  We provide a theory for scanning tunneling microscopy and spectroscopy using
a spin-polarized tip. It it shown that the tunneling conductance can be
partitioned into three separate contributions, a background conductance which
is independent of the local spin, a dynamical conductance which is proportional
to the local spin moment, and a conductance which is proportional to the noise
spectrum of the local spin interactions. The presented theory is applicable to
setups with magnetic tip and substrate in non-collinear arrangement, as well as
for non-magnetic situations. The partitioning of the tunneling current suggests
a possibility to extract the total spin moment of the local spin from the
dynamical conductance. The dynamical conductance suggests a possibility to
generate very high frequency spin-dependent ac currents and/or voltages. We
also propose a measurement of the dynamical conductance that can be used to
determine the character of the effective exchange interaction between
individual spins in clusters. The third contribution to the tunneling current
is associated with the spin-spin correlations induced by the exchange
interaction between the local spin moment and the tunneling electrons. We
demonstrate how this term can be used in the analysis of spin excitations
recorded in conductance measurements. Finally, we propose to use spin-polarized
scanning tunneling microscopy for detailed studies of the spin excitation
spectrum.
