Angle-resolved photoemission spectroscopy with an $\textit{in situ}$ tunable magnetic field

Angle-resolved photoemission spectroscopy (ARPES) is a powerful tool for probing the momentum-resolved single-particle spectral function of materials. Historically, $\textit{in situ}$ magnetic fields have been carefully avoided as they are detrimental to the control of photoelectron trajectory during the photoelectron detection process. However, magnetic field is an important experimental knob for both probing and tuning symmetry-breaking phases and electronic topology in quantum materials. In this paper, we introduce an easily implementable method for realizing an $\textit{in situ}$ tunable magnetic field at the sample position in an ARPES experiment and analyze magnetic field induced artifacts in ARPES data. Specifically, we identified and quantified three distinct extrinsic effects of a magnetic field: Fermi surface rotation, momentum shrinking, and momentum broadening. We examined these effects in three prototypical quantum materials, i.e., a topological insulator (Bi$_2$Se$_3$), an iron-based superconductor (LiFeAs), and a cuprate superconductor (Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$), and demonstrate the feasibility of ARPES measurements in the presence of a controllable magnetic field. Our studies lay the foundation for the future development of the technique and interpretation of ARPES measurements of field-tunable quantum phases.