Information of spin space group $C\ce{^{1}{2/}}\ce{^{1}{c}}\ce{^{\infty m}{1}}$ ( nSSG:15.15.1.1 )

General Positions

The continuously infinite group ^∞1 is omitted.

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

Wyckoff Positions

WP	Site symmetry	Representative
4a	$\ce{^{1}{-1}}\ce{^{\infty m}{1}} $	(0,0,0 |0,0,z)
4b	$\ce{^{1}{-1}}\ce{^{\infty m}{1}} $	(0,1/2,0 |0,0,z)
4c	$\ce{^{1}{-1}}\ce{^{\infty m}{1}} $	(1/4,1/4,0 |0,0,z)
4d	$\ce{^{1}{-1}}\ce{^{\infty m}{1}} $	(1/4,1/4,1/2 |0,0,z)
4e	$\ce{^{1}{2}}\ce{^{\infty m}{1}} $	(0,b,1/4 |0,0,z)
8f	$\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:(0,0,1/2)	$\ce{^{1}{2/}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $
Γ:(0,0,0)	$\ce{^{1}{2/}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $
M:(0,1,1/2)	$\ce{^{1}{2/}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $
Y:(0,1,0)	$\ce{^{1}{2/}}\ce{^{1}{m}}\ce{^{\infty m}{1}} $
L:(1/2,1/2,1/2)	$\ce{^{1}{-1}}\ce{^{\infty m}{1}} $
V:(1/2,1/2,0)	$\ce{^{1}{-1}}\ce{^{\infty m}{1}} $
B:(u,0,w)	$\ce{^{m}{2/}}\ce{^{1}{m}}\ce{^{\infty}{1}} $
Λ:(0,v,0)	$\ce{^{1}{2/}}\ce{^{m}{m}}\ce{^{\infty}{1}} $
U:(0,v,1/2)	$\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)

4a

k-vector	Ag↑G(2)
A:(0,0,1/2)	$A_{1}^{S}(2) $
Γ:(0,0,0)	$Γ_{1}^{S,+}(1)⊕Γ_{2}^{S,+}(1) $
M:(0,1,1/2)	$M_{1}^{S}(2) $
Y:(0,1,0)	$Y_{1}^{S,+}(1)⊕Y_{2}^{S,+}(1) $
L:(1/2,1/2,1/2)	$L_{1}^{S,+}(1)⊕L_{1}^{S,-}(1) $
V:(1/2,1/2,0)	$2V_{1}^{S,+}(1) $
B:(u,0,w)	$B_{1}^{S}(1)⊕B_{2}^{S}(1) $
Λ:(0,v,0)	$Λ_{1}^{S}(1)⊕Λ_{2}^{S}(1) $
U:(0,v,1/2)	$U_{1}^{S}U_{2}^{S}(2) $
GP:(u,v,w)	$2GP_{1}^{S}(1) $

4b

k-vector	Ag↑G(2)
A:(0,0,1/2)	$A_{1}^{S}(2) $
Γ:(0,0,0)	$Γ_{1}^{S,+}(1)⊕Γ_{2}^{S,+}(1) $
M:(0,1,1/2)	$M_{1}^{S}(2) $
Y:(0,1,0)	$Y_{1}^{S,+}(1)⊕Y_{2}^{S,+}(1) $
L:(1/2,1/2,1/2)	$L_{1}^{S,+}(1)⊕L_{1}^{S,-}(1) $
V:(1/2,1/2,0)	$2V_{1}^{S,-}(1) $
B:(u,0,w)	$B_{1}^{S}(1)⊕B_{2}^{S}(1) $
Λ:(0,v,0)	$Λ_{1}^{S}(1)⊕Λ_{2}^{S}(1) $
U:(0,v,1/2)	$U_{1}^{S}U_{2}^{S}(2) $
GP:(u,v,w)	$2GP_{1}^{S}(1) $

