Information of spin space group $P{\phantom{A}}_{\phantom{}}^{\phantom{1}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}1}\text{m}{\phantom{A}}_{\phantom{}}^{\phantom{\mathrm{\infty }\mathrm{m}}}{\phantom{A}}_{\phantom{2}}^{\phantom{2}\mathrm{\infty }\mathrm{m}}\text{1}$ ( nSSG:6.6.1.1 )

General Positions

The continuously infinite group ^∞1 is omitted.

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

Wyckoff Positions

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

Spin Brillouin Zone & k-little co-groups

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

Spin Brillouin Zone

Band Representations (Magnon)

1a

k-vector	A'↑G(1)
A:(1/2,0,1/2)	$A_1^S(1)$
B:(0,0,1/2)	$B_1^S(1)$
C:(1/2,1/2,0)	$C_1^S(1)$
D:(0,1/2,1/2)	$D_1^S(1)$
E:(1/2,1/2,1/2)	$E_1^S(1)$
Γ:(0,0,0)	${\Gamma }_1^S(1)$
Y:(1/2,0,0)	$Y_1^S(1)$
Z:(0,1/2,0)	$Z_1^S(1)$
F:(u,0,w)	$F_1^S(1)$
G:(u,1/2,w)	$G_1^S(1)$
Λ:(0,v,0)	${\Lambda }_1^S(1)$
U:(1/2,v,1/2)	$U_1^S(1)$
V:(0,v,1/2)	$V_1^S(1)$
W:(1/2,v,0)	$W_1^S(1)$
GP:(u,v,w)	$G{P}_1^S(1)$

1b

k-vector	A'↑G(1)
A:(1/2,0,1/2)	$A_1^S(1)$
B:(0,0,1/2)	$B_1^S(1)$
C:(1/2,1/2,0)	$C_2^S(1)$
D:(0,1/2,1/2)	$D_2^S(1)$
E:(1/2,1/2,1/2)	$E_2^S(1)$
Γ:(0,0,0)	${\Gamma }_1^S(1)$
Y:(1/2,0,0)	$Y_1^S(1)$
Z:(0,1/2,0)	$Z_2^S(1)$
F:(u,0,w)	$F_1^S(1)$
G:(u,1/2,w)	$G_2^S(1)$
Λ:(0,v,0)	${\Lambda }_1^S(1)$
U:(1/2,v,1/2)	$U_1^S(1)$
V:(0,v,1/2)	$V_1^S(1)$
W:(1/2,v,0)	$W_1^S(1)$
GP:(u,v,w)	$G{P}_1^S(1)$

2c

k-vector	A↑G(2)
A:(1/2,0,1/2)	$A_1^S(1)\oplus A_2^S(1)$
B:(0,0,1/2)	$B_1^S(1)\oplus B_2^S(1)$
C:(1/2,1/2,0)	$C_1^S(1)\oplus C_2^S(1)$
D:(0,1/2,1/2)	$D_1^S(1)\oplus D_2^S(1)$
E:(1/2,1/2,1/2)	$E_1^S(1)\oplus E_2^S(1)$
Γ:(0,0,0)	${\Gamma }_1^S(1)\oplus {\Gamma }_2^S(1)$
Y:(1/2,0,0)	$Y_1^S(1)\oplus Y_2^S(1)$
Z:(0,1/2,0)	$Z_1^S(1)\oplus Z_2^S(1)$
F:(u,0,w)	$F_1^S(1)\oplus F_2^S(1)$
G:(u,1/2,w)	$G_1^S(1)\oplus G_2^S(1)$
Λ:(0,v,0)	$2{\Lambda }_1^S(1)$
U:(1/2,v,1/2)	$2U_1^S(1)$
V:(0,v,1/2)	$2V_1^S(1)$
W:(1/2,v,0)	$2W_1^S(1)$
GP:(u,v,w)	$2G{P}_1^S(1)$