Aims: We aim to probe the magnetic field geometry and particle acceleration mechanism in the relativistic jets of supermassive black holes.
Methods: We conducted a polarimetry campaign from radio to X-ray wavelengths of the high-synchrotron-peak (HSP) blazar Mrk 421, including Imaging X-ray Polarimetry Explorer (IXPE) measurements from 2022 December 6-8. During the IXPE observation, we also monitored Mrk 421 using Swift-XRT and obtained a single observation with XMM-Newton to improve the X-ray spectral analysis. The time-averaged X-ray polarization was determined consistently using the event-by-event Stokes parameter analysis, spectropolarimetric fit, and maximum likelihood methods. We examined the polarization variability over both time and energy, the former via analysis of IXPE data obtained over a time span of 7 months.