4c

k-vector	Ag↑G(2)
A:(0,0,1/2)	$A_{1}^{S}(2) $
Γ:(0,0,0)	$Γ_{1}^{S,+}(1)⊕Γ_{2}^{S,+}(1) $
M:(0,1,1/2)	$M_{1}^{S}(2) $
Y:(0,1,0)	$Y_{1}^{S,-}(1)⊕Y_{2}^{S,-}(1) $
L:(1/2,1/2,1/2)	$2L_{1}^{S,-}(1) $
V:(1/2,1/2,0)	$V_{1}^{S,+}(1)⊕V_{1}^{S,-}(1) $
B:(u,0,w)	$B_{1}^{S}(1)⊕B_{2}^{S}(1) $
Λ:(0,v,0)	$Λ_{1}^{S}(1)⊕Λ_{2}^{S}(1) $
U:(0,v,1/2)	$U_{1}^{S}U_{2}^{S}(2) $
GP:(u,v,w)	$2GP_{1}^{S}(1) $

4d

k-vector	Ag↑G(2)
A:(0,0,1/2)	$A_{1}^{S}(2) $
Γ:(0,0,0)	$Γ_{1}^{S,+}(1)⊕Γ_{2}^{S,+}(1) $
M:(0,1,1/2)	$M_{1}^{S}(2) $
Y:(0,1,0)	$Y_{1}^{S,-}(1)⊕Y_{2}^{S,-}(1) $
L:(1/2,1/2,1/2)	$2L_{1}^{S,+}(1) $
V:(1/2,1/2,0)	$V_{1}^{S,+}(1)⊕V_{1}^{S,-}(1) $
B:(u,0,w)	$B_{1}^{S}(1)⊕B_{2}^{S}(1) $
Λ:(0,v,0)	$Λ_{1}^{S}(1)⊕Λ_{2}^{S}(1) $
U:(0,v,1/2)	$U_{1}^{S}U_{2}^{S}(2) $
GP:(u,v,w)	$2GP_{1}^{S}(1) $

4e

k-vector	A↑G(2)
A:(0,0,1/2)	$A_{1}^{S}(2) $
Γ:(0,0,0)	$Γ_{1}^{S,+}(1)⊕Γ_{1}^{S,-}(1) $
M:(0,1,1/2)	$M_{1}^{S}(2) $
Y:(0,1,0)	$Y_{1}^{S,+}(1)⊕Y_{1}^{S,-}(1) $
L:(1/2,1/2,1/2)	$L_{1}^{S,+}(1)⊕L_{1}^{S,-}(1) $
V:(1/2,1/2,0)	$V_{1}^{S,+}(1)⊕V_{1}^{S,-}(1) $
B:(u,0,w)	$B_{1}^{S}(1)⊕B_{2}^{S}(1) $
Λ:(0,v,0)	$2Λ_{1}^{S}(1) $
U:(0,v,1/2)	$U_{1}^{S}U_{2}^{S}(2) $
GP:(u,v,w)	$2GP_{1}^{S}(1) $

8f

k-vector	A↑G(4)
A:(0,0,1/2)	$2A_{1}^{S}(2) $
Γ:(0,0,0)	$Γ_{1}^{S,+}(1)⊕Γ_{1}^{S,-}(1)⊕Γ_{2}^{S,+}(1)⊕Γ_{2}^{S,-}(1) $
M:(0,1,1/2)	$2M_{1}^{S}(2) $
Y:(0,1,0)	$Y_{1}^{S,+}(1)⊕Y_{1}^{S,-}(1)⊕Y_{2}^{S,+}(1)⊕Y_{2}^{S,-}(1) $
L:(1/2,1/2,1/2)	$2L_{1}^{S,+}(1)⊕2L_{1}^{S,-}(1) $
V:(1/2,1/2,0)	$2V_{1}^{S,+}(1)⊕2V_{1}^{S,-}(1) $
B:(u,0,w)	$2B_{1}^{S}(1)⊕2B_{2}^{S}(1) $
Λ:(0,v,0)	$2Λ_{1}^{S}(1)⊕2Λ_{2}^{S}(1) $
U:(0,v,1/2)	$2U_{1}^{S}U_{2}^{S}(2) $
GP:(u,v,w)	$4GP_{1}^{S}(1) $