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File Name	Spin Space Group	G0 Symbol	L0 Symbol	it	ik
$0.20 / M n T e 2$	$P^{2_{100}} a^{3_{111}^{1}} - 3$	$P a - 3 (205)$	$P - 1 (2)$	$12$	$1$

Space Group	Magnetic Space Group	Spin Part PG	Configuration	Magnetic Phase
$P a - 3 (205)$	$\begin{aligned} P a - 3 (205.33) \\ T y p e I \end{aligned}$	$\begin{array}{r} T \\ 23 \end{array}$	$N o n c o p l a n a r$	$A F M$

Little Cogroup at General Position		Spin Splitting
without SOC	with SOC	without SOC	with SOC
$^{1} 1$	$1$	$k - d e p e n d e n t$	$Y e s$

Effective Magnetic Point Group	Anomalous Hall Effect
$m - 3$	without SOC	with SOC
$m - 3$	$N o$	$N o$

Effective MPG Constraint on Order-3 Tensor
T-odd	Quantum metric dipole	$O n l y z e r o s$
T-odd	Inversed mass dipole	$O n l y z e r o s$
T-even	Berry curvature dipole	$O n l y z e r o s$

G0-std Unit Magnetic Cell:

a	b	c	alpha	beta	gamma
6.9	6.9	6.9	90.0	90.0	90.0

Fractional Coordinates & Moments (in G0-std Unit Magnetic Cell)

No.	Atom	Site	Moment (in lattice)
1	Mn	[0.0, 0.0, 0.0]	[2.47, 2.47, 2.47]
2	Mn	[0.5, 0.5, 0.0]	[2.47, -2.47, -2.47]
3	Mn	[0.0, 0.5, 0.5]	[-2.47, 2.47, -2.47]
4	Mn	[0.5, 0.0, 0.5]	[-2.47, -2.47, 2.47]
5	Te	[0.3847, 0.3847, 0.3847]	[0.0, 0.0, 0.0]
6	Te	[0.8847, 0.1153, 0.6153]	[0.0, 0.0, 0.0]
7	Te	[0.6153, 0.8847, 0.1153]	[0.0, 0.0, 0.0]
8	Te	[0.1153, 0.6153, 0.8847]	[0.0, 0.0, 0.0]
9	Te	[0.6153, 0.6153, 0.6153]	[0.0, 0.0, 0.0]
10	Te	[0.1153, 0.8847, 0.3847]	[0.0, 0.0, 0.0]
11	Te	[0.3847, 0.1153, 0.8847]	[0.0, 0.0, 0.0]
12	Te	[0.8847, 0.3847, 0.1153]	[0.0, 0.0, 0.0]

Elements of the Spin Space Group (G0-std-setting):

Real Space Elements are under the basis of the lattice given above.

Spin Part Elements are represented corresponding to the SpinPartPG.

