La0.67Sr0.33MnO3 (LSMO) thin films were fabricated on (011)- and (001)-Pb(Mg1/3Nb2/3)1 − xTixO3 (PMN-PT) substrates to investigate the mechanism of electric field regulation. Both (011)- and (001)-LSMO/PMN-PT heterostructures exhibit electric-field-dependent resistance curves with an asymmetric butterfly shape under a bipolar electric field (±10 kV/cm). Confirmed through a mathematical method, the "butterfly" and "asymmetric" characteristics indicate the volatile strain and non-volatile ferroelectric field effects, respectively. However, by applying a unipolar electric field, the electric-field-dependent resistance curves of the (011)-LSMO/PMN-PT heterostructures present a larger loop shape than those in the (001)-LSMO/PMN-PT heterostructure, which is related to the non-volatile strain effect. The volatile strain, non-volatile strain, and ferroelectric field effects on the resistance of the LSMO films are associated with the enhanced or weakened double exchange coupling. [ABSTRACT FROM AUTHOR]