As with other emotions, hate has a basis in the brain. Here are two studies that describe loathing. One deals with straightforward hate and the other discusses the closely related emotion of schadenfreude, a less intense version of hate which is combined with envy.
Neural correlates of hate. (Link)
This study shows that hate involves increased activity in multiple areas of the brain:
1. medial frontal gyrus
2. right putamen
3. premotor cortex
4. frontal pole
5. medial insula
6. right insula
7. right premotor cortex
8. right fronto-medial gyrus
When your gain is my pain and your pain is my gain: neural correlates of envy and schadenfreude. (Link)
This study shows that schadenfreude involves increased activity in:
1. anterior cingulate cortex
2. ventral striatum