We study experimentally nanoscale Josephson junctions and Josephson spin valves containing strongly ferromagnetic Ni interlayers. We observe that in contrast to junctions, spin valves with the same geometry exhibit anomalous I_{c}(H) patterns with two peaks separated by a dip. We develop several techniques for in situ characterization of micromagnetic states in our nanodevices, including magnetoresistance, absolute Josephson fluxometry, and first-order-reversal-curves analysis. They reveal a clear correlation of the dip in supercurrent with the antiparallel state of a spin valve and the peaks with two noncollinear magnetic states, thus providing evidence for generation of spin-triplet superconductivity. A quantitative analysis, based on micromagnetic simulations, brings us to the conclusion that the triplet current in our Ni-based spin valves is approximately three times larger than the conventional spin-singlet supercurrent.
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