I am no geologist and I don't lnow the answer to this for certain. One of the varieties looks a good starting point - this page in wikipedia: https://en.wikipedia.org/wiki/Garnet#Properties mentions varieties of Garnet that change colour appearance depending on the light source, but not red to purple.
Alexandrite - a variety of Chrysoberyl - is another possible: https://en.wikipedia.org/wiki/Chrysoberyl#Alexandrite
Another famous colour changer under UV light is Flourite, but that flouresces brightly, so I don't think it fits your specimens.
Thanks everyone, I am waiting on an order for a neodymium magnet, but I think I will pop down to a Jewellery store tomorrow morning. I will let you all know the results.