Information of spin space group $P{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{4/}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\text{-}1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\text{-}1}\text{c}{\phantom{A}}_{\phantom{}}^{\phantom{\text{-}1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\text{-}1}\text{c}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$ ( nSSG:83.124.1.1 )

General Positions

The continuously infinite group ^∞1 is omitted.

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

Wyckoff Positions

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

Spin Brillouin Zone & k-little co-groups

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

2b

k-vector	k-vector-G↑	Ag↑G(2)
Γ:(0,0,0)	Γ:(0,0,0)	${\Gamma }_1^{S,+}(2)$
A:(1/2,1/2,1/2)	A:(1/2,1/2,1/2)	$A_1^{S,+}(2)$
M:(1/2,1/2,0)	M:(1/2,1/2,0)	$M_1^{S,+}(2)$
R:(0,1/2,1/2)	R:(0,1/2,1/2)	$R_1^{S,+}(2)$
X:(0,1/2,0)	X:(0,1/2,0)	$X_1^{S,+}(2)$
Z:(0,0,1/2)	Z:(0,0,1/2)	$Z_1^{S,+}(2)$
Δ:(0,v,0)	Δ:(0,v,0)	${\Delta }_1^S(2)$
Λ:(0,0,w)	Λ:(0,0,w)	${\Lambda }_1^S(2)$
S:(u,u,1/2)	S:(u,u,1/2)	$S_1^S(2)$
Σ:(u,u,0)	Σ:(u,u,0)	${\Sigma }_1^S(2)$
T:(u,1/2,1/2)	T:(u,1/2,1/2)	$T_1^S(2)$
U:(0,v,1/2)	U:(0,v,1/2)	$U_1^S(2)$
V:(1/2,1/2,w)	V:(1/2,1/2,w)	$V_1^S(2)$
W:(0,1/2,w)	W:(0,1/2,w)	$W_1^S(2)$
Y:(u,1/2,0)	Y:(u,1/2,0)	$Y_1^S(2)$
B:(0,v,w)	B:(0,v,w)	$B_1^S(2)$
C:(u,u,w)	C:(u,u,w)	$C_1^S(2)$
D:(u,v,0)	D:(u,v,0)	$2D_1^S(1)$	Spin Splitting
E:(u,v,1/2)	E:(u,v,1/2)	$2E_1^S(1)$	Spin Splitting
F:(u,1/2,w)	F:(u,1/2,w)	$F_1^S(2)$
GP:(u,v,w)	GP:(u,v,w)	$2G{P}_1^S(1)$	Spin Splitting

2d

k-vector	k-vector-G↑	Ag↑G(2)
Γ:(0,0,0)	Γ:(0,0,0)	${\Gamma }_1^{S,+}(2)$
A:(1/2,1/2,1/2)	A:(1/2,1/2,1/2)	$A_2^{S,+}(2)$
M:(1/2,1/2,0)	M:(1/2,1/2,0)	$M_2^{S,+}(2)$
R:(0,1/2,1/2)	R:(0,1/2,1/2)	$R_2^{S,-}(2)$
X:(0,1/2,0)	X:(0,1/2,0)	$X_2^{S,-}(2)$
Z:(0,0,1/2)	Z:(0,0,1/2)	$Z_1^{S,+}(2)$
Δ:(0,v,0)	Δ:(0,v,0)	${\Delta }_1^S(2)$
Λ:(0,0,w)	Λ:(0,0,w)	${\Lambda }_1^S(2)$
S:(u,u,1/2)	S:(u,u,1/2)	$S_1^S(2)$
Σ:(u,u,0)	Σ:(u,u,0)	${\Sigma }_1^S(2)$
T:(u,1/2,1/2)	T:(u,1/2,1/2)	$T_1^S(2)$
U:(0,v,1/2)	U:(0,v,1/2)	$U_1^S(2)$
V:(1/2,1/2,w)	V:(1/2,1/2,w)	$V_2^S(2)$
W:(0,1/2,w)	W:(0,1/2,w)	$W_2^S(2)$
Y:(u,1/2,0)	Y:(u,1/2,0)	$Y_1^S(2)$
B:(0,v,w)	B:(0,v,w)	$B_1^S(2)$
C:(u,u,w)	C:(u,u,w)	$C_1^S(2)$
D:(u,v,0)	D:(u,v,0)	$2D_1^S(1)$	Spin Splitting
E:(u,v,1/2)	E:(u,v,1/2)	$2E_1^S(1)$	Spin Splitting
F:(u,1/2,w)	F:(u,1/2,w)	$F_1^S(2)$
GP:(u,v,w)	GP:(u,v,w)	$2G{P}_1^S(1)$	Spin Splitting

