, z	{ 1 ‖ -3+1-1-1 | 0 }
b, c, -a | x, y, z	{ 1 ‖ -3--11-1 | 0 }
-c, a, b | x, y, z	{ 1 ‖ -3+-11-1 | 0 }
-b, c, a | x, y, z	{ 1 ‖ -3--1-11 | 0 }
c, -a, b | x, y, z	{ 1 ‖ -3+-1-11 | 0 }
a, -c, b | -x, -y, -z	{ -1 ‖ 4+100 | 0 }
a, c, -b | -x, -y, -z	{ -1 ‖ 4-100 | 0 }
c, b, -a | -x, -y, -z	{ -1 ‖ 4+010 | 0 }
-c, b, a | -x, -y, -z	{ -1 ‖ 4-010 | 0 }
-b, a, c | -x, -y, -z	{ -1 ‖ 4+001 | 0 }
b, -a, c | -x, -y, -z	{ -1 ‖ 4-001 | 0 }
b, a, -c | -x, -y, -z	{ -1 ‖ 2110 | 0 }
-b, -a, -c | -x, -y, -z	{ -1 ‖ 21-10 | 0 }
-a, c, b | -x, -y, -z	{ -1 ‖ 2011 | 0 }
-a, -c, -b | -x, -y, -z	{ -1 ‖ 201-1 | 0 }
c, -b, a | -x, -y, -z	{ -1 ‖ 2101 | 0 }
-c, -b, -a | -x, -y, -z	{ -1 ‖ 2-101 | 0 }
-a, c, -b | -x, -y, -z	{ -1 ‖ -4+100 | 0 }
-a, -c, b | -x, -y, -z	{ -1 ‖ -4-100 | 0 }
-c, -b, a | -x, -y, -z	{ -1 ‖ -4+010 | 0 }
c, -b, -a | -x, -y, -z	{ -1 ‖ -4-010 | 0 }
b, -a, -c | -x, -y, -z	{ -1 ‖ -4+001 | 0 }
-b, a, -c | -x, -y, -z	{ -1 ‖ -4-001 | 0 }
-b, -a, c | -x, -y, -z	{ -1 ‖ m110 | 0 }
b, a, c | -x, -y, -z	{ -1 ‖ m1-10 | 0 }
a, -c, -b | -x, -y, -z	{ -1 ‖ m011 | 0 }
a, c, b | -x, -y, -z	{ -1 ‖ m01-1 | 0 }
-c, b, -a | -x, -y, -z	{ -1 ‖ m101 | 0 }
c, b, a | -x, -y, -z	{ -1 ‖ m-101 | 0 }
a, b, c | -x, y, z	{ m ‖ 1 | 0 }
a, -b, -c | -x, y, z	{ m ‖ 2100 | 0 }
-a, b, -c | -x, y, z	{ m ‖ 2010 | 0 }
-a, -b, c | -x, y, z	{ m ‖ 2001 | 0 }
c, a, b | -x, y, z	{ m ‖ 3+111 | 0 }
b, c, a | -x, y, z	{ m ‖ 3-111 | 0 }
-b, c, -a | -x, y, z	{ m ‖ 3-1-1-1 | 0 }
-c, -a, b | -x, y, z	{ m ‖ 3+1-1-1 | 0 }
-b, -c, a | -x, y, z	{ m ‖ 3--11-1 | 0 }
