I have an article in the field I am just interest and has no overlap with my major. Should I mention it my SOP?
I wouldn't mention it. As Chris C states in the comments, it is not peer-reviewed and is not directly relevant to your area of future research. 

My answer would change if the article were peer-reviewed and/or published in a journal, however. I think demonstrating that you have the ability and motivation to submit an article for publication is a positive attribute for a potential graduate student, regardless of whether the paper is in your field of research or not. For example, my first publication was not in my current research area, but several reviewers of my application later told me that just having a published paper set me apart from other applicants.

Since you claim that at least one person in the field finds it interesting and that the topic is new, why don't you want to publish it? Is there a way to at least submit it for publication before your applications are due? 

In my opinion, it is a little dangerous to put unpublished articles on a SOP or CV. A reviewer might arrive at the (potentially false) conclusion that you're trying to pad your CV or SOP with articles that may never actually be published, which can hurt you. Others might wonder why you feel that the article is important enough to include on a graduate application, but not be important enough for publication. 

Overall, I think the safer thing to do is omit it for now. If you end up moving forward with disseminating it further, then I would consider mentioning it.