Inelastic Tunneling Spectroscopy in a D-wave Superconductor

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.