Ergodic dynamics near the order-disorder transition of spin-helices in amorphous Fe-Ge thin-film*

Coherent X-ray scattering techniques near the thermodynamic phase boundaries can provide valuable and novel insights into the dynamics of the underlying spin or charge states. Ergodicity is an important property of any dynamical or stochastic system where each particle will visit all parts of the phase space in time, for example, particles in a system displaying Brownian motion. For a magnetic system exhibiting ergodic dynamics, we expect thermal fluctuations of the magnetic domains to follow a Gaussian distribution. Here in this study by taking series of snapshots of the scattered X-ray photons from an amorphous Fe-Ge thin film at intervals of 0.9 sec, we developed “fluctuation maps” of magnetic domains in q-space and found that at temperatures close to the domain order-disorder transition, the histogram of the fluctuation amplitude shows Gaussian distribution. However, just below the transition the histograms shows a significant asymmetry or skewness implying non-ergodic behavior, and which can be resolved into two distinct distributions indicating two different fluctuating spin-structures. Our approach provides a new and deeper way to study the statistics of the fluctuations in disordered systems, and moreover sheds light on the non-ergodicity associated with dynamical heterogeneity.