if false statements of fact are being published about you and/or your company, which are causing you economic harm, then you may have a vaild basis for a defamation aciton against the former employees. You don't actually need that to be put into writing to be able to sue. However, the fact that you have a writing, may add an additional cause of action for "breach of contract". As Mr. Lassen has sharply pointed out, there is also a potential "tortious interference with business" claim. You need to consult with an attorney in a face to face meeting (preferable to posting sensitve information on a website such as Avvo which is open for all public to see ). Good luck.
A defamation tort claim, whether it's libel or slander, doesn't require any signed agreement to be valid. If their conduct meets the elements of defamation, then you can pursue it.
The written contract could open other avenues of relief. For example, if they are revealing negative facts about your business that happen to be true. In that case, they would have an absolute defense to your defamation claim. But you could still have a breach of contract claim for not abiding by the no compete agreement.
It's definitely worth seeing a lawyer to discuss the facts in more detail and determine your options.
This answer is for informational purposes only, and it not intended to create an attorney-client relationship. I've had only the limited amount of information provided in the question from which to form an answer. Your best course of action is to set up a formal consultation with a qualified attorney in your area.
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