Viscosity, breakdown of Stokes-Einstein relation and dynamical heterogeneity in supercooled liquid Ge$_2$Sb$_2$Te$_5$ from simulations with a neural network potential

Phase change materials are exploited in non-volatile electronic memories and photonic devices that rely on a fast and reversible transformation between the amorphous and crystalline phase upon heating. The recrystallization of the amorphous phase at the operation conditions of the memories occurs in the supercooled liquid phase above the glass transition temperature $T_g$. The dynamics of the supercooled liquid is thus of great relevance for the operation of the devices and, close to $T_g$, also for the structural relaxations of the glass that affect the performances of the memories. Information on the atomic dynamics is provided by the diffusion coefficient ($D$) and by the viscosity ($\eta$) which are, however, both difficult to be measured experimentally at the operation conditions of the devices due to the fast crystallization. In this work, we leverage a machine learning interatomic potential for the flagship phase change compound compound Ge$_2$Sb$_2$Te$_5$ to compute $\eta$, $D$ and the $\alpha$-relaxation time in a wide temperature range from 1200 K to about 100 K above $T_g$. Large scale molecular dynamics simulations allowed quantifying the fragility of the liquid and the occurrence of a breakdown of the Stokes-Einstein relation between $\eta$ and $D$ in the supercooled phase. Isoconfigurational analysis provided a visualization of the emergence of dynamical heterogeneities responsible for the breakdown of the Stokes-Einstein relation. The analysis revealed that the regions of most mobile atoms are related to the presence of Ge atoms with particular local environments.