Let $\alpha$ be an algebraic integer with minimal polynomial $f$. Is there some natural condition on $f$ to guarantee that all Galois conjugates of $\alpha$ have absolute value at least $1$? Equivalently, under any embedding of $\alpha$ into $\mathbb{C}$, $\alpha$ has absolute value at least $1$?
The corresponding question with absolute values less than or equal to $1$ seems to be have been studied quite a bit ("Pisot numbers").
EDIT: In the definition of Pisot numbers, we actually require that all of the conjugates except for $1$ have absolute value less than or equal to $1$. Indeed, an algebraic integer whose conjugates all lie inside the unit disk is a root of unity.
I would also be interested in necessary conditions. For example, if one embedding of $\alpha$ has absolute value greater than $1$, then the constant term of the minimal polynomial cannot be $\pm 1$.