  We study the effect of an external magnetic field in the Kondo regime of a
double-quantum-dot system in which a strongly correlated dot (the "hanging
dot") is coupled to a second, noninteracting dot that also bridges the gap
between two external leads. In zero field, the spectral function of the hanging
dot has previously been shown to exhibit a split-peak structure near the Fermi
level due to "Kondo resonance filtering" by the bridging dot. We show using the
numerical renormalization group that application of a magnetic field leads to a
subtle interplay between electronic interference, Kondo physics, and Zeeman
splitting with nontrivial consequences for the spectral and transport
properties. The value of the hanging-dot spectral function at the Fermi level
exhibits a nonuniversal field dependence that can be explained using a
generalized Friedel sum rule for a Kondo system with energy-dependent
hybridization. The magnetic field also accentuates the exchange-mediated
interdot coupling, which dominates the ground state at intermediate fields
leading to the formation of antiparallel magnetic moments on the dots. By
tuning gate voltages and the magnetic field, one can achieve complete spin
polarization of the linear conductance between the leads, raising the prospect
of applications of the device as a highly tunable spin filter. The system's
low-energy properties are qualitatively unchanged by the presence of weak
on-site Coulomb repulsion within the bridging dot.
