We study the effect of an external magnetic field in the Kondo regime of adouble-quantum-dot system in which a strongly correlated dot (the "hangingdot") is coupled to a second, noninteracting dot that also bridges the gapbetween two external leads. In zero field, the spectral function of the hangingdot has previously been shown to exhibit a split-peak structure near the Fermilevel due to "Kondo resonance filtering" by the bridging dot. We show using thenumerical renormalization group that application of a magnetic field leads to asubtle interplay between electronic interference, Kondo physics, and Zeemansplitting with nontrivial consequences for the spectral and transportproperties. The value of the hanging-dot spectral function at the Fermi levelexhibits a nonuniversal field dependence that can be explained using ageneralized Friedel sum rule for a Kondo system with energy-dependenthybridization. The magnetic field also accentuates the exchange-mediatedinterdot coupling, which dominates the ground state at intermediate fieldsleading to the formation of antiparallel magnetic moments on the dots. Bytuning gate voltages and the magnetic field, one can achieve complete spinpolarization of the linear conductance between the leads, raising the prospectof applications of the device as a highly tunable spin filter. The system'slow-energy properties are qualitatively unchanged by the presence of weakon-site Coulomb repulsion within the bridging dot.
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