Rust's memory semantics are definitely a kind of 'automatic memory management' though. I mean, that's the whole premise - to have the kind of guarantees about memory safety that until Rust where only available in GC'ed languages running on some runtime.
Not sure if Cyclone and ATS don't predate it, but Rust's memory management is a bit like 1/3rd of Linear Lisp (specifically, the compil time garbage optimizer)