  The non-Hermitian skin effect is a unique phenomenon in which an extensive
number of eigenstates are localized at the boundaries of a non-Hermitian
system. Recent studies show that the non-Hermitian skin effect is significantly
suppressed by magnetic fields. In contrast, we demonstrate that the
second-order skin effect (SOSE) is robust and can even be enhanced by magnetic
fields. Remarkably, SOSE can also be induced by magnetic fields from a trivial
non-Hermitian system that does not experience any skin effect at zero field.
These properties are intimately related to to the persistence and emergence of
topological line gaps in the complex energy spectrum in presence of magnetic
fields. Moreover, we show that a magnetic field can drive a non-Hermitian
system from a hybrid skin effect, where the first-order skin effect and SOSE
coexist, to pure SOSE. Our results describe a qualitatively new magnetic field
behavior of the non-Hermitian skin effect.
