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ABSTRACT We calculate spectra of escaping cosmic rays (CRs) accelerated at shocks produced by expanding Galactic superbubbles powered by multiple supernovae producing a continuous energy outflow in star-forming galaxies. We solve the generalized Kompaneets’ equations adapted to expansion in various external density profiles, including exponential and power-law shapes, and take into account that escaping CRs are dominated by those around their maximum energies. We find that the escaping CR spectrum largely depends on the specific density profiles and power source properties, and the results are compared to and constrained by the observed CR spectrum. As a generic demonstration, we apply the scheme to a superbubble occurring in the centre of the Milky Way, and find that under specific parameter sets the CRs produced in our model can explain the observed CR flux and spectrum around the second knee at 1017 eV. 

Abstract Internal magnetic moments induced by magnetic dopants in MoS₂monolayers are shown to serve as a new means to engineer valley Zeeman splitting (VZS). Specifically, successful synthesis of monolayer MoS₂doped with the magnetic element Co is reported, and the magnitude of the valley splitting is engineered by manipulating the dopant concentration. Valley splittings of 3.9, 5.2, and 6.15 meV at 7 T in Co‐doped MoS₂with Co concentrations of 0.8%, 1.7%, and 2.5%, respectively, are achieved as revealed by polarization‐resolved photoluminescence (PL) spectroscopy. Atomic‐resolution electron microscopy studies clearly identify the magnetic sites of Co substitution in the MoS₂lattice, forming two distinct types of configurations, namely isolated single dopants and tridopant clusters. Density functional theory (DFT) and model calculations reveal that the observed enhanced VZS arises from an internal magnetic field induced by the tridopant clusters, which couples to the spin, atomic orbital, and valley magnetic moment of carriers from the conduction and valence bands. The present study demonstrates a new method to control the valley pseudospin via magnetic dopants in layered semiconducting materials, paving the way toward magneto‐optical and spintronic devices.