A micromechanical device includes a tiltable structure that is rotatable about a first rotation axis. The tiltable structure is coupled to a fixed structure through an actuation structure of a piezoelectric type. The actuation structure is formed by spring elements having a spiral shape. The spring elements each include actuation arms extending transversely to the first rotation axis. Each actuation arm carries a respective piezoelectric band of piezoelectric material. The actuation arms are divided into two sets with the piezoelectric bands thereof biased in phase opposition to obtain rotation in opposite directions of the tiltable structure about the first rotation axis.