c, -a, -b | -x, y, z	{ m ‖ 3+-11-1 | 0 }
b, -c, -a | -x, y, z	{ m ‖ 3--1-11 | 0 }
-c, a, -b | -x, y, z	{ m ‖ 3+-1-11 | 0 }
-a, -b, -c | -x, y, z	{ m ‖ -1 | 0 }
-a, b, c | -x, y, z	{ m ‖ m100 | 0 }
a, -b, c | -x, y, z	{ m ‖ m010 | 0 }
a, b, -c | -x, y, z	{ m ‖ m001 | 0 }
-c, -a, -b | -x, y, z	{ m ‖ -3+111 | 0 }
-b, -c, -a | -x, y, z	{ m ‖ -3-111 | 0 }
b, -c, a | -x, y, z	{ m ‖ -3-1-1-1 | 0 }
c, a, -b | -x, y, z	{ m ‖ -3+1-1-1 | 0 }
b, c, -a | -x, y, z	{ m ‖ -3--11-1 | 0 }
-c, a, b | -x, y, z	{ m ‖ -3+-11-1 | 0 }
-b, c, a | -x, y, z	{ m ‖ -3--1-11 | 0 }
c, -a, b | -x, y, z	{ m ‖ -3+-1-11 | 0 }
a, -c, b | x, -y, -z	{ 2 ‖ 4+100 | 0 }
a, c, -b | x, -y, -z	{ 2 ‖ 4-100 | 0 }
c, b, -a | x, -y, -z	{ 2 ‖ 4+010 | 0 }
-c, b, a | x, -y, -z	{ 2 ‖ 4-010 | 0 }
-b, a, c | x, -y, -z	{ 2 ‖ 4+001 | 0 }
b, -a, c | x, -y, -z	{ 2 ‖ 4-001 | 0 }
b, a, -c | x, -y, -z	{ 2 ‖ 2110 | 0 }
-b, -a, -c | x, -y, -z	{ 2 ‖ 21-10 | 0 }
-a, c, b | x, -y, -z	{ 2 ‖ 2011 | 0 }
-a, -c, -b | x, -y, -z	{ 2 ‖ 201-1 | 0 }
c, -b, a | x, -y, -z	{ 2 ‖ 2101 | 0 }
-c, -b, -a | x, -y, -z	{ 2 ‖ 2-101 | 0 }
-a, c, -b | x, -y, -z	{ 2 ‖ -4+100 | 0 }
-a, -c, b | x, -y, -z	{ 2 ‖ -4-100 | 0 }
-c, -b, a | x, -y, -z	{ 2 ‖ -4+010 | 0 }
c, -b, -a | x, -y, -z	{ 2 ‖ -4-010 | 0 }
b, -a, -c | x, -y, -z	{ 2 ‖ -4+001 | 0 }
-b, a, -c | x, -y, -z	{ 2 ‖ -4-001 | 0 }
-b, -a, c | x, -y, -z	{ 2 ‖ m110 | 0 }
b, a, c | x, -y, -z	{ 2 ‖ m1-10 | 0 }
a, -c, -b | x, -y, -z	{ 2 ‖ m011 | 0 }
a, c, b | x, -y, -z	{ 2 ‖ m01-1 | 0 }
-c, b, -a | x, -y, -z	{ 2 ‖ m101 | 0 }
c, b, a | x, -y, -z	{ 2 ‖ m-101 | 0 }

