The magnetic dead layers in films a few nanometers thick are investigated for La$_{0.7}$Sr$_{0.3}$MnO$_3$ on (001)-oriented SrTiO$_3$ (STO), LaAlO$_3$ (LAO) and (LaAlO$_3$)$_{0.3}$(Sr$_2$TaAlO$_6$)$_{0.7}$ (LSAT) substrates. An anomalous moment found to persist above the Curie temperature of the La$_{0.7}$Sr$_{0.3}$MnO$_3$ films is not attributed to the films, but to oxygen vacancies at or near the surface of the substrate. The contribution to the moment from the substrate is as high as 20 $mu$B/nm$^2$ in the case of STO or LSAT. The effect is increased by adding an STO cap layer. Taking this d-zero magnetism into account, extrapolated magnetic dead layer thicknesses of 0.8 nm, 1.5 nm and 3.0 nm are found for the manganite films grown on LSAT, STO and LAO substrates, respectively. An STO cap layer eliminates the LSMO dead layer.
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