4e

k-vector	k-vector-G↑	Ag↑G(4)
Γ:(0,0,0)	Γ:(0,0,0)	${\Gamma }_1^{S,+}(2)\oplus {\Gamma }_2^{S,+}(2)$
A:(1/2,1/2,1/2)	A:(1/2,1/2,1/2)	$A_3^{S,-}{A}_4^{S,-}(4)$
M:(1/2,1/2,0)	M:(1/2,1/2,0)	$M_3^{S,-}{M}_4^{S,-}(4)$
R:(0,1/2,1/2)	R:(0,1/2,1/2)	$R_1^{S,+}(2)\oplus R_2^{S,-}(2)$
X:(0,1/2,0)	X:(0,1/2,0)	$X_1^{S,+}(2)\oplus X_2^{S,-}(2)$
Z:(0,0,1/2)	Z:(0,0,1/2)	$Z_1^{S,+}(2)\oplus Z_2^{S,+}(2)$
Δ:(0,v,0)	Δ:(0,v,0)	$2{\Delta }_1^S(2)$
Λ:(0,0,w)	Λ:(0,0,w)	${\Lambda }_1^S(2)\oplus {\Lambda }_2^S(2)$
S:(u,u,1/2)	S:(u,u,1/2)	$2S_1^S(2)$
Σ:(u,u,0)	Σ:(u,u,0)	$2{\Sigma }_1^S(2)$
T:(u,1/2,1/2)	T:(u,1/2,1/2)	$2T_1^S(2)$
U:(0,v,1/2)	U:(0,v,1/2)	$2U_1^S(2)$
V:(1/2,1/2,w)	V:(1/2,1/2,w)	$V_3^S{V}_4^S(4)$
W:(0,1/2,w)	W:(0,1/2,w)	$W_1^S(2)\oplus W_2^S(2)$
Y:(u,1/2,0)	Y:(u,1/2,0)	$2Y_1^S(2)$
B:(0,v,w)	B:(0,v,w)	$2B_1^S(2)$
C:(u,u,w)	C:(u,u,w)	$2C_1^S(2)$
D:(u,v,0)	D:(u,v,0)	$4D_1^S(1)$	Spin Splitting
E:(u,v,1/2)	E:(u,v,1/2)	$4E_1^S(1)$	Spin Splitting
F:(u,1/2,w)	F:(u,1/2,w)	$2F_1^S(2)$
GP:(u,v,w)	GP:(u,v,w)	$4G{P}_1^S(1)$	Spin Splitting

4g

k-vector	k-vector-G↑	A↑G(4)
Γ:(0,0,0)	Γ:(0,0,0)	${\Gamma }_1^{S,+}(2)\oplus {\Gamma }_1^{S,-}(2)$
A:(1/2,1/2,1/2)	A:(1/2,1/2,1/2)	$A_1^{S,+}(2)\oplus A_1^{S,-}(2)$
M:(1/2,1/2,0)	M:(1/2,1/2,0)	$M_1^{S,+}(2)\oplus M_1^{S,-}(2)$
R:(0,1/2,1/2)	R:(0,1/2,1/2)	$R_1^{S,+}(2)\oplus R_1^{S,-}(2)$
X:(0,1/2,0)	X:(0,1/2,0)	$X_1^{S,+}(2)\oplus X_1^{S,-}(2)$
Z:(0,0,1/2)	Z:(0,0,1/2)	$Z_1^{S,+}(2)\oplus Z_1^{S,-}(2)$
Δ:(0,v,0)	Δ:(0,v,0)	${\Delta }_1^S(2)\oplus {\Delta }_2^S(2)$
Λ:(0,0,w)	Λ:(0,0,w)	$2{\Lambda }_1^S(2)$
S:(u,u,1/2)	S:(u,u,1/2)	$S_1^S(2)\oplus S_2^S(2)$
Σ:(u,u,0)	Σ:(u,u,0)	${\Sigma }_1^S(2)\oplus {\Sigma }_2^S(2)$
T:(u,1/2,1/2)	T:(u,1/2,1/2)	$T_1^S(2)\oplus T_2^S(2)$
U:(0,v,1/2)	U:(0,v,1/2)	$U_1^S(2)\oplus U_2^S(2)$
V:(1/2,1/2,w)	V:(1/2,1/2,w)	$2V_1^S(2)$
W:(0,1/2,w)	W:(0,1/2,w)	$2W_1^S(2)$
Y:(u,1/2,0)	Y:(u,1/2,0)	$Y_1^S(2)\oplus Y_2^S(2)$
B:(0,v,w)	B:(0,v,w)	$2B_1^S(2)$
C:(u,u,w)	C:(u,u,w)	$2C_1^S(2)$
D:(u,v,0)	D:(u,v,0)	$2D_1^S(1)\oplus 2D_2^S(1)$	Spin Splitting
E:(u,v,1/2)	E:(u,v,1/2)	$2E_1^S(1)\oplus 2E_2^S(1)$	Spin Splitting
F:(u,1/2,w)	F:(u,1/2,w)	$2F_1^S(2)$
GP:(u,v,w)	GP:(u,v,w)	$4G{P}_1^S(1)$	Spin Splitting

