TLDR: Coworker falsely told HR that I made racist comments about him, which never happened (nor anything close). He is also making those claims to our other coworkers, which is creating tension between me and the rest of the office.

I'm going to leave out some irrelevance detail like workplace and such, but this takes place in New Jersey. I have a co-worker who everyone agrees is lazy and a nightmare to work with. We used to be on good terms, until I complained to a manager that he had rudely refused to do some work and I've avoided him since then. Last time that we worked together he was making pointed comments, passive aggressive remarks, and borderline threatening me in comments to another co-worker. When it affected actual work, I sent a letter to our manager talking about his unprofessional behavior, but I otherwise ignored him. My manager told me the next day that this worker had sent a letter to HR saying that I'm creating "a difficult work environment" for him, which is untrue as we've never interacted that closely and lately I've been completely ignoring him.

The killer is he claimed that I had made racial remarks about him, which is completely false. I never made or remotely implied anything racial about him or any other co-worker. Since this is a he-said-she-said situation, I don't know what protection I have as our workplace is very catty and there are people who might lie about each other just because they don't like them. I don't know where this came from, and I know 100% that it's entirely fabricated. This is a kind of person to absolutely run his mouth to as many people as possible, so even after the situation is completed it's still going to affect the workplace and how others interact with me. This is a comment that I refuse to let go, but I'm not sure what legal resources or options I have. Even after HR does their investigation and I'm cleared, I plan on pursuing legal action against this person and I need to know what I can do.