Wyckoff Positions

WP	Site symmetry	Representative
1a	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{-3}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(0,0,0 | 0,0,0)
1b	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{-3}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(1/2,1/2,1/2 | 0,0,0)
3c	${\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{4}/{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}.{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(0,1/2,1/2 | 0,0,0)
3d	${\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{4}/{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}.{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(1/2,0,0 | 0,0,0)
6e	${\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{4}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}.{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(a,0,0 | 0,0,0)
6f	${\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{4}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}.{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(a,1/2,1/2 | 0,0,0)
8g	$.{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{3}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(a,a,a | 0,0,0)
12h	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{2}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}..{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(a,1/2,0 | 0,0,z)
12i	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}.{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{2}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(0,b,b | 0,0,0)
12j	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}.{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{2}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(1/2,b,b | 0,0,0)
24k	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}..{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(0,b,c | 0,0,z)
24l	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}..{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(1/2,b,c | 0,0,z)
24m	$..{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(a,a,c | 0,0,0)
48n	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{1}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(a,b,c | 0,0,z)

Spin Brillouin Zone & k-little co-groups

Wavevector-k	Little co-group
Γ:(0,0,0)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{-3}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$
R:(1/2,1/2,1/2)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{-3}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$
M:(1/2,1/2,0)	${\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{4/}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$
X:(0,1/2,0)	${\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{4/}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$
Δ:(0,v,0)	${\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{4/}{\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
T:(1/2,1/2,w)	${\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{4/}{\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
Λ:(u,u,u)	${\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{-3}{\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
S:(u,1/2,u)	${\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
Σ:(u,u,0)	${\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
Z:(u,1/2,0)	${\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
A:(u,v,0)	${\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{2/}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
B:(u,1/2,w)	${\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{2/}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
C:(u,u,w)	${\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{2/}{\phantom{A}}_{\phantom{}}^{\phantom{2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}2}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }}\text{1}$
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)

12h

k-vector	k-vector-G↑	A1↑G(12)
Γ:(0,0,0)	Γ:(0,0,0)	${\Gamma }_1^{S,+}(2)\oplus {\Gamma }_2^{S,+}{\Gamma }_3^{S,+}(4)\oplus {\Gamma }_4^{S,-}(6)$
M:(1/2,1/2,0)	M:(1/2,1/2,0)	$M_1^{S,+}(2)\oplus M_2^{S,+}(2)\oplus M_3^{S,-}(2)\oplus M_4^{S,+}(2)\oplus 2M_4^{S,-}(2)$
R:(1/2,1/2,1/2)	R:(1/2,1/2,1/2)	$R_4^{S,+}(6)\oplus R_4^{S,-}(6)$
X:(0,1/2,0)	X:(0,1/2,0)	$2X_1^{S,+}(2)\oplus X_2^{S,+}(2)\oplus X_2^{S,-}(2)\oplus 2X_4^{S,-}(2)$
Δ:(0,v,0)	Δ:(0,v,0)	$4{\Delta }_1^S(2)\oplus {\Delta }_3^S(2)\oplus {\Delta }_4^S(2)$
Λ:(u,u,u)	Λ:(u,u,u)	$2{\Lambda }_1^S(2)\oplus 2{\Lambda }_2^S{\Lambda }_3^S(4)$
S:(u,1/2,u)	S:(u,1/2,u)	$3S_1^S(2)\oplus 3S_2^S(2)$
Σ:(u,u,0)	Σ:(u,u,0)	$5{\Sigma }_1^S(2)\oplus {\Sigma }_2^S(2)$
T:(1/2,1/2,w)	T:(1/2,1/2,w)	$T_1^S(2)\oplus T_2^S(2)\oplus 2T_3^S(2)\oplus 2T_4^S(2)$
Z:(u,1/2,0)	Z:(u,1/2,0)	$4Z_1^S(1)\oplus 2Z_3^S(1)\oplus 6Z_4^S(1)$	Spin Splitting
A:(u,v,0)	A:(u,v,0)	$10A_1^S(1)\oplus 2A_2^S(1)$	Spin Splitting
B:(u,1/2,w)	B:(u,1/2,w)	$6B_1^S(1)\oplus 6B_2^S(1)$	Spin Splitting
C:(u,u,w)	C:(u,u,w)	$6C_1^S(2)$
GP:(u,v,w)	GP:(u,v,w)	$12G{P}_1^S(1)$	Spin Splitting

