Many of the bibliographic databases offer APIs, but they might not be 100% open. Typically, you can't get access to the ones that charge for access unless your institution has a subscription to the service.
I know that link-only answers are bad, but the problem is that policies change over time, and the folks at MIT libraries has a rather long list of bibiometric APIs and info about how open they are, which I assume they'd maintain/update over time:
For your purposes, I'd avoid the subject specific ones (pubmed, arXiv) or publisher specific ones, and look to JSTOR Data for Research or Web of Science (the one run by Thomspon-Reuters).
As you're interested in tracking by people, I'd like to recommend ORCID, but it requires your faculty registering with them and acknowledging their papers, so they don't mis-attribute papers because of similar names.