We call that plant Lychnis diocia (not sure about the spelling of second part) in Ireland, and there's an old double form available too. The stems are a little shorter.
I know the stems of the Lychnis viscaria are sticky - there's also a double form of that.
I have both Silene diocia and lychnis viscaria splendens plena. L. viscaria usually has sticky stems but not all, the one we have isn't sticky. I still think its L. viscaria it may even be the cultivar 'fever' which has that great magenta colour.