You cannot do this through configuration as far as I know.
You will need to use some client code to query the existing values ββfor this field to find out if the new value entered is unique. You can use something like jQuery and the REST CRM service (ODATA) to perform asynchronous field validation; this may not be instantaneous, you may need to consider how this is presented to the user.
Alternatively, you can do this using a workflow, but it will be even less instantaneous - it probably should be called after saving.
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