  A double quantum dot device, connected to two channels that only see each
other through interdot Coulomb repulsion, is analyzed using the numerical
renormalization group technique. By using a two-impurity Anderson model, and
parameter values obtained from experiment [S. Amasha {\it et al.}, Phys. Rev.
Lett. {\bf 110}, 046604 (2013)], it is shown that, by applying a moderate
magnetic field, and adjusting the gate potential of each quantum dot, opposing
spin polarizations are created in each channel. Furthermore, through a well
defined change in the gate potentials, the polarizations can be reversed. This
polarization effect is clearly associated to a spin-orbital Kondo state having
a Kondo peak that originates from spatially separated parts of the device. This
fact opens the exciting possibility of experimentally probing the internal
structure of an SU(2) Kondo state.

Strongly Correlated Electrons;Mesoscale and Nanoscale Physics