Stigma (聖痕, Sutiguma): Only a person who has a Stigma can become a Magika Stigma (聖痕魔法使い, Magika Sutiguma, lit. "Stigma Magician"). These Enigma are under strict control by the government. The contract ceremony will change the Enigma into Stigma. People with an Enigma are mandated to enroll to the Magic Division and are chosen to bear an Enigma when they turn 14.
However this is just the usual case. The expenditure of stigma is entirely at the discretion of Diva's. Diva's can hand out as many stigma as they want to whoever they want whenever they want, the 14th birthday is just a matter of convenience. However the Diva's themselves can't remove stigma.