Nat

Cute, but this looks way too masculine for a diminutive for Natalie/Natalia. For a girl, you could use Nattie instead.

Due to vowels pitch contrast in Nathaniel and Natalie "Nat" appears to shorten Natalie while retaining its brightness or strength. I was given the name Nathaniel and nickname Nat in late 70's at a time when Nathan appears the more prominent masculine choice. I treat them as Formal and Informal. I've yet to meet another using Nat, 2 Natalie's and 3 Nathaniel's.

It sounds like gnat.

I really like this name, it has a good kick to it that makes me like it!