  We report a high-pressure 75As NMR study on the heavily hole-doped iron
pnictide superconductor KFe2As2 (Tc~3.8 K). The low-energy spin fluctuations
are found to decrease with applied pressure up to 2 GPa, but then increase
again, changing in lockstep with the pressure-induced evolution of Tc. Their
diverging nature suggests close proximity to a magnetic quantum critical point
at a negative pressure of P~-0.6 GPa. Above 2.4 GPa, the 75As satellite spectra
split below 40 K, indicating a breaking of As site symmetry and an incipient
charge order. These pressure-controlled phenomena demonstrate the presence of
nearly-critical fluctuations in both spin and charge, providing essential input
for the origin of superconductivity.
