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Electrical resistivity measurements were performed on single crystals ofURu$_2-x$Os$_x$Si$_2$ up to $x$ = 0.28 under hydrostatic pressure up to $P$ = 2GPa. As the Os concentration, $x$ , is increased, (1) the lattice expands,creating an effective negative chemical pressure $P_{ch}$($x$), (2) the hiddenorder (HO) phase is enhanced and the system is driven toward a large-momentantiferromagnetic (LMAFM) phase, and (3) less external pressure $P_{c}$ isrequired to induce the HO to LMAFM phase transition. We compare the $T(x)$,$T(P)$ phase behavior reported here for the URu$_2-x$Os$_x$Si$_2$ system withprevious reports of enhanced HO in URu$_2$Si$_2$ upon tuning with $P$, orsimilarly in URu$_2-x$Fe$_x$Si$_2$ upon tuning with positive $P_{ch}$($x$). Itis noted that pressure, Fe substitution, and Os substitution are the only knownperturbations that enhance the HO phase and induce the first order transitionto the LMAFM phase in URu$_2$Si$_2$. We present a scenario in which theapplication of pressure or the isoelectronic substitution of Fe and Os ions forRu results in an increase in the hybridization of the U-5$f$- and transitionmetal $d$-electron states which leads to electronic instability in theparamagnetic phase and a concurrent stability of HO (and LMAFM) inURu$_2$Si$_2$. Calculations in the tight binding approximation are included todetermine the strength of hybridization between the U-5$f$ electrons and eachof the isoelectronic transition metal $d$-electron states of Fe, Ru, and Os.

Isoelectronic perturbations to $f$-$d$-electron hybridization and the enhancement of hidden order in URu$_2$Si$_2$