No.	Spin Rotation	Space Rotation	Space Translation	Seitz Symbol
1	$[\begin{matrix} 1.0 & 0.0 & 0.0 \\ 0.0 & 1.0 & 0.0 \\ 0.0 & 0.0 & 1.0 \end{matrix}]$	$[\begin{matrix} 1.0 & 0.0 & 0.0 \\ 0.0 & 1.0 & 0.0 \\ 0.0 & 0.0 & 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 \\ 0.0 \\ 0.0 \end{matrix}]$	${1 \| \| 1 \| τ_{(0.0, 0.0, 0.0)}}$
2	$[\begin{matrix} - 1.0 & 0.0 & 0.0 \\ 0.0 & - 1.0 & 0.0 \\ 0.0 & 0.0 & 1.0 \end{matrix}]$	$[\begin{matrix} 1.0 & 0.0 & 0.0 \\ 0.0 & 1.0 & 0.0 \\ 0.0 & 0.0 & - 1.0 \end{matrix}]$	$[\begin{matrix} 0.5 \\ 0.0 \\ 0.5 \end{matrix}]$	${2_{001} \| \| m_{001} \| τ_{(0.5, 0.0, 0.5)}}$
3	$[\begin{matrix} - 1.0 & 0.0 & 0.0 \\ 0.0 & 1.0 & 0.0 \\ 0.0 & 0.0 & - 1.0 \end{matrix}]$	$[\begin{matrix} 1.0 & 0.0 & 0.0 \\ 0.0 & - 1.0 & 0.0 \\ 0.0 & 0.0 & 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 \\ 0.5 \\ 0.5 \end{matrix}]$	${2_{010} \| \| m_{010} \| τ_{(0.0, 0.5, 0.5)}}$
4	$[\begin{matrix} 1.0 & 0.0 & 0.0 \\ 0.0 & - 1.0 & 0.0 \\ 0.0 & 0.0 & - 1.0 \end{matrix}]$	$[\begin{matrix} 1.0 & 0.0 & 0.0 \\ 0.0 & - 1.0 & 0.0 \\ 0.0 & 0.0 & - 1.0 \end{matrix}]$	$[\begin{matrix} 0.5 \\ 0.5 \\ 0.0 \end{matrix}]$	${2_{100} \| \| 2_{100} \| τ_{(0.5, 0.5, 0.0)}}$
5	$[\begin{matrix} 0.0 & 1.0 & 0.0 \\ 0.0 & 0.0 & 1.0 \\ 1.0 & 0.0 & 0.0 \end{matrix}]$	$[\begin{matrix} 0.0 & 1.0 & 0.0 \\ 0.0 & 0.0 & 1.0 \\ 1.0 & 0.0 & 0.0 \end{matrix}]$	$[\begin{matrix} 0.0 \\ 0.0 \\ 0.0 \end{matrix}]$	${3_{111}^{2} \| \| 3_{111}^{2} \| τ_{(0.0, 0.0, 0.0)}}$
6	$[\begin{matrix} 0.0 & - 1.0 & 0.0 \\ 0.0 & 0.0 & - 1.0 \\ 1.0 & 0.0 & 0.0 \end{matrix}]$	$[\begin{matrix} 0.0 & 1.0 & 0.0 \\ 0.0 & 0.0 & 1.0 \\ - 1.0 & 0.0 & 0.0 \end{matrix}]$	$[\begin{matrix} 0.5 \\ 0.0 \\ 0.5 \end{matrix}]$	${3_{- 11 - 1}^{2} \| \| 3_{- 11 - 1}^{2} \| τ_{(0.5, 0.0, 0.5)}}$
7	$[\begin{matrix} 0.0 & - 1.0 & 0.0 \\ 0.0 & 0.0 & 1.0 \\ - 1.0 & 0.0 & 0.0 \end{matrix}]$	$[\begin{matrix} 0.0 & 1.0 & 0.0 \\ 0.0 & 0.0 & - 1.0 \\ 1.0 & 0.0 & 0.0 \end{matrix}]$	$[\begin{matrix} 0.0 \\ 0.5 \\ 0.5 \end{matrix}]$	${3_{1 - 1 - 1}^{2} \| \| - 3_{1 - 1 - 1}^{2} \| τ_{(0.0, 0.5, 0.5)}}$
8	$[\begin{matrix} 0.0 & 1.0 & 0.0 \\ 0.0 & 0.0 & - 1.0 \\ - 1.0 & 0.0 & 0.0 \end{matrix}]$	$[\begin{matrix} 0.0 & 1.0 & 0.0 \\ 0.0 & 0.0 & - 1.0 \\ - 1.0 & 0.0 & 0.0 \end{matrix}]$	$[\begin{matrix} 0.5 \\ 0.5 \\ 0.0 \end{matrix}]$	${3_{- 1 - 11}^{2} \| \| 3_{- 1 - 11}^{2} \| τ_{(0.5, 0.5, 0.0)}}$
