Alexandrite engagement rings? Absolutely! Diamonds may be a girl's best friend, but Alexandrite engagement rings are a unique, original, and a far more affordable choice. The birthstone of June, Alexandrite is an amazing and mysterious stone. A created alexandrite ring is a unique and entertaining attention getter. The birthstone of December, the tranquil azure color of a blue topaz ring can evoke thoughts of warm Caribbean seas on a cold winter day.