We present a time-dependent microscopic model for Coulomb blockade transport through an experimentally realized supramolecular spin-valve device driven by an oscillating magnetic field, in which the $4f$-electron magnetic states of an array of $\mathrm{Tb}{\mathrm{Pc}}_2$ single-molecule magnets (SMMs) were observed to modulate a sequential tunneling current through an underlying substrate nanoconstriction. Our model elucidates the dynamical mechanism at the origin of the observed hysteresis loops of the magnetoconductance, a signature of the SMM-modulated spin-valve effect, in terms of a phonon-assisted multi-spin-reversal cascade relaxation process, which mediates the switching of the device between the two conductive all-parallel spin configurations of the SMM array. Moreover, our proposed model can explain the zero-bias giant magnetoresistive transport gap measured in this device, solely within the incoherent transport regime, consistently with the experimental observations, as opposed to previous interpretations invoking Fano-resonance conductance suppression within a coherent ballistic transport regime. Finally, according to the proposed Coulomb blockade scenario, the SMM-mediated giant magnetoresistance effect is predicted to increase with the number of SMMs aligned on the nanoconstriction surface, on account of the increased number of intermediate nonconducting spin-flip states intervening in the phonon-assisted multi-spin-reversal cascade relaxation process necessary to switch between the two conducting all-parallel SMM spin configurations.

• Received 30 April 2020
• Revised 10 September 2020
• Accepted 14 September 2020

DOI:https://doi.org/10.1103/PhysRevB.102.125310