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A Half-Semiconductor is a material with a narrow band-gap for one spin channel and a wide band-gap for the other channel.
Knowing that for this material :
$E_{gap}(up)$ = 0.9609 eV
$E_{gap}(down)$ = 2.4974 eV
Can I consider the spin-up gap as narrow, and the spin-down as wide and call it a Half-Semiconductor material ?
For the up-spin channel, you can absolutely consider it as a semiconductor; for the down-spin channel, you can consider it as an insulator (may someone also consider it as a semiconductor, just different conventions). Thus, you can say your material is a half-semiconductor (HSC). (HSC is a semiconductor in one spin channel but an insulator in the other spin channel.)
One more thing you should check is the band alignment (don't mix the HSG and bipolar magnetic semiconductors (BMS)), seeing (d) and (f) below:
Ref: https://academic.oup.com/nsr/article/3/3/365/2236578?login=true
PS: As @Tristan Maxson said, it's hard to identify insulators (with a large bandgap) and semiconductors (with a moderate or small bandgap) with a definitive gap value.
Finally how you obtained these gaps listed above? DFT, HSE06, or GW? I suggest that you calculate them with HSE06 or GW. DFT usually underestimates the bandgap of the semiconductors. If the GW gap of the up-spin channel is below 1.5eV and the GW gap of the down-spin channel is above 3eV, then it must be classified into HSCs.
I think you will be hard pressed to find a definitive answer, however I would say you are within reason to call it a half semiconductor. Just be aware that this doesn't seem to be a well defined term and you may need to give the audience / reader a prompting on what you mean by half semiconductor.
