Free automorphism groups of K3 surfaces with Picard number 3

It is known that the automorphism group of any projective K3 surface is finitely generated. In this paper, we consider a certain kind of K3 surfaces with Picard number 3 whose automorphism groups are isomorphic to congruence subgroups of the modular group $PS{L}_2\left(Z\right)$. In particular, we show that a free group of arbitrarily large rank appears as the automorphism group of such a K3 surface.