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It has been theoretically demonstrated that two spins (qubits or qutrits),coupled by exchange interaction only, undergo a coupling-based jointLandau-Majorana-St\"uckelberg-Zener (LMSZ) transition when a linear ramp actsupon one of the two spins. Such a transition, under appropriate conditions onthe parameters, drives the two-spin system toward a maximally entangled state.In this paper, effects on the quantum dynamics of the two qudits, stemming fromthe Dzyaloshinskii-Moriya (DM) and dipole-dipole (d-d) interactions, areinvestigated qualitatively and quantitatively. The enriched Hamiltonian modelof the two spins, shares with the previous microscopic one the same C2-symmetrywhich once more brings about an exact treatment of the new quantum dynamicalproblem. This paper transparently reveals that the DM and d-d interactionsgenerate independent, enhancing or hindering, modifications in the dynamicalbehaviour predicted for the two spins coupled exclusively by the exchangeinteraction. It is worthy noticing that, on the basis of the theory heredeveloped, the measurement of the time evolution of the magnetization in acontrolled LMSZ scenario, can furnish information on the relative weights ofthe three kinds of couplings describing the spin system. This possibility isvery important since it allows in principle to legitimate the choice of themicroscopic model to be adopted in a given physical scenario.

Dzyaloshinskii-Moriya and dipole-dipole interactions affect coupling-based Landau-Majorana-St\"uckelberg-Zener transitions