Microstructure-controlled vortex phases and two-phase superconductivity in (TaNb)0.7(HfZrTi)0.5 revealed by ac magnetostrictive coefficients

Abstract: We investigate flux dynamics in the high-entropy alloy superconductor (TaNb)0.7(HfZrTi)0.5 after annealing (as-cast, 500 °C, 550 °C, and 1000 °C) using a sensitive ac composite magnetoelectric method that measures the complex ac magnetostrictive coefficient (dλ/dH)ac. The resulting vortex phase diagrams show that intermediate annealing (500-550 °C) induces nanoscale clustering, enhances pinning, and produces a pronounced fishtail effect with successive elastic- and plastic-vortex-glass regimes. Flux-jump instabilities appear at 550 °C and persist at 1000 °C, indicating strong pinning and thermomagnetic instability in the low-temperature, low-field regime. Remarkably, the 1000 °C sample exhibits a two-step superconducting response-a double plateau or drop in dλ'/dH and two dissipation peaks in dλ''/dH-demonstrating the coexistence of two superconducting phases with distinct irreversibility and critical-field value. We further show that the resolvability of the two-step (dλ/dH)ac signature is governed by the topological connectivity of the phase-separated microstructure, which controls magnetic shielding between the TaNb-rich network and the (TaNb)0.7(HfZrTi)0.5 parent phase. These results establish a direct microstructure-vortex-state correlation and provide a route to tailoring flux pinning in chemically complex superconductors via thermal processing.