  The spin degree of freedom is crucial for the understanding of any condensed
matter system. Knowledge of spin-mixing mechanisms is not only essential for
successful control and manipulation of spin-qubits, but also uncovers
fundamental properties of investigated devices and material. For
electrostatically-defined bilayer graphene quantum dots, in which recent
studies report spin-relaxation times T1 up to 50ms with strong magnetic field
dependence, we study spin-blockade phenomena at charge configuration
$(1,2)\leftrightarrow(0,3)$. We examine the dependence of the spin-blockade
leakage current on interdot tunnel coupling and on the magnitude and
orientation of externally applied magnetic field. In out-of-plane magnetic
field, the observed zero-field current peak could arise from finite-temperature
co-tunneling with the leads; though involvement of additional spin- and
valley-mixing mechanisms are necessary for explaining the persistent sharp side
peaks observed. In in-plane magnetic field, we observe a zero-field current
dip, attributed to the competition between the spin Zeeman effect and the
Kane-Mele spin-orbit interaction. Details of the line shape of this current dip
however, suggest additional underlying mechanisms are at play.
