Length Scale Dependence of the Anomalous Atomic Motion in Metallic Glasses

Establishing microscopic structure–dynamics relations in glasses is essential for developing a comprehensive theory, yet remains challenging due to limited access to the relevant time and length scales. By probing density fluctuations in metallic glasses (MGs) across six decades in time and over both mesoscopic and atomic length scales, we reveal a hierarchical organization of the dynamics and provide a comprehensive framework of their anomalous compressed relaxation universally observed at the atomic level. We demonstrate that this faster-than-exponential motion emerges only at wavelengths comparable to the cluster size, and originates from internal stresses frozen during a transition from liquid-like to hyper-diffusive dynamics across the glass transition. At mesoscopic scales, stress effects vanish, and the dynamics become stationary and heterogeneous, with stretched exponential relaxations reflecting the statistically-averaged motions of rigid domains. We also identify a second independent relaxation, associated to persistent liquid-like motions, whose strength increases at large wavelength. These findings reveal the cooperative, multiscale nature of relaxations in glasses.