  We investigate characteristic features in the spin response of doped
three-dimensional topological insulators with odd-parity unequal-spin
superconducting pairing, which are predicted to have gapless Majorana surface
modes. These Majorana modes contribute to the local spin susceptibility, giving
rise to a characteristic temperature behavior of the Knight shift and the
spin-lattice relaxation time in magnetic resonance experiments. Because of
their different decay lengths, the Majorana modes can be observed and clearly
distinguished from the Dirac modes of the topological insulator by local probes
which allow for a depth-controlled study of the electron spins on the nanometer
length scale.
