Information of spin space group $P\ce{^{\text{-}1}{\text{-}1}}\ce{^{\infty m}{1}}$ ( nSSG:1.2.1.1 )

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 ‖ -1 | 0 }
a, b, c | -x, y, z	{ m ‖ 1 | 0 }
-a, -b, -c | x, -y, -z	{ 2 ‖ -1 | 0 }

Wyckoff Positions

WP	Site symmetry	Representative
1a	$\ce{^{-1}{-1}}\ce{^{\infty m}{1}} $	(0,0,0 | 0,0,0)
1b	$\ce{^{-1}{-1}}\ce{^{\infty m}{1}} $	(0,0,1/2 | 0,0,0)
1c	$\ce{^{-1}{-1}}\ce{^{\infty m}{1}} $	(0,1/2,0 | 0,0,0)
1d	$\ce{^{-1}{-1}}\ce{^{\infty m}{1}} $	(1/2,0,0 | 0,0,0)
1e	$\ce{^{-1}{-1}}\ce{^{\infty m}{1}} $	(1/2,1/2,0 | 0,0,0)
1f	$\ce{^{-1}{-1}}\ce{^{\infty m}{1}} $	(1/2,0,1/2 | 0,0,0)
1g	$\ce{^{-1}{-1}}\ce{^{\infty m}{1}} $	(0,1/2,1/2 | 0,0,0)
1h	$\ce{^{-1}{-1}}\ce{^{\infty m}{1}} $	(1/2,1/2,1/2 | 0,0,0)
2i	$\ce{^{1}{1}}\ce{^{\infty m}{1}} $	(a,b,c | 0,0,z)

Spin Brillouin Zone & k-little co-groups

Wavevector-k	Little co-group
Γ:(0,0,0)	$\ce{^{-1}{-1}}\ce{^{\infty m}{1}} $
R:(1/2,1/2,1/2)	$\ce{^{-1}{-1}}\ce{^{\infty m}{1}} $
T:(0,1/2,1/2)	$\ce{^{-1}{-1}}\ce{^{\infty m}{1}} $
U:(1/2,0,1/2)	$\ce{^{-1}{-1}}\ce{^{\infty m}{1}} $
V:(1/2,1/2,0)	$\ce{^{-1}{-1}}\ce{^{\infty m}{1}} $
X:(1/2,0,0)	$\ce{^{-1}{-1}}\ce{^{\infty m}{1}} $
Y:(0,1/2,0)	$\ce{^{-1}{-1}}\ce{^{\infty m}{1}} $
Z:(0,0,1/2)	$\ce{^{-1}{-1}}\ce{^{\infty m}{1}} $
GP:(u,v,w)	$\ce{^{-1}{-1}}\ce{^{\infty}{1}} $

Spin Brillouin Zone

Band Representations (Magnon)

2i

k-vector	k-vector-G↑	A↑G(2)
Γ:(0,0,0)	Γ:(0,0,0)	$Γ_{1}^{S}(2) $
R:(1/2,1/2,1/2)	R:(1/2,1/2,1/2)	$R_{1}^{S}(2) $
T:(0,1/2,1/2)	T:(0,1/2,1/2)	$T_{1}^{S}(2) $
U:(1/2,0,1/2)	U:(1/2,0,1/2)	$U_{1}^{S}(2) $
V:(1/2,1/2,0)	V:(1/2,1/2,0)	$V_{1}^{S}(2) $
X:(1/2,0,0)	X:(1/2,0,0)	$X_{1}^{S}(2) $
Y:(0,1/2,0)	Y:(0,1/2,0)	$Y_{1}^{S}(2) $
Z:(0,0,1/2)	Z:(0,0,1/2)	$Z_{1}^{S}(2) $
GP:(u,v,w)	GP:(u,v,w)	$GP_{1}^{S}(2)$