Hi there, ATMA are drops you get from participating in FATES in various locations. They are required as part of acquiring your Zodiac Weapon (also known as +2 relic). In order to start the quest, you need to have your +1 relic weapon equiped and return to Gerolt. This will start the 'Up In Arms' quest. For more info, go to:

http://ffxiv.consolegameswiki.com/wiki/Up_in_Arms

You need 12 ATMA's to complete the first part of the quest which can be a right grind (Some people reporting to have logged 15 hours before they get their first drop). I spent 3 hours yesterday without getting a drop but 2 members of my FC got a drop after about 30 minutes FATE grinding. It is completely random so good luck. I hope this info helps.