  We predict strong, dynamical effects in the dc magnetoresistance of current
flowing from a spin-polarized electrical contact through a magnetic dopant in a
nonmagnetic host. Using the stochastic Liouville formalism we calculate
clearly-defined resonances in the dc magnetoresistance when the applied
magnetic field matches the exchange interaction with a nearby spin. At these
resonances spin precession in the applied magnetic field is canceled by spin
evolution in the exchange field, preserving a dynamic bottleneck for spin
transport through the dopant. Similar features emerge when the dopant spin is
coupled to nearby nuclei through the hyperfine interaction. These features
provide a precise means of measuring exchange or hyperfine couplings between
localized spins near a surface using spin-polarized scanning tunneling
microscopy, without any ac electric or magnetic fields, even when the exchange
or hyperfine energy is orders of magnitude smaller than the thermal energy.
