This article says that the three likely possibilities for 'sunstone' (if it really was used for navigation) are calcite, tourmaline, and cordierite.

It was Thorkild Ramskou who made this hypothesis in the 1960s. I strongly suspect it didn't gain the poetic moniker 'Viking's compass" until afterwards.

Moreover, if it were used in the jewelry industry before the 1960s then it would be strong supporting evidence for the hypothesis.