Tuning Hidden Order (HO) and Antiferromagnetism (AFM) in the Correlated f-Electron Superconductor (SC) URu₂₋ₓMₓSi₂ (M = Co, Ir): Interplay of Electron Doping, Chemical Pressure, and Disorder.

The heavy-fermion (HF) SC URu₂Si₂ (T_c ≈ 1.5 K) exhibits a HO transition at T_HO ≈ 17.5 K, whose order parameter remains unresolved despite decades of study. To elucidate the competing interactions governing its correlated ground states, we performed comprehensive investigation of the pseudo-ternary series URu₂₋ₓMₓSi₂ (M = Co, Ir) using X-ray diffraction, resistivity, magnetization, and specific heat measurements on polycrystalline samples. Substitution of Co or Ir at the Ru site progressively suppresses both the HO and SC phases, which vanish near x ≈ 0.1. Analysis of transport and thermodynamic data reveals that the HO energy gap (Δ) decreases faster than T_HO, implying the existence of a “gapless” HO regime prior to its collapse. Beyond this point, Co and Ir substitution series exhibit distinct evolutions of coherence and magnetic order. For M = Co, the coherence temperature T_ρ* rises up to x ≈ 0.4 but becomes ill-defined for x ≥ 0.6, where strong disorder (ρ_₀ /ρ_₂₇₀K > 1) disrupts HF coherence and no AFM1 phase is detected; instead, a distinct AFM2 phase emerges near x ≈ 1.0 with T_N₂ ≈ 80–106 K. In contrast, Ir substitution induces an AFM1 phase near x ≈ 0.3, developing three successive magnetic transitions (T_N₁a, T_N₁b, T_N₁c ≈ 38–51 K) persisting up to x ≈ 1.0. The intertwined evolution of HO and AFM highlights the delicate interplay of electron doping, chemical pressure, and structural disorder governing competing interactions and emergent quantum phases in URu₂₋ₓMₓSi₂.