  The ground state of frustrated (antiferromagnetic) triangular molecular
magnets is characterized by two total-spin $S =1/2$ doublets with opposite
chirality. According to a group theory analysis [M. Trif \textit{et al.}, Phys.
Rev. Lett. \textbf{101}, 217201 (2008)] an external electric field can
efficiently couple these two chiral spin states, even when the spin-orbit
interaction (SOI) is absent. The strength of this coupling, $d$, is determined
by an off-diagonal matrix element of the dipole operator, which can be
calculated by \textit{ab-initio} methods [M. F. Islam \textit{et al.}, Phys.
Rev. B \textbf{82}, 155446 (2010)]. In this work we propose that
Coulomb-blockade transport experiments in the cotunneling regime can provide a
direct way to determine the spin-electric coupling strength. Indeed, an
electric field generates a $d$-dependent splitting of the ground state
manifold, which can be detected in the inelastic cotunneling conductance. Our
theoretical analysis is supported by master-equation calculations of quantum
transport in the cotunneling regime. We employ a Hubbard-model approach to
elucidate the relationship between the Hubbard parameters $t$ and $U$, and the
spin-electric coupling constant $d$. This allows us to predict the regime in
which the coupling constant $d$ can be extracted from experiment.

Mesoscale and Nanoscale Physics