4h

k-vector	k-vector-G↑	A↑G(4)
Γ:(0,0,0)	Γ:(0,0,0)	${\Gamma }_1^{S,+}(2)\oplus {\Gamma }_1^{S,-}(2)$
A:(1/2,1/2,1/2)	A:(1/2,1/2,1/2)	$A_2^{S,+}(2)\oplus A_2^{S,-}(2)$
M:(1/2,1/2,0)	M:(1/2,1/2,0)	$M_2^{S,+}(2)\oplus M_2^{S,-}(2)$
R:(0,1/2,1/2)	R:(0,1/2,1/2)	$R_2^{S,+}(2)\oplus R_2^{S,-}(2)$
X:(0,1/2,0)	X:(0,1/2,0)	$X_2^{S,+}(2)\oplus X_2^{S,-}(2)$
Z:(0,0,1/2)	Z:(0,0,1/2)	$Z_1^{S,+}(2)\oplus Z_1^{S,-}(2)$
Δ:(0,v,0)	Δ:(0,v,0)	${\Delta }_1^S(2)\oplus {\Delta }_2^S(2)$
Λ:(0,0,w)	Λ:(0,0,w)	$2{\Lambda }_1^S(2)$
S:(u,u,1/2)	S:(u,u,1/2)	$S_1^S(2)\oplus S_2^S(2)$
Σ:(u,u,0)	Σ:(u,u,0)	${\Sigma }_1^S(2)\oplus {\Sigma }_2^S(2)$
T:(u,1/2,1/2)	T:(u,1/2,1/2)	$T_1^S(2)\oplus T_2^S(2)$
U:(0,v,1/2)	U:(0,v,1/2)	$U_1^S(2)\oplus U_2^S(2)$
V:(1/2,1/2,w)	V:(1/2,1/2,w)	$2V_2^S(2)$
W:(0,1/2,w)	W:(0,1/2,w)	$2W_2^S(2)$
Y:(u,1/2,0)	Y:(u,1/2,0)	$Y_1^S(2)\oplus Y_2^S(2)$
B:(0,v,w)	B:(0,v,w)	$2B_1^S(2)$
C:(u,u,w)	C:(u,u,w)	$2C_1^S(2)$
D:(u,v,0)	D:(u,v,0)	$2D_1^S(1)\oplus 2D_2^S(1)$	Spin Splitting
E:(u,v,1/2)	E:(u,v,1/2)	$2E_1^S(1)\oplus 2E_2^S(1)$	Spin Splitting
F:(u,1/2,w)	F:(u,1/2,w)	$2F_1^S(2)$
GP:(u,v,w)	GP:(u,v,w)	$4G{P}_1^S(1)$	Spin Splitting

