Information of spin space group $P{\phantom{A}}_{\phantom{}}^{\phantom{\text{-}1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\text{-}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{n}{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{a}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$ ( nSSG:30.53.1.1 )

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

4e

k-vector	k-vector-G↑	A↑G(4)
Γ:(0,0,0)	Γ:(0,0,0)	${\Gamma }_1^S(2)\oplus {\Gamma }_2^S(2)$
R:(1/2,-1/2,-1/2)	R:(1/2,1/2,1/2)	$R_1^S(4)$
S:(1/2,-1/2,0)	U:(1/2,0,1/2)	$(S)U_1^S{U}_2^S(4)$
T:(0,-1/2,-1/2)	S:(1/2,1/2,0)	$(T)S_1^S(4)$
U:(1/2,0,-1/2)	T:(0,1/2,1/2)	$(U)T_1^S(4)$
X:(1/2,0,0)	Z:(0,0,1/2)	$(X)Z_1^S{Z}_2^S(4)$
Y:(0,-1/2,0)	X:(1/2,0,0)	$(Y)X_1^S(2)\oplus (Y)X_2^S(2)$
Z:(0,0,-1/2)	Y:(0,1/2,0)	$(Z)Y_1^S(4)$
A:(u,0,-1/2)	H:(0,1/2,u)	$(A)H_1^S(4)$
B:(0,v,-1/2)	C:(-v,1/2,0)	$(B)C_1^S{C}_2^S(4)$
C:(u,-1/2,0)	G:(1/2,0,u)	$(C)G_1^S(2)\oplus (C)G_2^S(2)$
D:(1/2,v,0)	A:(-v,0,1/2)	$(D)A_1^S{A}_2^S(4)$
Δ:(0,v,0)	Σ:(-v,0,0)	$(\Delta ){\Sigma }_1^S(2)\oplus (\Delta ){\Sigma }_2^S(2)$
E:(u,-1/2,-1/2)	Q:(1/2,1/2,u)	$(E)Q_1^S(4)$
G:(1/2,0,w)	B:(0,-w,1/2)	$(G)B_1^S{B}_2^S(4)$
H:(0,-1/2,w)	D:(1/2,-w,0)	$(H)D_1^S(2)\oplus (H)D_2^S(2)$
Λ:(0,0,w)	Δ:(0,-w,0)	$(\Lambda ){\Delta }_1^S(2)\oplus (\Lambda ){\Delta }_2^S(2)$
P:(1/2,v,-1/2)	E:(-v,1/2,1/2)	$(P)E_1^S(2)\oplus (P)E_2^S(2)$
Q:(1/2,-1/2,w)	P:(1/2,-w,1/2)	$(Q)P_1^S{P}_2^S(4)$
Σ:(u,0,0)	Λ:(0,0,u)	$(\Sigma ){\Lambda }_1^S(2)\oplus (\Sigma ){\Lambda }_2^S(2)$
K:(0,v,w)	V:(-v,-w,0)	$2(K)V_1^S(2)$
L:(1/2,v,w)	W:(-v,-w,1/2)	$2(L)W_1^S(2)$
M:(u,0,w)	K:(0,-w,u)	$(M)K_1^S(2)\oplus (M)K_2^S(2)$
N:(u,-1/2,w)	L:(1/2,-w,u)	$(N)L_1^S(2)\oplus (N)L_2^S(2)$
V:(u,v,0)	M:(-v,0,u)	$(V)M_1^S(2)\oplus (V)M_2^S(2)$
W:(u,v,-1/2)	N:(-v,1/2,u)	$(W)N_1^S(2)\oplus (W)N_2^S(2)$
GP:(u,v,w)	GP:(-v,-w,u)	$2G{P}_1^S(2)$

