"Later" and "latter" are synonymous in the meaning of "more advanced in a period". So "later" and "latter" are both correct in your sentence, though people seem to prefer the "latter".
1. I read Arabic in the afternoon, and Greek in the morning. In my opinion, the latter half of the day is more conducive to the study of an ancient tongue.
2. I read Greek in the morning, and Arabic during the later half of the day.