Exploring potential energy surface of magnetic materials with non-collinear self-consistent constrain method and deep learning model

In magnetic materials, the energy surface is a function of coordinates R and the magnetization vectors M of each atom. Therefore, exploring the energy surface concerning R and M using ab-initial calculation methods has been a meaningful way to search magnetic candidate materials. However, this task is hindered by the difficulty of precisely anchoring the magnetization among the parameter space of arbitrarily varying direction or magnitude.  In this talk, we would like to present our newly developed non-collinear self-consistent magnetization constrain method and deep learning-based predicting model that explore the full M and R space, with the tolerance of magnetization up to 1e-6 Bohr magneton. Moreover, using our deep learning model, the energy, atomic force and magnetic torque (or effective field) can be predicted with quantum accuracy with respective to variables R and M. We are confident that our method can provide the possibility for applications, for example the exploring the magenetic phase space and analyzing spin interaction hamiltonian, etc.