8i

k-vector	k-vector-G↑	A↑G(8)
Γ:(0,0,0)	Γ:(0,0,0)	${\Gamma }_1^{S,+}(2)\oplus {\Gamma }_1^{S,-}(2)\oplus {\Gamma }_2^{S,+}(2)\oplus {\Gamma }_2^{S,-}(2)$
A:(1/2,1/2,1/2)	A:(1/2,1/2,1/2)	$A_3^{S,+}{A}_4^{S,+}(4)\oplus A_3^{S,-}{A}_4^{S,-}(4)$
M:(1/2,1/2,0)	M:(1/2,1/2,0)	$M_3^{S,+}{M}_4^{S,+}(4)\oplus M_3^{S,-}{M}_4^{S,-}(4)$
R:(0,1/2,1/2)	R:(0,1/2,1/2)	$R_1^{S,+}(2)\oplus R_1^{S,-}(2)\oplus R_2^{S,+}(2)\oplus R_2^{S,-}(2)$
X:(0,1/2,0)	X:(0,1/2,0)	$X_1^{S,+}(2)\oplus X_1^{S,-}(2)\oplus X_2^{S,+}(2)\oplus X_2^{S,-}(2)$
Z:(0,0,1/2)	Z:(0,0,1/2)	$Z_1^{S,+}(2)\oplus Z_1^{S,-}(2)\oplus Z_2^{S,+}(2)\oplus Z_2^{S,-}(2)$
Δ:(0,v,0)	Δ:(0,v,0)	$2{\Delta }_1^S(2)\oplus 2{\Delta }_2^S(2)$
Λ:(0,0,w)	Λ:(0,0,w)	$2{\Lambda }_1^S(2)\oplus 2{\Lambda }_2^S(2)$
S:(u,u,1/2)	S:(u,u,1/2)	$2S_1^S(2)\oplus 2S_2^S(2)$
Σ:(u,u,0)	Σ:(u,u,0)	$2{\Sigma }_1^S(2)\oplus 2{\Sigma }_2^S(2)$
T:(u,1/2,1/2)	T:(u,1/2,1/2)	$2T_1^S(2)\oplus 2T_2^S(2)$
U:(0,v,1/2)	U:(0,v,1/2)	$2U_1^S(2)\oplus 2U_2^S(2)$
V:(1/2,1/2,w)	V:(1/2,1/2,w)	$2V_3^S{V}_4^S(4)$
W:(0,1/2,w)	W:(0,1/2,w)	$2W_1^S(2)\oplus 2W_2^S(2)$
Y:(u,1/2,0)	Y:(u,1/2,0)	$2Y_1^S(2)\oplus 2Y_2^S(2)$
B:(0,v,w)	B:(0,v,w)	$4B_1^S(2)$
C:(u,u,w)	C:(u,u,w)	$4C_1^S(2)$
D:(u,v,0)	D:(u,v,0)	$4D_1^S(1)\oplus 4D_2^S(1)$	Spin Splitting
E:(u,v,1/2)	E:(u,v,1/2)	$4E_1^S(1)\oplus 4E_2^S(1)$	Spin Splitting
F:(u,1/2,w)	F:(u,1/2,w)	$4F_1^S(2)$
GP:(u,v,w)	GP:(u,v,w)	$8G{P}_1^S(1)$	Spin Splitting

8m

k-vector	k-vector-G↑	A'↑G(8)
Γ:(0,0,0)	Γ:(0,0,0)	${\Gamma }_1^{S,+}(2)\oplus {\Gamma }_2^{S,+}(2)\oplus {\Gamma }_3^{S,-}{\Gamma }_4^{S,-}(4)$
A:(1/2,1/2,1/2)	A:(1/2,1/2,1/2)	$A_1^{S,+}(2)\oplus A_2^{S,+}(2)\oplus A_3^{S,-}{A}_4^{S,-}(4)$
M:(1/2,1/2,0)	M:(1/2,1/2,0)	$M_1^{S,+}(2)\oplus M_2^{S,+}(2)\oplus M_3^{S,-}{M}_4^{S,-}(4)$
R:(0,1/2,1/2)	R:(0,1/2,1/2)	$2R_1^{S,+}(2)\oplus 2R_2^{S,-}(2)$
X:(0,1/2,0)	X:(0,1/2,0)	$2X_1^{S,+}(2)\oplus 2X_2^{S,-}(2)$
Z:(0,0,1/2)	Z:(0,0,1/2)	$Z_1^{S,+}(2)\oplus Z_2^{S,+}(2)\oplus Z_3^{S,-}{Z}_4^{S,-}(4)$
Δ:(0,v,0)	Δ:(0,v,0)	$4{\Delta }_1^S(2)$
Λ:(0,0,w)	Λ:(0,0,w)	${\Lambda }_1^S(2)\oplus {\Lambda }_2^S(2)\oplus {\Lambda }_3^S{\Lambda }_4^S(4)$
S:(u,u,1/2)	S:(u,u,1/2)	$4S_1^S(2)$
Σ:(u,u,0)	Σ:(u,u,0)	$4{\Sigma }_1^S(2)$
T:(u,1/2,1/2)	T:(u,1/2,1/2)	$4T_1^S(2)$
U:(0,v,1/2)	U:(0,v,1/2)	$4U_1^S(2)$
V:(1/2,1/2,w)	V:(1/2,1/2,w)	$V_1^S(2)\oplus V_2^S(2)\oplus V_3^S{V}_4^S(4)$
W:(0,1/2,w)	W:(0,1/2,w)	$2W_1^S(2)\oplus 2W_2^S(2)$
Y:(u,1/2,0)	Y:(u,1/2,0)	$4Y_1^S(2)$
B:(0,v,w)	B:(0,v,w)	$4B_1^S(2)$
C:(u,u,w)	C:(u,u,w)	$4C_1^S(2)$
D:(u,v,0)	D:(u,v,0)	$8D_1^S(1)$	Spin Splitting
E:(u,v,1/2)	E:(u,v,1/2)	$8E_1^S(1)$	Spin Splitting
F:(u,1/2,w)	F:(u,1/2,w)	$4F_1^S(2)$
GP:(u,v,w)	GP:(u,v,w)	$8G{P}_1^S(1)$	Spin Splitting

