  Self-assembled nanowire (NW) crystals can be grown into nearly defect-free
nanomechanical resonators with exceptional properties, including small motional
mass, high resonant frequency, and low dissipation. Furthermore, by virtue of
slight asymmetries in geometry, a NW's flexural modes are split into doublets
oscillating along orthogonal axes. These characteristics make bottom-up grown
NWs extremely sensitive vectorial force sensors. Here, taking advantage of its
adaptability as a scanning probe, we use a single NW to image a sample surface.
By monitoring the frequency shift and direction of oscillation of both modes as
we scan above the surface, we construct a map of all spatial tip-sample force
derivatives in the plane. Finally, we use the NW to image electric force fields
distinguishing between forces arising from the NW charge and polarizability.
This universally applicable technique enables a form of atomic force microscopy
particularly suited to mapping the size and direction of weak tip-sample
forces.
