Quantum tunnelling with tunable spin geometric phases in van der Waals antiferromagnets

Electron tunnelling in solids, a fundamental quantum phenomenon, lays the foundation for various modern technologies. The emergence of van der Waals magnets presents opportunities for discovering unconventional tunnelling phenomena. Here, we demonstrate quantum tunnelling with tunable spin geometric phases in a multilayer van der Waals antiferromagnet CrPS₄. The spin geometric phase of electron tunnelling is controlled by magnetic-field-dependent metamagnetic phase transitions. The square lattice of a CrPS₄ monolayer causes strong t_2g-orbital delocalization near the conduction band minimum. This creates a one-dimensional spin system with reversed energy ordering between the t_2g and e_g spin channels, which prohibits both intralayer spin relaxation by means of collective magnon excitations and interlayer spin hopping between the t_2g and e_g spin channels. The resulting coherent electron transmission shows pronounced tunnel magnetoresistance oscillations, manifesting quantum interference of cyclic quantum evolutions of individual electron Bloch waves by means of the time-reversal symmetrical tunnelling loops. Our results suggest the appearance of Aharonov–Anandan phases that originate from the non-adiabatic generalization of the Berry’s phase.