Transferability of neural network potentials for varying stoichiometry: phonons and thermal conductivity of Mn$_x$Ge$_y$ compounds

Germanium manganese compounds exhibit a variety of stable and metastable phases with different stoichiometry. These materials entail interesting electronic, magnetic and thermal properties both in their bulk form and as heterostructures. Here we develop and validate a transferable machine learning potential, based on the high-dimensional neural network formalism, to enable the study of Mn$_x$Ge$_y$ materials over a wide range of compositions. We show that a neural network potential fitted on a minimal training set reproduces successfully the structural and vibrational properties and the thermal conductivity of systems with different local chemical environments, and it can be used to predict phononic effects in nanoscale heterostructures.