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I am sorry to hear about this situation. An employer (and an employer's agents such as management, etc) have discretion whether or not to give a bonus, raise, etc. Unless it is speculated in the employee's contract that they must receive one, I am afraid that one cannot mandate that they receive the raise/bonus.
This does not matter if the decision was reached due to proper facts, or facts believed but that did not actually happen (including a faulty write up). The fact it, it is up to the company and they can do whatever they want to - as long as it is not unlawful discrimination. They can choose to fire you for not liking the color of your shoes one day.
As such, there may not be much of a case here, I am afraid. Technically - technically - one can pursue the middle management that is responsible for the faulty write up for defamation in Court. However, this would likely be at the expense of the actual employment, thus making it not practical.
If it were me, I would leave it alone.
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