Information of spin space group $P_{a}\ce{^{1}{2_{1}}}\ce{^{\infty m}{1}}$ ( nSSG:4.4.2.1 )

General Positions

The continuously infinite group ^∞1 is omitted.

Coordinates	Seitz symbol
a, b, c | x, y, z	{ 1 ‖ 1 | 0 }
-a, b+1/2, -c | x, y, z	{ 1 ‖ 2010 | 0 1/2 0 }
a+1/2, b, c | -x, -y, -z	{ -1 ‖ 1 | 1/2 0 0 }
-a+1/2, b+1/2, -c | -x, -y, -z	{ -1 ‖ 2010 | 1/2 1/2 0 }
a, b, c | -x, y, z	{ m ‖ 1 | 0 }
-a, b+1/2, -c | -x, y, z	{ m ‖ 2010 | 0 1/2 0 }
a+1/2, b, c | x, -y, -z	{ 2 ‖ 1 | 1/2 0 0 }
-a+1/2, b+1/2, -c | x, -y, -z	{ 2 ‖ 2010 | 1/2 1/2 0 }

Wyckoff Positions

WP	Site symmetry	Representative
4a	$\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
A:(1/2,0,1/2)	$\ce{^{1}{2}}\ce{^{\infty /mm}{1}} $
B:(0,0,1/2)	$\ce{^{1}{2}}\ce{^{\infty /mm}{1}} $
C:(1/2,1/2,0)	$\ce{^{1}{2}}\ce{^{\infty /mm}{1}} $
D:(0,1/2,1/2)	$\ce{^{1}{2}}\ce{^{\infty /mm}{1}} $
E:(1/2,1/2,1/2)	$\ce{^{1}{2}}\ce{^{\infty /mm}{1}} $
Γ:(0,0,0)	$\ce{^{1}{2}}\ce{^{\infty /mm}{1}} $
Y:(1/2,0,0)	$\ce{^{1}{2}}\ce{^{\infty /mm}{1}} $
Z:(0,1/2,0)	$\ce{^{1}{2}}\ce{^{\infty /mm}{1}} $
F:(u,0,w)	$\ce{^{m}{2}}\ce{^{\infty 2}{1}} $
G:(u,1/2,w)	$\ce{^{m}{2}}\ce{^{\infty 2}{1}} $
Λ:(0,v,0)	$\ce{^{1}{2}}\ce{^{\infty 2}{1}} $
U:(1/2,v,1/2)	$\ce{^{1}{2}}\ce{^{\infty 2}{1}} $
V:(0,v,1/2)	$\ce{^{1}{2}}\ce{^{\infty 2}{1}} $
W:(1/2,v,0)	$\ce{^{1}{2}}\ce{^{\infty 2}{1}} $
GP:(u,v,w)	$\ce{^{1}{1}}\ce{^{\infty 2}{1}} $

Spin Brillouin Zone

Band Representations (Magnon)

4a

k-vector	A↑G(4)
A:(1/2,0,1/2)	$A_{1}^{S}(2)⊕A_{2}^{S}(2) $
B:(0,0,1/2)	$B_{1}^{S}(2)⊕B_{2}^{S}(2) $
C:(1/2,1/2,0)	$C_{1}^{S}C_{2}^{S}(4) $
D:(0,1/2,1/2)	$D_{1}^{S}D_{2}^{S}(4) $
E:(1/2,1/2,1/2)	$E_{1}^{S}E_{2}^{S}(4) $
Γ:(0,0,0)	$Γ_{1}^{S}(2)⊕Γ_{2}^{S}(2) $
Y:(1/2,0,0)	$Y_{1}^{S}(2)⊕Y_{2}^{S}(2) $
Z:(0,1/2,0)	$Z_{1}^{S}Z_{2}^{S}(4) $
F:(u,0,w)	$2F_{1}^{S}(2) $
G:(u,1/2,w)	$G_{1}^{S}G_{1}^{S}(4) $
Λ:(0,v,0)	$Λ_{1}^{S}(2)⊕Λ_{2}^{S}(2) $
U:(1/2,v,1/2)	$U_{1}^{S}(2)⊕U_{2}^{S}(2) $
V:(0,v,1/2)	$V_{1}^{S}(2)⊕V_{2}^{S}(2) $
W:(1/2,v,0)	$W_{1}^{S}(2)⊕W_{2}^{S}(2) $
GP:(u,v,w)	$2GP_{1}^{S}(2) $