  The combination of electronic correlations and Fermi surfaces with multiple
nesting vectors can lead to the appearance of complex multi-Q magnetic ground
states, hosting unusual states such as chiral density-waves and quantum Hall
insulators. Distinguishing single-Q and multi-Q magnetic phases is however a
notoriously difficult experimental problem. Here we propose theoretically that
the local density of states near a magnetic impurity, whose orientation may be
controlled by an external magnetic field, can be used to map out the detailed
magnetic configuration of an itinerant system and distinguish unambiguously
between single-Q and multi-Q phases. We demonstrate this concept by computing
and contrasting the LDOS near a magnetic impurity embedded in three different
magnetic ground states relevant to iron-based superconductors -- one single-Q
and two double-Q phases. Our results open a promising avenue to investigate
complex magnetic configurations in itinerant systems via standard scanning
tunneling spectroscopy, without requiring spin-resolved capability.
