Information of spin space group $P_{S}\ce{^{1}{\text{-}1}}\ce{^{\infty m}{1}}$ ( nSSG:2.2.2.1 )

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

Wyckoff Positions

WP	Site symmetry	Representative
2a	$\ce{^{1}{-1}}\ce{^{\infty m}{1}} $	(0,0,0 | 0,0,z)
2b	$\ce{^{-1}{-1}}\ce{^{\infty m}{1}} $	(0,0,1/4 | 0,0,0)
2c	$\ce{^{1}{-1}}\ce{^{\infty m}{1}} $	(0,1/2,0 | 0,0,z)
2d	$\ce{^{1}{-1}}\ce{^{\infty m}{1}} $	(1/2,0,0 | 0,0,z)
2e	$\ce{^{1}{-1}}\ce{^{\infty m}{1}} $	(1/2,1/2,0 | 0,0,z)
2f	$\ce{^{-1}{-1}}\ce{^{\infty m}{1}} $	(1/2,0,1/4 | 0,0,0)
2g	$\ce{^{-1}{-1}}\ce{^{\infty m}{1}} $	(0,1/2,1/4 | 0,0,0)
2h	$\ce{^{-1}{-1}}\ce{^{\infty m}{1}} $	(1/2,1/2,1/4 | 0,0,0)
4i	$\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 /mm}{1}} $
R:(1/2,1/2,1/2)	$\ce{^{1}{-1}}\ce{^{\infty /mm}{1}} $
T:(0,1/2,1/2)	$\ce{^{1}{-1}}\ce{^{\infty /mm}{1}} $
U:(1/2,0,1/2)	$\ce{^{1}{-1}}\ce{^{\infty /mm}{1}} $
V:(1/2,1/2,0)	$\ce{^{1}{-1}}\ce{^{\infty /mm}{1}} $
X:(1/2,0,0)	$\ce{^{1}{-1}}\ce{^{\infty /mm}{1}} $
Y:(0,1/2,0)	$\ce{^{1}{-1}}\ce{^{\infty /mm}{1}} $
Z:(0,0,1/2)	$\ce{^{1}{-1}}\ce{^{\infty /mm}{1}} $
GP:(u,v,w)	$\ce{^{m}{-1}}\ce{^{\infty 2}{1}} $

Spin Brillouin Zone

Band Representations (Magnon)

2a

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

2c

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

2d

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

2e

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

4i

k-vector	A↑G(4)
Γ:(0,0,0)	$Γ_{1}^{S,+}(2)⊕Γ_{1}^{S,-}(2) $
R:(1/2,1/2,1/2)	$R_{1}^{S,+}(2)⊕R_{1}^{S,-}(2) $
T:(0,1/2,1/2)	$T_{1}^{S,+}(2)⊕T_{1}^{S,-}(2) $
U:(1/2,0,1/2)	$U_{1}^{S,+}(2)⊕U_{1}^{S,-}(2) $
V:(1/2,1/2,0)	$V_{1}^{S,+}(2)⊕V_{1}^{S,-}(2) $
X:(1/2,0,0)	$X_{1}^{S,+}(2)⊕X_{1}^{S,-}(2) $
Y:(0,1/2,0)	$Y_{1}^{S,+}(2)⊕Y_{1}^{S,-}(2) $
Z:(0,0,1/2)	$Z_{1}^{S,+}(2)⊕Z_{1}^{S,-}(2) $
GP:(u,v,w)	$2GP_{1}^{S}(2) $