Probing inelastic signatures of dark matter detection via polarized nucleus* * Supported by the National Natural Science Foundation of China (12275232, 12005180), the Natural Science Foundation of Shandong Province, China (ZR2020QA083) and the Project of Higher Educational Science and Technology Program of Shandong Province, China (2022KJ271)

We investigate the inelastic signatures of dark matter-nucleus interactions, explicitly focusing on the ramifications of polarization, dark matter splitting, and the Migdal effect. Direct detection experiments, crucial for testing the existence of dark matter, encounter formidable obstacles, such as indomitable neutrino backgrounds and elusive determination of dark matter spin. To overcome these challenges, we explore the potential of polarized-target dark matter scattering, examining the impact of nonvanishing mass splitting, and the role of the Migdal effect in detecting dark matter. Our analysis demonstrates the valuable utility of the polarized triple-differential event rate as an effective tool for examining inelastic dark matter. It enables us to investigate angular and energy dependencies, providing valuable insights into the scattering process.