Complex spin Hamiltonian represented by an artificial neural network
Hongyu Yu, Changsong Xu, Xueyang Li, Feng Lou, L. Bellaïche, Zhenpeng Hu, Xin-Gao Gong, Hongjun Xiang
Abstract
The effective spin Hamiltonian method is very useful for simulating and understanding the behavior of magnetism. However, it is not easy to construct an appropriate spin Hamiltonian for a magnetic system, especially for complex magnets such as itinerant topological magnets. Here, we put forward a machine learning (ML) approach, applying an artificial neural network (ANN) and a local spin descriptor to construct an effective spin Hamiltonian for any magnetic system. The obtained Hamiltonians include an explicit Heisenberg part and an implicit nonlinear ANN part. Such a method successfully reproduces artificially constructed models and also accurately describes the itinerant magnetism of bulk ${\mathrm{Fe}}_{3}\mathrm{Ge}{\mathrm{Te}}_{2}$. Our work paves a new way for investigating complex magnetic phenomena (e.g., skyrmions) using ML techniques.