16n

k-vector	k-vector-G↑	A↑G(16)
Γ:(0,0,0)	Γ:(0,0,0)	${\Gamma }_1^{S,+}(2)\oplus {\Gamma }_1^{S,-}(2)\oplus {\Gamma }_2^{S,+}(2)\oplus {\Gamma }_2^{S,-}(2)\oplus {\Gamma }_3^{S,+}{\Gamma }_4^{S,+}(4)\oplus {\Gamma }_3^{S,-}{\Gamma }_4^{S,-}(4)$
A:(1/2,1/2,1/2)	A:(1/2,1/2,1/2)	$A_1^{S,+}(2)\oplus A_1^{S,-}(2)\oplus A_2^{S,+}(2)\oplus A_2^{S,-}(2)\oplus A_3^{S,+}{A}_4^{S,+}(4)\oplus A_3^{S,-}{A}_4^{S,-}(4)$
M:(1/2,1/2,0)	M:(1/2,1/2,0)	$M_1^{S,+}(2)\oplus M_1^{S,-}(2)\oplus M_2^{S,+}(2)\oplus M_2^{S,-}(2)\oplus M_3^{S,+}{M}_4^{S,+}(4)\oplus M_3^{S,-}{M}_4^{S,-}(4)$
R:(0,1/2,1/2)	R:(0,1/2,1/2)	$2R_1^{S,+}(2)\oplus 2R_1^{S,-}(2)\oplus 2R_2^{S,+}(2)\oplus 2R_2^{S,-}(2)$
X:(0,1/2,0)	X:(0,1/2,0)	$2X_1^{S,+}(2)\oplus 2X_1^{S,-}(2)\oplus 2X_2^{S,+}(2)\oplus 2X_2^{S,-}(2)$
Z:(0,0,1/2)	Z:(0,0,1/2)	$Z_1^{S,+}(2)\oplus Z_1^{S,-}(2)\oplus Z_2^{S,+}(2)\oplus Z_2^{S,-}(2)\oplus Z_3^{S,+}{Z}_4^{S,+}(4)\oplus Z_3^{S,-}{Z}_4^{S,-}(4)$
Δ:(0,v,0)	Δ:(0,v,0)	$4{\Delta }_1^S(2)\oplus 4{\Delta }_2^S(2)$
Λ:(0,0,w)	Λ:(0,0,w)	$2{\Lambda }_1^S(2)\oplus 2{\Lambda }_2^S(2)\oplus 2{\Lambda }_3^S{\Lambda }_4^S(4)$
S:(u,u,1/2)	S:(u,u,1/2)	$4S_1^S(2)\oplus 4S_2^S(2)$
Σ:(u,u,0)	Σ:(u,u,0)	$4{\Sigma }_1^S(2)\oplus 4{\Sigma }_2^S(2)$
T:(u,1/2,1/2)	T:(u,1/2,1/2)	$4T_1^S(2)\oplus 4T_2^S(2)$
U:(0,v,1/2)	U:(0,v,1/2)	$4U_1^S(2)\oplus 4U_2^S(2)$
V:(1/2,1/2,w)	V:(1/2,1/2,w)	$2V_1^S(2)\oplus 2V_2^S(2)\oplus 2V_3^S{V}_4^S(4)$
W:(0,1/2,w)	W:(0,1/2,w)	$4W_1^S(2)\oplus 4W_2^S(2)$
Y:(u,1/2,0)	Y:(u,1/2,0)	$4Y_1^S(2)\oplus 4Y_2^S(2)$
B:(0,v,w)	B:(0,v,w)	$8B_1^S(2)$
C:(u,u,w)	C:(u,u,w)	$8C_1^S(2)$
D:(u,v,0)	D:(u,v,0)	$8D_1^S(1)\oplus 8D_2^S(1)$	Spin Splitting
E:(u,v,1/2)	E:(u,v,1/2)	$8E_1^S(1)\oplus 8E_2^S(1)$	Spin Splitting
F:(u,1/2,w)	F:(u,1/2,w)	$8F_1^S(2)$
GP:(u,v,w)	GP:(u,v,w)	$16G{P}_1^S(1)$	Spin Splitting