Does the MIT open source license require work derivatives to be made public (under MIT license)?

Question

I am looking for an open source license for a library I want to publish. Ideally, one should be allowed to use this library in free or commercial applications without paying me a fee, but if any derivative work from the library is created (any improvement of the library for example), it should be made available to everyone under that same license.

In other words, I want to put the following ethics: "You benefit from this piece of work for free, and if you improve it, I can benefit from your improvement for free too". It's a type copyleft license I am looking for.

The MIT license looks like a possible solution, but it is unclear to me whether derivative works of the code covered by this license MUST be made available PUBLICLY to everyone. Can anyone clarify/confirm this? If there is another more appropriate open source license covering my needs, I am interested too. Thanks.