A Stigma is an ocular condition with five variations, the Magic Eyes give their hosts incredible inherent magical abilities. Despite their increased magical power, or perhaps because of it, Magic Eye bearers are almost universally hated and feared in all known countries. Once a person is confirmed a bearer they and their close family and friends are killed.
While the majority of people refer to the Magic Eyes as "Demon Eyes," the bearers themselves have taken to calling them "God's Eyes." The three most common types seen throughout the anime series are: the Alpha Stigma, Lino Doue, and Ebra Crypt. Others like Torch Curse and Will Heim have only been seen in the manga thus far and not the anime, but are referred to.
"... Alpha Stigma, which is said to analyze and comprehend all magic." Kiefer Knolles reading the book on Magic Eyes.
The Alpha Stigma is known as a trait which happens in a rare few humans across the land of the series. It is the magic eye which is able to analyse and understand all magic. It is also possible for the Alpha Stigma to analyse structures around the bearer. The Alpha Stigma is usually activated by the death of a friend or family member, which causes the user to go on a rampage, seeking destruction and death for those around the user. Users seem to have a god-like persona, which has to wreak havoc until either the body burns out and the user kills him/herself, or the Alpha Stigma is crystallized and gouged out. (This can be done with all Stigmas).
Besides Ryner, there were two other Alpha Stigma Bearers introduced in the anime. Both of them were driven into madness as a result of the death of a loved one. The first one, Arua, was able to return back to normal after being knocked unconscious by Ryner. The second one, Pueka, had her crystal gouged out and died as soon as she broke down. In the end, Ryner was the only one that rampaged for longer than a moment.
The most probable reason for the Alpha Stigma to be more common is due to the nature of the Alpha Stigma. The Alpha Stigma's tendency to go berserk and kill, in comparison to the other types, might be the reason it is the only one so widely known.
Crystallization occurs by disruption of the user's eyes or mind, which drives the user to the edge of madness and beyond, allowing the crystal to be gouged out. Ryner Lute is the first case in which a user has been able to return to sanity after going on a rampage. This is possibly due to the Lonely Devil inside him.
These crystal forms of various Stigma are then usable as items in combat, each crystal containing immense power within, as seen by its use primarily by the nation of Gastark. The seemingly callous methodology of mass producing these crystals as weapons of war is not lost of them, as Lir, Sui, Kuu (all dispatches from Gastark) are seen intent on doing the above as a secondary objective.