  We analyse a system of two interacting spin-qubits subjected to a
Landau-Majorana-St\"uckelberg-Zener (LMSZ) ramp. We prove that LMSZ transitions
of the two spin-qubits are possible without an external transverse static field
since its role is played by the coupling between the spin-qubits. We show how
such a physical effect could be exploited to estimate the strength of the
interaction between the two spin-qubits and to generate entangled states of the
system by appropriately setting the slope of the ramp. Moreover, the study of
effects of the coupling parameters on the time-behaviour of the entanglement is
reported. Finally, our symmetry-based approach allows us to discuss also
effects stemming from the presence of a classical noise or non-Hermitian
dephasing terms.
