We show that the pinning of collective charge and spin modes by impurities in
the cuprate superconductors leads to qualitatively different fingerprints in
the local density of states (LDOS). In particular, in a pinned (static) spin
droplet, the creation of a resonant impurity state is suppressed, the
spin-resolved LDOS exhibits a characteristic spatial pattern, and the LDOS
undergoes significant changes with increasing magnetic field. Since all of
these fingerprints are absent in a charge droplet, impurities are a new probe
for identifying the nature and relative strength of collective modes.Comment: 4 pages, 4 figure