1. Radical weapon: 20.0% to 50.0% chance to cause Bleeding on Hit:

Heat aura (from psalm doctrine) cannot do it during teamplay.

2. Radical armor:  +50% Damage Bonus for Bleeding effects but Take Damage equal to 10% of Bleeding Damage Dealt:

Meanwhile, during team play, this enchant seems to make the player suffer from more than bleeding:

Heat aura only applies burning to enemy, not bleeding. But still the player seems to take damage from burning on enemy as well.