9	$[\begin{matrix} 0.0 & 0.0 & 1.0 \\ 1.0 & 0.0 & 0.0 \\ 0.0 & 1.0 & 0.0 \end{matrix}]$	$[\begin{matrix} 0.0 & 0.0 & 1.0 \\ 1.0 & 0.0 & 0.0 \\ 0.0 & 1.0 & 0.0 \end{matrix}]$	$[\begin{matrix} 0.0 \\ 0.0 \\ 0.0 \end{matrix}]$	${3_{111}^{1} \| \| 3_{111}^{1} \| τ_{(0.0, 0.0, 0.0)}}$
10	$[\begin{matrix} 0.0 & 0.0 & - 1.0 \\ - 1.0 & 0.0 & 0.0 \\ 0.0 & 1.0 & 0.0 \end{matrix}]$	$[\begin{matrix} 0.0 & 0.0 & 1.0 \\ 1.0 & 0.0 & 0.0 \\ 0.0 & - 1.0 & 0.0 \end{matrix}]$	$[\begin{matrix} 0.5 \\ 0.0 \\ 0.5 \end{matrix}]$	${3_{1 - 1 - 1}^{1} \| \| - 3_{1 - 1 - 1}^{1} \| τ_{(0.5, 0.0, 0.5)}}$
11	$[\begin{matrix} 0.0 & 0.0 & - 1.0 \\ 1.0 & 0.0 & 0.0 \\ 0.0 & - 1.0 & 0.0 \end{matrix}]$	$[\begin{matrix} 0.0 & 0.0 & 1.0 \\ - 1.0 & 0.0 & 0.0 \\ 0.0 & 1.0 & 0.0 \end{matrix}]$	$[\begin{matrix} 0.0 \\ 0.5 \\ 0.5 \end{matrix}]$	${3_{- 1 - 11}^{1} \| \| - 3_{- 1 - 11}^{1} \| τ_{(0.0, 0.5, 0.5)}}$
12	$[\begin{matrix} 0.0 & 0.0 & 1.0 \\ - 1.0 & 0.0 & 0.0 \\ 0.0 & - 1.0 & 0.0 \end{matrix}]$	$[\begin{matrix} 0.0 & 0.0 & 1.0 \\ - 1.0 & 0.0 & 0.0 \\ 0.0 & - 1.0 & 0.0 \end{matrix}]$	$[\begin{matrix} 0.5 \\ 0.5 \\ 0.0 \end{matrix}]$	${3_{- 11 - 1}^{1} \| \| 3_{- 11 - 1}^{1} \| τ_{(0.5, 0.5, 0.0)}}$
13	$[\begin{matrix} 0.0 & 0.0 & 1.0 \\ - 1.0 & 0.0 & 0.0 \\ 0.0 & - 1.0 & 0.0 \end{matrix}]$	$[\begin{matrix} 0.0 & 0.0 & - 1.0 \\ 1.0 & 0.0 & 0.0 \\ 0.0 & 1.0 & 0.0 \end{matrix}]$	$[\begin{matrix} 0.5 \\ 0.5 \\ 0.0 \end{matrix}]$	${3_{- 11 - 1}^{1} \| \| 3_{- 11 - 1}^{1} \| τ_{(0.5, 0.5, 0.0)}}$
14	$[\begin{matrix} 0.0 & 0.0 & - 1.0 \\ 1.0 & 0.0 & 0.0 \\ 0.0 & - 1.0 & 0.0 \end{matrix}]$	$[\begin{matrix} 0.0 & 0.0 & - 1.0 \\ 1.0 & 0.0 & 0.0 \\ 0.0 & - 1.0 & 0.0 \end{matrix}]$	$[\begin{matrix} 0.0 \\ 0.5 \\ 0.5 \end{matrix}]$	${3_{- 1 - 11}^{1} \| \| 3_{- 1 - 11}^{1} \| τ_{(0.0, 0.5, 0.5)}}$
15	$[\begin{matrix} 0.0 & 0.0 & - 1.0 \\ - 1.0 & 0.0 & 0.0 \\ 0.0 & 1.0 & 0.0 \end{matrix}]$	$[\begin{matrix} 0.0 & 0.0 & - 1.0 \\ - 1.0 & 0.0 & 0.0 \\ 0.0 & 1.0 & 0.0 \end{matrix}]$	$[\begin{matrix} 0.5 \\ 0.0 \\ 0.5 \end{matrix}]$	${3_{1 - 1 - 1}^{1} \| \| 3_{1 - 1 - 1}^{1} \| τ_{(0.5, 0.0, 0.5)}}$
16	$[\begin{matrix} 0.0 & 0.0 & 1.0 \\ 1.0 & 0.0 & 0.0 \\ 0.0 & 1.0 & 0.0 \end{matrix}]$	$[\begin{matrix} 0.0 & 0.0 & - 1.0 \\ - 1.0 & 0.0 & 0.0 \\ 0.0 & - 1.0 & 0.0 \end{matrix}]$	$[\begin{matrix} 0.0 \\ 0.0 \\ 0.0 \end{matrix}]$	${3_{111}^{1} \| \| - 3_{111}^{1} \| τ_{(0.0, 0.0, 0.0)}}$
