  We propose a mechanism to use inelastic tunneling spectrosopy STM to detect a
single spin in a d-wave superconductor and in a pseudogap state, based on a
direct exchange coupling J between the surface electrons and the local spin S
in a magnetic field. This coupling will produce a kink in a dI/dV
characteristic at Zeeman energy of the spin \omega_0. We find that for relevant
values of parameters signal scales as dI^2/dV^2 \simeq (JN_0)^2 \Theta(eV -
\omega_0) and could be in the range of 10^{-2} of the bare density of states
where N_0 is the density of states for surface electrons. Scattering in
superconductor with the coherence peak at gap maximum \Delta leads also to
strong features at \Delta + \omega_0. This suggests a new technique for a
detection of a local spin excitation with STM. We also consider a detection of
a local vibrational mode as a simple extension of the spin case.
