The Sword, the School, and the Fire Cat-Girl

Areishia Spirit Academy: a place where young girls train to become elementalers, where no men are allowed. Kazehaya Kamito gets lost trying to head to the school, and runs into Claire Rouge, a girl purifying herself for a spirit contracting ceremony. She tries to contract with the Demon Slayer, a sword that no one had succeeded in contacting with before, but it goes out of control...