  Nitrogen vacancy (NV) centers can couple to confined phonons in diamond
mechanical resonators via the effect of lattice strain on their energy levels.
Access to the strong spin-phonon coupling regime with this system requires
resonators with nanoscale dimensions in order to overcome the weak strain
response of the NV ground state spin sublevels. In this work, we study NVs in
diamond cantilevers with lateral dimensions of a few hundred nm. Coupling of
the NV ground state spin to the mechanical mode is detected in electron spin
resonance (ESR), and its temporal dynamics are measured via spin echo. Our
small mechanical mode volume leads to a 10-100X enhancement in spin-phonon
coupling strength over previous NV-strain coupling demonstrations. This is an
important step towards strong spin-phonon coupling, which can enable
phonon-mediated quantum information processing and quantum metrology.