4f

k-vector	k-vector-G↑	A↑G(4)
Γ:(0,0,0)	Γ:(0,0,0)	${\Gamma }_1^S(2)\oplus {\Gamma }_2^S(2)$
R:(1/2,-1/2,-1/2)	R:(1/2,1/2,1/2)	$R_1^S(4)$
S:(1/2,-1/2,0)	U:(1/2,0,1/2)	$(S)U_3^S{U}_4^S(4)$
T:(0,-1/2,-1/2)	S:(1/2,1/2,0)	$(T)S_1^S(4)$
U:(1/2,0,-1/2)	T:(0,1/2,1/2)	$(U)T_1^S(4)$
X:(1/2,0,0)	Z:(0,0,1/2)	$(X)Z_1^S{Z}_2^S(4)$
Y:(0,-1/2,0)	X:(1/2,0,0)	$(Y)X_3^S(2)\oplus (Y)X_4^S(2)$
Z:(0,0,-1/2)	Y:(0,1/2,0)	$(Z)Y_1^S(4)$
A:(u,0,-1/2)	H:(0,1/2,u)	$(A)H_1^S(4)$
B:(0,v,-1/2)	C:(-v,1/2,0)	$(B)C_1^S{C}_2^S(4)$
C:(u,-1/2,0)	G:(1/2,0,u)	$(C)G_3^S(2)\oplus (C)G_4^S(2)$
D:(1/2,v,0)	A:(-v,0,1/2)	$(D)A_1^S{A}_2^S(4)$
Δ:(0,v,0)	Σ:(-v,0,0)	$(\Delta ){\Sigma }_1^S(2)\oplus (\Delta ){\Sigma }_2^S(2)$
E:(u,-1/2,-1/2)	Q:(1/2,1/2,u)	$(E)Q_1^S(4)$
G:(1/2,0,w)	B:(0,-w,1/2)	$(G)B_1^S{B}_2^S(4)$
H:(0,-1/2,w)	D:(1/2,-w,0)	$(H)D_1^S(2)\oplus (H)D_2^S(2)$
Λ:(0,0,w)	Δ:(0,-w,0)	$(\Lambda ){\Delta }_1^S(2)\oplus (\Lambda ){\Delta }_2^S(2)$
P:(1/2,v,-1/2)	E:(-v,1/2,1/2)	$(P)E_1^S(2)\oplus (P)E_2^S(2)$
Q:(1/2,-1/2,w)	P:(1/2,-w,1/2)	$(Q)P_1^S{P}_2^S(4)$
Σ:(u,0,0)	Λ:(0,0,u)	$(\Sigma ){\Lambda }_1^S(2)\oplus (\Sigma ){\Lambda }_2^S(2)$
K:(0,v,w)	V:(-v,-w,0)	$2(K)V_1^S(2)$
L:(1/2,v,w)	W:(-v,-w,1/2)	$2(L)W_1^S(2)$
M:(u,0,w)	K:(0,-w,u)	$(M)K_1^S(2)\oplus (M)K_2^S(2)$
N:(u,-1/2,w)	L:(1/2,-w,u)	$(N)L_1^S(2)\oplus (N)L_2^S(2)$
V:(u,v,0)	M:(-v,0,u)	$(V)M_1^S(2)\oplus (V)M_2^S(2)$
W:(u,v,-1/2)	N:(-v,1/2,u)	$(W)N_1^S(2)\oplus (W)N_2^S(2)$
GP:(u,v,w)	GP:(-v,-w,u)	$2G{P}_1^S(2)$

8i

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)	$2R_1^S(4)$
S:(1/2,-1/2,0)	U:(1/2,0,1/2)	$(S)U_1^S{U}_2^S(4)\oplus (S)U_3^S{U}_4^S(4)$
T:(0,-1/2,-1/2)	S:(1/2,1/2,0)	$2(T)S_1^S(4)$
U:(1/2,0,-1/2)	T:(0,1/2,1/2)	$2(U)T_1^S(4)$
X:(1/2,0,0)	Z:(0,0,1/2)	$(X)Z_1^S{Z}_2^S(4)\oplus (X)Z_3^S{Z}_4^S(4)$
Y:(0,-1/2,0)	X:(1/2,0,0)	$(Y)X_1^S(2)\oplus (Y)X_2^S(2)\oplus (Y)X_3^S(2)\oplus (Y)X_4^S(2)$
Z:(0,0,-1/2)	Y:(0,1/2,0)	$2(Z)Y_1^S(4)$
A:(u,0,-1/2)	H:(0,1/2,u)	$2(A)H_1^S(4)$
B:(0,v,-1/2)	C:(-v,1/2,0)	$2(B)C_1^S{C}_2^S(4)$
C:(u,-1/2,0)	G:(1/2,0,u)	$(C)G_1^S(2)\oplus (C)G_2^S(2)\oplus (C)G_3^S(2)\oplus (C)G_4^S(2)$
D:(1/2,v,0)	A:(-v,0,1/2)	$2(D)A_1^S{A}_2^S(4)$
Δ:(0,v,0)	Σ:(-v,0,0)	$2(\Delta ){\Sigma }_1^S(2)\oplus 2(\Delta ){\Sigma }_2^S(2)$
E:(u,-1/2,-1/2)	Q:(1/2,1/2,u)	$2(E)Q_1^S(4)$
G:(1/2,0,w)	B:(0,-w,1/2)	$2(G)B_1^S{B}_2^S(4)$
H:(0,-1/2,w)	D:(1/2,-w,0)	$2(H)D_1^S(2)\oplus 2(H)D_2^S(2)$
Λ:(0,0,w)	Δ:(0,-w,0)	$2(\Lambda ){\Delta }_1^S(2)\oplus 2(\Lambda ){\Delta }_2^S(2)$
P:(1/2,v,-1/2)	E:(-v,1/2,1/2)	$2(P)E_1^S(2)\oplus 2(P)E_2^S(2)$
Q:(1/2,-1/2,w)	P:(1/2,-w,1/2)	$2(Q)P_1^S{P}_2^S(4)$
Σ:(u,0,0)	Λ:(0,0,u)	$(\Sigma ){\Lambda }_1^S(2)\oplus (\Sigma ){\Lambda }_2^S(2)\oplus (\Sigma ){\Lambda }_3^S(2)\oplus (\Sigma ){\Lambda }_4^S(2)$
K:(0,v,w)	V:(-v,-w,0)	$4(K)V_1^S(2)$
L:(1/2,v,w)	W:(-v,-w,1/2)	$4(L)W_1^S(2)$
M:(u,0,w)	K:(0,-w,u)	$2(M)K_1^S(2)\oplus 2(M)K_2^S(2)$
N:(u,-1/2,w)	L:(1/2,-w,u)	$2(N)L_1^S(2)\oplus 2(N)L_2^S(2)$
V:(u,v,0)	M:(-v,0,u)	$2(V)M_1^S(2)\oplus 2(V)M_2^S(2)$
W:(u,v,-1/2)	N:(-v,1/2,u)	$2(W)N_1^S(2)\oplus 2(W)N_2^S(2)$
GP:(u,v,w)	GP:(-v,-w,u)	$4G{P}_1^S(2)$