  We investigate the effects of spin-orbit interaction (SOI) on the exchange
cotunneling through a spinful Coulomb blockaded quantum dot. In the case of
zero magnetic field, Kondo effect is shown to take place via a Kramers doublet
and the SOI will merely affect the Kondo temperature. In contrast, we find that
the breaking of time-reversal symmetry in a finite field has a marked influence
on the effective Anderson, and Kondo models for a single level. The nonlinear
conductance can now be asymmetric in bias voltage and may depend strongly on
direction of the magnetic field. A measurement of the angle dependence of
finite-field cotunneling spectroscopy thus provides valuable information about
orbital, and spin degrees of freedom and their mutual coupling.
