Kondo effect in a quantum dot coupled to ferromagnetic leads and side-coupled to a nonmagnetic reservoir

Equilibrium transport properties of a single-level quantum dot tunnel-coupled to ferromagnetic leads and exchange-coupled to a side nonmagnetic reservoir are analyzed theoretically in the Kondo regime. The equilibrium spectral functions and conductance through the dot are calculated using the numerical renormalization group (NRG) method. It is shown that in the antiparallel magnetic configuration, the system undergoes a quantum phase transition with increasing exchange coupling $J$, where the conductance drops from its maximum value to zero. In the parallel configuration, on the other hand, the conductance is generally suppressed due to an effective spin splitting of the dot level caused by the presence of ferromagnetic leads, irrespective of the strength of exchange constant. However, for $J$ ranging from J=0 up to the corresponding critical value, the Kondo effect and quantum critical behavior can be restored by applying properly tuned compensating magnetic field.