How do I market a professional journal to libraries?

I am working with a small, newly published professional journal on the topic of gestalt psychotherapy. It is self-published, not published through a scientific publisher. I would like to market subscriptions to the the journal to libraries.

It would be most suitable for academic libraries (universities and professional organizations), or research libraries such as big city libraries.

Can I do the library marketing directly, through mailing a letter and brochure to a list of libraries, such as big city libraries, institute libraries, or university libraries? Or do libraries normally acquire professional journals only through distributors? I don’t want to incur the time and effort of a direct mail approach if that’s not the way libraries work in the real world.

Thanks for any information or ideas.