Stolarek et al: Genetic history of East-Central Europe...

[bolek]

 However, linguistic Slavs have existed for a thousand years.

From the last lecture of David W Anthony on PIE. He is using Ringe's Phylogenetic tree of IE languages. Indo-Iranian and Balto-Slavic split in the beginning of the third millennium BC. So at the end of the third millennium Slavic languages were formed.