Alexandrite is the birthstone for June according to both the modern list, but it’s a very rare gemstone in general. On the ancient list, June is a Pearl, which is more often used because of the rarity of Alexandrite.
Recently Moonstone is also often used for June babies.
If you're a June baby, you're funny and talkative. People with this stone are great with people, show character, and know how to make a point. You're sensitive and polite but can take a long time to recover from being hurt.