Influence of hydrostatic pressure on hidden order, the Kondo lattice, and magnetism in URu 2 Si 2 − x P x

Within the chemical substitution series ${\mathrm{URu}}_{2}{\mathrm{Si}}_{2\ensuremath{-}x}{\mathrm{P}}_{x}$, there is an evolution in the ground-state behavior from hidden ordered (HO) for $x\ensuremath{\lesssim}0.03$, to Kondo lattice behavior with no ordering (NO) for $0.03\ensuremath{\lesssim}x\ensuremath{\lesssim}0.26$, to antiferromagnetism (AFM-2) for $0.26\ensuremath{\lesssim}x\ensuremath{\lesssim}0.5$ [A. Gallagher et al., Nat. Commun. 7, 10712 (2016); A. Gallagher et al., J. Phys.: Condens. Matter 29, 024004 (2016)]. To better understand what factors control this behavior, temperature-dependent electrical resistivity measurements are performed for this series under applied pressures $P$ up to 20.5 kbar. Specimens in the HO $x$ region show similarities to the parent compound, where HO transforms into antiferromagnetism (AFM-1) at a critical pressure (${P}_{\mathrm{c}}$). ${P}_{\mathrm{c}}$ decreases with increasing $x$ and collapses towards $P=0$ near $x\ensuremath{\approx}0.03$, suggesting that AFM-1 occurs at ambient pressure for this concentration. No pressure-induced phase transitions are observed in the NO $x$ region and the AFM-2 state is only weakly suppressed by $P$. Measurements further reveal that AFM-1 and AFM-2 are distinct from each other. Calculations of the wave functions using the tight-binding Hartree-Fock approximation are performed and show (i) that the radial probability distributions for the phosphorus ions are more tightly bound than those for the silicon and (ii) that the energy difference between the orbitals decreases with increasing $x$. The cumulative effect of these two factors is that $\mathrm{Si}\ensuremath{\rightarrow}\mathrm{P}$ substitution decreases the hybridization strength, which correlates with the weakening of HO. At large $x$, additional effects such as electrical charge tuning also play an important role in determining the ground-state behavior.