Ferromagnetic Josephson junctions play a key role in understanding the interplay between superconductivity and ferromagnetism in condensed matter physics. The magnetic domain structures of the ferromagnet in such junctions can significantly affect the tunneling of the superconducting Cooper pairs due to the strong interactions between Cooper pairs and local magnetic moments in the ferromagnetic tunnel barrier. However, the underlying microscopic mechanism of relevant quasiparticle tunneling processes with magnetic domain structures remains largely unexplored. Here, the manipulation of Cooper-pair tunneling in the NbSe/CrGeTe/NbSe ferromagnetic Josephson junction is demonstrated by using a multidomain ferromagnetic barrier with anisotropic magnetic moments. The evolution of up-, down-magnetized domain and Bloch domain structures in CrGeTe barrier under external magnetic fields leads to the enhancement of the critical tunneling supercurrent and an unconventional dual-peak feature with two local maxima in the field-dependent critical current curve. The phenomenon of magnetic-field-modulated critical tunneling supercurrent can be well explained by the competition between the coherence length of tunneling Cooper pairs and the size of magnetic domain walls in CrGeTe barrier. This kind of ferromagnetic Josephson junction provides an intriguing material system for manipulating Cooper-pair tunneling by tuning the local magnetic moments within magnetic Josephson junction devices.
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