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Quasiparticle nonequilibrium due to spin-polarized current injection in perovskite superconductor/ferromagnet (S/F) thin-film heterostructures has been studied with the technique of cryogenic scanning tunneling spectroscopy. The spin-injection heterostructures consisted of epitaxial bilayers of the high-Tc superconductor YBa2Cu3O7−δ and the half-metallic ferromagnet La0.7Ca0.3MnO3, with a spin-polarized quasiparticle current injected into the cuprate layer from the manganite layer. The tunneling conductance measured at 4.2 K on the cuprate layer showed a distinctly nonequilibrium quasiparticle spectrum as a result of the spin injection. Quantitative analysis of the tunneling spectral evolution versus the injection current yielded an estimate of the quasiparticle spin-diffusion depth and the spin-relaxation time in the superconducting cuprate.