Size-Driven Magnetic Transitions in Electron-Doped Cuprates: A Muon Spin Relaxation Study

Nanoscale confinement in correlated electron systems provides a powerful route to manipulate emergent quantum phenomena. Here, we explore size-dependent magnetism in electron-doped cuprate nanoparticles, focusing on Eu1.85Ce0.15CuO4+α-δ (ECCO). Compared to hole-doped cuprates, electron-doped variants face experimental challenges due to the sensitivity of superconductivity and magnetism to oxygen nonstoichiometry. To overcome this, we optimized δ within the critical range of 0.040–0.090, where superconductivity can emerge, by annealing under argon at 700 °C for 8 hours. Using a sol–gel method, we synthesized phase-pure ECCO with sizes of 56, 108, and 169 nm. Magnetic measurements show a transition from paramagnetism at 169 nm to spin-glass behavior and emergent ferromagnetism in smaller particles. Curie-law analysis confirms enhanced magnetic moments with decreasing size. To clarify the magnetic ground state and spin dynamics, we propose muon spin relaxation (μSR) measurements. Zero-field μSR (2–300 K) will detect static magnetism and spin freezing, while longitudinal-field μSR (10–1000 G) will probe fluctuation dynamics near the spin-glass transition. These experiments will advance understanding of size-tuned magnetism and its relation to superconductivity in electron-doped cuprates.