Information of spin space group $P\ce{^{1}{2_{1}/}}\ce{^{1}{m}}\ce{^{\infty m}{1}}$ ( nSSG:11.11.1.1 )

General Positions

The continuously infinite group ^∞1 is omitted.

Coordinates	Seitz symbol
a, b, c | x, y, z	{ 1 ‖ 1 | 0 }
-a, b+1/2, -c | x, y, z	{ 1 ‖ 2010 | 0 1/2 0 }
-a, -b, -c | x, y, z	{ 1 ‖ -1 | 0 }
a, -b+1/2, c | x, y, z	{ 1 ‖ m010 | 0 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, -b, -c | -x, y, z	{ m ‖ -1 | 0 }
a, -b+1/2, c | -x, y, z	{ m ‖ m010 | 0 1/2 0 }

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}} $	(1/2,0,0 |0,0,z)
2c	$\ce{^{1}{-1}}\ce{^{\infty m}{1}} $	(0,0,1/2 |0,0,z)
2d	$\ce{^{1}{-1}}\ce{^{\infty m}{1}} $	(1/2,0,1/2 |0,0,z)
2e	$\ce{^{1}{m}}\ce{^{\infty m}{1}} $	(a,1/4,c |0,0,z)
4f	$\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{^{1}{m}}\ce{^{\infty m}{1}} $
B:(0,0,1/2)	$\ce{^{1}{2/}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $
C:(1/2,1/2,0)	$\ce{^{1}{2/}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $
D:(0,1/2,1/2)	$\ce{^{1}{2/}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $
E:(1/2,1/2,1/2)	$\ce{^{1}{2/}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $
Γ:(0,0,0)	$\ce{^{1}{2/}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $
Y:(1/2,0,0)	$\ce{^{1}{2/}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $
Z:(0,1/2,0)	$\ce{^{1}{2/}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $
F:(u,0,w)	$\ce{^{m}{2/}}\ce{^{1}{m}}\ce{^{\infty}{1}} $
G:(u,1/2,w)	$\ce{^{m}{2/}}\ce{^{1}{m}}\ce{^{\infty}{1}} $
Λ:(0,v,0)	$\ce{^{1}{2/}}\ce{^{m}{m}}\ce{^{\infty}{1}} $
U:(1/2,v,1/2)	$\ce{^{1}{2/}}\ce{^{m}{m}}\ce{^{\infty}{1}} $
V:(0,v,1/2)	$\ce{^{1}{2/}}\ce{^{m}{m}}\ce{^{\infty}{1}} $
W:(1/2,v,0)	$\ce{^{1}{2/}}\ce{^{m}{m}}\ce{^{\infty}{1}} $
GP:(u,v,w)	$\ce{^{m}{-1}}\ce{^{\infty}{1}} $

Spin Brillouin Zone

Band Representations (Magnon)

2a

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

2b

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

2c

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

2d

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

2e

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

4f

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