A lot of the details of modeling something like this is going to depend on the flavour of FATE being played, as the small differences will make the implementation different, i.e. SOTC to The Dresden Files, etc. With that in mind, the following explanation is genericized in the beginning of the explanation, before I go into system-specific implementation using The Dresden Files (as this is the flavour I have the most experience with).
The corrupting influence of the ring is only constant against the person wielding; others experience it intermittently. Because of this distinction, I believe there are two parts to modeling this in FATE, from my experience.
- The Item of Power has an aspect on it that directly affects the person wielding the item.
- The Item of Power has a power/ability that allows it to attack the people around it to represent the influence on others.
Specifically modeling this artifact in The Dresden Files, I'd say that it had aspect(s) related specifically to Wants to return to its master (Sauron) and/or The Corrupting Influence of the One Ring. These aspects can be utilized on the wielder of the item in way of compels; I'd also allow the aspects to be utilized in relation to the wielder's own natural abilities in a positive manner.
Apart from the veil, I'd also give it incite emotion (Greed/Power Hungry) at range (YS172). This could be wielded on the wielder and on any around; consequences related to such would represent the corruption that the ring spreads; being taken out would result in Gollum or (to a lesser extent) Boromir.