There actually isn't such a thing as a 'Spartan" helmet. This is the classic Corinthian style helmet, probably the one most associated with the Hoplites. In fact, though, it restricted vision so much that it was pretty quickly (by 490 BCE) replaced by the Calcidian helmet, which was much more open in front and on the lower face.
The nearest thing to a Spartan 'style' was that by 400 BCE they weren't wearing metal helmets or body armor at all: to increase mobility they lightened their load to a leather or canvas 'spolas' or tunic and a leather or felt 'pilos' conical cap. Since they drilled with their shields constantly, they had come to rely on the big Aspis wood, leather and metal shield for most of their protection.