At 11th level, a paladin gains Improved Divine Smite. This means (PHB p85):
you are so suffused with righteous might that all your melee weapon strikes carry divine power with them.
Given that the normal Divine Smite requires a spell slot to be expended, I took it to be considered as a spell and therefore unusable within an Antimagic Field (PHB, p213):
This area is divorced from the magical energy that suffuses the multiverse. Within the sphere, spells can’t be cast, summoned creatures disappear, and even magic items become mundane. [...] Spells and other magical effects, except those created by an artifact or a deity, are suppressed in the sphere and can’t protrude into it.
Improved Divine Smite, however, appears to be a quality innate to a paladin of 11th level or higher. Is it affected by an Antimagic Field?