TensorSymmetry: a package to get symmetry-adapted tensors disentangling spin-orbit coupling effect and establishing analytical relationship with magnetic order

The symmetry-constrained response tensors on transport, optical, and electromagnetic effects are of central importance in condensed matter physics because they can guide experimental detections and verify theoretical calculations. These tensors encompass various forms, including polar, axial, i-type (time-reversal even), and c-type (time-reversal odd) matrixes. The commonly used magnetic groups, however, fail to describe the phenomena without the spin-orbit coupling (SOC) effect and cannot build the analytical relationship between magnetic orders with response tensors in magnetic materials. Developing approaches on these two aspects is quite demanding for theory and experiment. In this paper, we use the magnetic group, spin group, and extrinsic parameter method comprehensively to investigate the symmetry-constrained response tensors, then implement the above method in a platform called "TensorSymmetry". With the package, we can get the response tensors disentangling the effect free of SOC and establish the analytical relationship with magnetic order, which provides useful guidance for theoretical and experimental investigation for magnetic materials.