24k

k-vector	k-vector-G↑	A'↑G(24)
Γ:(0,0,0)	Γ:(0,0,0)	${\Gamma }_1^{S,+}(2)\oplus {\Gamma }_2^{S,+}{\Gamma }_3^{S,+}(4)\oplus {\Gamma }_4^{S,+}(6)\oplus 2{\Gamma }_4^{S,-}(6)$
M:(1/2,1/2,0)	M:(1/2,1/2,0)	$3M_1^{S,+}(2)\oplus M_2^{S,+}(2)\oplus 2M_2^{S,-}(2)\oplus M_3^{S,+}(2)\oplus 2M_3^{S,-}(2)\oplus M_4^{S,+}(2)\oplus 2M_4^{S,-}(2)$
R:(1/2,1/2,1/2)	R:(1/2,1/2,1/2)	$R_1^{S,+}(2)\oplus R_2^{S,+}{R}_3^{S,+}(4)\oplus R_4^{S,+}(6)\oplus 2R_4^{S,-}(6)$
X:(0,1/2,0)	X:(0,1/2,0)	$3X_1^{S,+}(2)\oplus X_2^{S,+}(2)\oplus 2X_2^{S,-}(2)\oplus X_3^{S,+}(2)\oplus 2X_3^{S,-}(2)\oplus X_4^{S,+}(2)\oplus 2X_4^{S,-}(2)$
Δ:(0,v,0)	Δ:(0,v,0)	$5{\Delta }_1^S(2)\oplus {\Delta }_2^S(2)\oplus 3{\Delta }_3^S(2)\oplus 3{\Delta }_4^S(2)$
Λ:(u,u,u)	Λ:(u,u,u)	$4{\Lambda }_1^S(2)\oplus 4{\Lambda }_2^S{\Lambda }_3^S(4)$
S:(u,1/2,u)	S:(u,1/2,u)	$8S_1^S(2)\oplus 4S_2^S(2)$
Σ:(u,u,0)	Σ:(u,u,0)	$8{\Sigma }_1^S(2)\oplus 4{\Sigma }_2^S(2)$
T:(1/2,1/2,w)	T:(1/2,1/2,w)	$5T_1^S(2)\oplus T_2^S(2)\oplus 3T_3^S(2)\oplus 3T_4^S(2)$
Z:(u,1/2,0)	Z:(u,1/2,0)	$10Z_1^S(1)\oplus 2Z_2^S(1)\oplus 6Z_3^S(1)\oplus 6Z_4^S(1)$	Spin Splitting
A:(u,v,0)	A:(u,v,0)	$16A_1^S(1)\oplus 8A_2^S(1)$	Spin Splitting
B:(u,1/2,w)	B:(u,1/2,w)	$16B_1^S(1)\oplus 8B_2^S(1)$	Spin Splitting
C:(u,u,w)	C:(u,u,w)	$12C_1^S(2)$
GP:(u,v,w)	GP:(u,v,w)	$24G{P}_1^S(1)$	Spin Splitting

24l

k-vector	k-vector-G↑	A'↑G(24)
Γ:(0,0,0)	Γ:(0,0,0)	${\Gamma }_1^{S,+}(2)\oplus {\Gamma }_2^{S,+}{\Gamma }_3^{S,+}(4)\oplus {\Gamma }_4^{S,+}(6)\oplus 2{\Gamma }_4^{S,-}(6)$
M:(1/2,1/2,0)	M:(1/2,1/2,0)	$M_1^{S,+}(2)\oplus 2M_1^{S,-}(2)\oplus 3M_2^{S,+}(2)\oplus M_3^{S,+}(2)\oplus 2M_3^{S,-}(2)\oplus M_4^{S,+}(2)\oplus 2M_4^{S,-}(2)$
R:(1/2,1/2,1/2)	R:(1/2,1/2,1/2)	$R_1^{S,-}(2)\oplus R_2^{S,-}{R}_3^{S,-}(4)\oplus 2R_4^{S,+}(6)\oplus R_4^{S,-}(6)$
X:(0,1/2,0)	X:(0,1/2,0)	$2X_1^{S,+}(2)\oplus X_1^{S,-}(2)\oplus 2X_2^{S,+}(2)\oplus X_2^{S,-}(2)\oplus 2X_3^{S,+}(2)\oplus X_3^{S,-}(2)\oplus 3X_4^{S,-}(2)$
Δ:(0,v,0)	Δ:(0,v,0)	$5{\Delta }_1^S(2)\oplus {\Delta }_2^S(2)\oplus 3{\Delta }_3^S(2)\oplus 3{\Delta }_4^S(2)$
Λ:(u,u,u)	Λ:(u,u,u)	$4{\Lambda }_1^S(2)\oplus 4{\Lambda }_2^S{\Lambda }_3^S(4)$
S:(u,1/2,u)	S:(u,1/2,u)	$4S_1^S(2)\oplus 8S_2^S(2)$
Σ:(u,u,0)	Σ:(u,u,0)	$8{\Sigma }_1^S(2)\oplus 4{\Sigma }_2^S(2)$
T:(1/2,1/2,w)	T:(1/2,1/2,w)	$T_1^S(2)\oplus 5T_2^S(2)\oplus 3T_3^S(2)\oplus 3T_4^S(2)$
Z:(u,1/2,0)	Z:(u,1/2,0)	$6Z_1^S(1)\oplus 6Z_2^S(1)\oplus 2Z_3^S(1)\oplus 10Z_4^S(1)$	Spin Splitting
A:(u,v,0)	A:(u,v,0)	$16A_1^S(1)\oplus 8A_2^S(1)$	Spin Splitting
B:(u,1/2,w)	B:(u,1/2,w)	$8B_1^S(1)\oplus 16B_2^S(1)$	Spin Splitting
C:(u,u,w)	C:(u,u,w)	$12C_1^S(2)$
GP:(u,v,w)	GP:(u,v,w)	$24G{P}_1^S(1)$	Spin Splitting

