We examine the anomalous inverse spin switch behavior in La$_{0.7}$Ca$_{0.3}$MnO$_3$ (LCMO)/YBa$_2$Cu$_3$O$_{7-delta}$ (YBCO)/LCMO trilayers by combined transport studies and polarized neutron reflectometry. Measuring magnetization profiles and magnetoresistance in an in-plane rotating magnetic field, we prove that, contrary to many accepted theoretical scenarios, the relative orientation between the two LCMOs magnetizations is not sufficient to determine the magnetoresistance. Rather the field dependence of magnetoresistance is explained by the interplay between the applied magnetic field and the (exponential tail of the) induced exchange field in YBCO, the latter originating from the electronic reconstruction at the LCMO/YBCO interfaces.
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