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Spin-glass-like freezing of inner and outer surface layers in hollow γFe$_2$O$_3$ nanoparticles

Disorder among surface spins largely dominates the magnetic response of ultrafine magnetic particle systems. In this work, we examine time-dependent magnetization in high-quality, monodisperse hollow maghemite nanoparticles with a 14.8 $\pm$ 0.5 nm outer diameter and enhanced surface-to-volume ratio. The nanoparticle ensemble exhibits spin-glass-like signatures in dc magnetic aging and memory protocols and ac magnetic susceptibility. The dynamics of the system slows near 50 K, and becomes frozen on experimental time scales below 20 K. Remanence curves indicate the development of magnetic irreversibility concurrent with the freezing of the spin dynamics. A strong exchange-bias effect and its training behavior point to highly frustrated surface spins that rearrange much more slowly than interior spins with bulk coordination. Monte Carlo simulations of a hollow particle reproducing the experimental morphology corroborated strongly disordered surface layers with complex energy landscapes that underlie both glass-like dynamics and magnetic irreversibility. Calculated hysteresis loops reveal that magnetic behavior is not identical at the inner and outer surfaces, with spins at the outer surface layer of the 15 nm hollow particles exhibiting a higher degree of frustration. Our study sheds light on the origin of spin-glass-like phenomena and the role of surface spins in magnetic hollow nanostructures.