48n

k-vector	k-vector-G↑	A↑G(48)
Γ:(0,0,0)	Γ:(0,0,0)	${\Gamma }_1^{S,+}(2)\oplus {\Gamma }_1^{S,-}(2)\oplus {\Gamma }_2^{S,+}{\Gamma }_3^{S,+}(4)\oplus {\Gamma }_2^{S,-}{\Gamma }_3^{S,-}(4)\oplus 3{\Gamma }_4^{S,+}(6)\oplus 3{\Gamma }_4^{S,-}(6)$
M:(1/2,1/2,0)	M:(1/2,1/2,0)	$3M_1^{S,+}(2)\oplus 3M_1^{S,-}(2)\oplus 3M_2^{S,+}(2)\oplus 3M_2^{S,-}(2)\oplus 3M_3^{S,+}(2)\oplus 3M_3^{S,-}(2)\oplus 3M_4^{S,+}(2)\oplus 3M_4^{S,-}(2)$
R:(1/2,1/2,1/2)	R:(1/2,1/2,1/2)	$R_1^{S,+}(2)\oplus R_1^{S,-}(2)\oplus R_2^{S,+}{R}_3^{S,+}(4)\oplus R_2^{S,-}{R}_3^{S,-}(4)\oplus 3R_4^{S,+}(6)\oplus 3R_4^{S,-}(6)$
X:(0,1/2,0)	X:(0,1/2,0)	$3X_1^{S,+}(2)\oplus 3X_1^{S,-}(2)\oplus 3X_2^{S,+}(2)\oplus 3X_2^{S,-}(2)\oplus 3X_3^{S,+}(2)\oplus 3X_3^{S,-}(2)\oplus 3X_4^{S,+}(2)\oplus 3X_4^{S,-}(2)$
Δ:(0,v,0)	Δ:(0,v,0)	$6{\Delta }_1^S(2)\oplus 6{\Delta }_2^S(2)\oplus 6{\Delta }_3^S(2)\oplus 6{\Delta }_4^S(2)$
Λ:(u,u,u)	Λ:(u,u,u)	$8{\Lambda }_1^S(2)\oplus 8{\Lambda }_2^S{\Lambda }_3^S(4)$
S:(u,1/2,u)	S:(u,1/2,u)	$12S_1^S(2)\oplus 12S_2^S(2)$
Σ:(u,u,0)	Σ:(u,u,0)	$12{\Sigma }_1^S(2)\oplus 12{\Sigma }_2^S(2)$
T:(1/2,1/2,w)	T:(1/2,1/2,w)	$6T_1^S(2)\oplus 6T_2^S(2)\oplus 6T_3^S(2)\oplus 6T_4^S(2)$
Z:(u,1/2,0)	Z:(u,1/2,0)	$12Z_1^S(1)\oplus 12Z_2^S(1)\oplus 12Z_3^S(1)\oplus 12Z_4^S(1)$	Spin Splitting
A:(u,v,0)	A:(u,v,0)	$24A_1^S(1)\oplus 24A_2^S(1)$	Spin Splitting
B:(u,1/2,w)	B:(u,1/2,w)	$24B_1^S(1)\oplus 24B_2^S(1)$	Spin Splitting
C:(u,u,w)	C:(u,u,w)	$24C_1^S(2)$
GP:(u,v,w)	GP:(u,v,w)	$48G{P}_1^S(1)$	Spin Splitting