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Electrical resistivity measurements were performed on single crystals of URu 2– x Os x Si 2 up to x = 0.28 under hydrostatic pressure up to P = 2 GPa. As the Os concentration, x , is increased, 1) the lattice expands, creating an effective negative chemical pressure P ch ( x ); 2) the hidden-order (HO) phase is enhanced and the system is driven toward a large-moment antiferromagnetic (LMAFM) phase; and 3) less external pressure P c is required to induce the HO→LMAFM phase transition. We compare the behavior of the T ( x , P ) phase boundary reported here for the URu 2- x Os x Si 2 system with previous reports of enhanced HO in URu 2 Si 2 upon tuning with P or similarly in URu 2– x Fe x Si 2 upon tuning with positive P ch ( x ). It is noteworthy that pressure, Fe substitution, and Os substitution are the only known perturbations that enhance the HO phase and induce the first-order transition to the LMAFM phase in URu 2 Si 2 . We present a scenario in which the application of pressure or the isoelectronic substitution of Fe and Os ions for Ru results in an increase in the hybridization of the U-5 f -electron and transition metal d -electron states which leads to electronic instability in the paramagnetic phase and the concurrent formation of HO (and LMAFM) in URu 2 Si 2 . Calculations in the tight-binding approximation are included to determine the strength of hybridization between the U-5 f -electron states and the d -electron states of Ru and its isoelectronic Fe and Os substituents in URu 2 Si 2 .
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