Information of spin space group $P_A{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{c}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$ ( nSSG:7.8.2.1 )

General Positions

The continuously infinite group ^∞1 is omitted.

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

Wyckoff Positions

WP	Site symmetry	Representative
2a	${\phantom{A}}_{\phantom{}}^{\phantom{-1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}-1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(a,1/4,c | 0,0,0)
4b	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{1}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$	(a,b,c | 0,0,z)

Spin Brillouin Zone & k-little co-groups

Wavevector-k	Little co-group
A:(1/2,0,1/2)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }/\mathrm{mm}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }/\mathrm{mm}}\text{1}$
B:(0,0,1/2)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }/\mathrm{mm}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }/\mathrm{mm}}\text{1}$
C:(1/2,1/2,0)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }/\mathrm{mm}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }/\mathrm{mm}}\text{1}$
D:(0,1/2,1/2)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }/\mathrm{mm}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }/\mathrm{mm}}\text{1}$
E:(1/2,1/2,1/2)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }/\mathrm{mm}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }/\mathrm{mm}}\text{1}$
Γ:(0,0,0)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }/\mathrm{mm}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }/\mathrm{mm}}\text{1}$
Y:(1/2,0,0)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }/\mathrm{mm}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }/\mathrm{mm}}\text{1}$
Z:(0,1/2,0)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }/\mathrm{mm}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }/\mathrm{mm}}\text{1}$
F:(u,0,w)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }2}\text{1}$
G:(u,1/2,w)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }2}\text{1}$
Λ:(0,v,0)	${\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }2}\text{1}$
U:(1/2,v,1/2)	${\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }2}\text{1}$
V:(0,v,1/2)	${\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }2}\text{1}$
W:(1/2,v,0)	${\phantom{A}}_{\phantom{}}^{\phantom{m}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}m}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }2}\text{1}$
GP:(u,v,w)	${\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{1}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }2}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }2}\text{1}$

Spin Brillouin Zone

2/mP

Band Representations (Magnon)

4b

k-vector	A↑G(4)
A:(1/2,0,1/2)	$A_1^S{A}_2^S(4)$
B:(0,0,1/2)	$B_1^S{B}_2^S(4)$
C:(1/2,1/2,0)	$C_1^S(2)\oplus C_2^S(2)$
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)	${\Gamma }_1^S(2)\oplus {\Gamma }_2^S(2)$
Y:(1/2,0,0)	$Y_1^S(2)\oplus Y_2^S(2)$
Z:(0,1/2,0)	$Z_1^S(2)\oplus Z_2^S(2)$
F:(u,0,w)	$F_1^S(2)\oplus F_2^S(2)$
G:(u,1/2,w)	$G_1^S(2)\oplus G_2^S(2)$
Λ:(0,v,0)	$2{\Lambda }_1^S(2)$
U:(1/2,v,1/2)	$U_1^S{U}_1^S(4)$
V:(0,v,1/2)	$V_1^S{V}_1^S(4)$
W:(1/2,v,0)	$2W_1^S(2)$
GP:(u,v,w)	$2G{P}_1^S(2)$