Measurements of magnetic fields in circumnuclear matter with the SKA telescopes

Magnetic fields are thought to regulate the angular momentum transfer in active galactic nuclei (AGNs), yet their strength and structure in circumnuclear regions remain poorly constrained across spatial scales and gas phases. We present a unified observational framework for probing circumnuclear magnetic fields using complementary diagnostics: direct measurements via the Zeeman effect in HI absorption and megamaser emission, and indirect constraints from broadband Faraday rotation of polarized continuum radiation. These approaches provide access to magnetized gas spanning spatial scales from 100 parsec (pc) circumnuclear disks down to sub-pc regions near supermassive black holes (SMBHs). The Square Kilometre Array (SKA) telescopes are expected to revolutionize such investigations through their outstanding sensitivities, wide frequency ranges and high spatial resolutions achievable via very long baseline interferometry (VLBI). These capabilities will enable the detection and detailed characterization of weakly polarized emission from magnetized circumnuclear matter, which has remained largely inaccessible with current instruments. In this chapter, we review previous measurements of magnetic fields in galactic nuclei and discuss the breakthroughs that SKA observations are expected to provide in elucidating the physical conditions and processes shaping AGN environments.