17	$[\begin{matrix} 0.0 & 1.0 & 0.0 \\ 0.0 & 0.0 & - 1.0 \\ - 1.0 & 0.0 & 0.0 \end{matrix}]$	$[\begin{matrix} 0.0 & - 1.0 & 0.0 \\ 0.0 & 0.0 & 1.0 \\ 1.0 & 0.0 & 0.0 \end{matrix}]$	$[\begin{matrix} 0.5 \\ 0.5 \\ 0.0 \end{matrix}]$	${3_{- 1 - 11}^{2} \| \| - 3_{- 1 - 11}^{2} \| τ_{(0.5, 0.5, 0.0)}}$
18	$[\begin{matrix} 0.0 & - 1.0 & 0.0 \\ 0.0 & 0.0 & 1.0 \\ - 1.0 & 0.0 & 0.0 \end{matrix}]$	$[\begin{matrix} 0.0 & - 1.0 & 0.0 \\ 0.0 & 0.0 & 1.0 \\ - 1.0 & 0.0 & 0.0 \end{matrix}]$	$[\begin{matrix} 0.0 \\ 0.5 \\ 0.5 \end{matrix}]$	${3_{1 - 1 - 1}^{2} \| \| 3_{1 - 1 - 1}^{2} \| τ_{(0.0, 0.5, 0.5)}}$
19	$[\begin{matrix} 0.0 & - 1.0 & 0.0 \\ 0.0 & 0.0 & - 1.0 \\ 1.0 & 0.0 & 0.0 \end{matrix}]$	$[\begin{matrix} 0.0 & - 1.0 & 0.0 \\ 0.0 & 0.0 & - 1.0 \\ 1.0 & 0.0 & 0.0 \end{matrix}]$	$[\begin{matrix} 0.5 \\ 0.0 \\ 0.5 \end{matrix}]$	${3_{- 11 - 1}^{2} \| \| 3_{- 11 - 1}^{2} \| τ_{(0.5, 0.0, 0.5)}}$
20	$[\begin{matrix} 0.0 & 1.0 & 0.0 \\ 0.0 & 0.0 & 1.0 \\ 1.0 & 0.0 & 0.0 \end{matrix}]$	$[\begin{matrix} 0.0 & - 1.0 & 0.0 \\ 0.0 & 0.0 & - 1.0 \\ - 1.0 & 0.0 & 0.0 \end{matrix}]$	$[\begin{matrix} 0.0 \\ 0.0 \\ 0.0 \end{matrix}]$	${3_{111}^{2} \| \| - 3_{111}^{2} \| τ_{(0.0, 0.0, 0.0)}}$
21	$[\begin{matrix} 1.0 & 0.0 & 0.0 \\ 0.0 & - 1.0 & 0.0 \\ 0.0 & 0.0 & - 1.0 \end{matrix}]$	$[\begin{matrix} - 1.0 & 0.0 & 0.0 \\ 0.0 & 1.0 & 0.0 \\ 0.0 & 0.0 & 1.0 \end{matrix}]$	$[\begin{matrix} 0.5 \\ 0.5 \\ 0.0 \end{matrix}]$	${2_{100} \| \| m_{100} \| τ_{(0.5, 0.5, 0.0)}}$
22	$[\begin{matrix} - 1.0 & 0.0 & 0.0 \\ 0.0 & 1.0 & 0.0 \\ 0.0 & 0.0 & - 1.0 \end{matrix}]$	$[\begin{matrix} - 1.0 & 0.0 & 0.0 \\ 0.0 & 1.0 & 0.0 \\ 0.0 & 0.0 & - 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 \\ 0.5 \\ 0.5 \end{matrix}]$	${2_{010} \| \| 2_{010} \| τ_{(0.0, 0.5, 0.5)}}$
23	$[\begin{matrix} - 1.0 & 0.0 & 0.0 \\ 0.0 & - 1.0 & 0.0 \\ 0.0 & 0.0 & 1.0 \end{matrix}]$	$[\begin{matrix} - 1.0 & 0.0 & 0.0 \\ 0.0 & - 1.0 & 0.0 \\ 0.0 & 0.0 & 1.0 \end{matrix}]$	$[\begin{matrix} 0.5 \\ 0.0 \\ 0.5 \end{matrix}]$	${2_{001} \| \| 2_{001} \| τ_{(0.5, 0.0, 0.5)}}$
24	$[\begin{matrix} 1.0 & 0.0 & 0.0 \\ 0.0 & 1.0 & 0.0 \\ 0.0 & 0.0 & 1.0 \end{matrix}]$	$[\begin{matrix} - 1.0 & 0.0 & 0.0 \\ 0.0 & - 1.0 & 0.0 \\ 0.0 & 0.0 & - 1.0 \end{matrix}]$	$[\begin{matrix} 0.0 \\ 0.0 \\ 0.0 \end{matrix}]$	${1 \| \| - 1 \| τ_{(0.0, 0.0, 0.0)}}$

FINDSPINGROUP: Identify Spin Group and Related Properties