Archimedes' Lever is the sword wielded by the original Storm King. Forged by master-Spark Van Rijn, along with being powerfully electrified in some fashion, it was "bound to its owner's soul", allowing him to sense and activate it from (at least) a fair distance away. According to Violetta, the blade was also sharp enough to "cut the day out of the night", whatever that means.
The Jägermonsters refer to it as Slasher.
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The sword's name is a reference to a quote from the ancient Greek philosopher-scientist-Spark Archimedes: "Give me a lever long enough and a fulcrum on which to place it, and I shall move the world."