We study the linear polarization of the radio cores of eight blazars simultaneously at 22, 43, and 86 GHz with observations obtained by the Korean VLBI Network (KVN) in three epochs between late 2016 and early 2017 in the frame of the Plasma-physics of Active Galactic Nuclei (PAGaN) project. We investigate the Faraday rotation measure (RM) of the cores; the RM is expected to increase with observing frequency if core positions depend on frequency due to synchrotron self-absorption. We find a systematic increase of RMs at higher observing frequencies in our targets. The RM--$ u$ relations follow power-laws with indices distributed around 2, indicating conically expanding outflows serving as Faraday rotating media. Comparing our KVN data with contemporaneous optical polarization data from the Steward Observatory for a few sources, we find indication that the increase of RM with frequency saturates at frequencies of a few hundreds GHz. This suggests that blazar cores are physical structures rather than simple $tau=1$ surfaces. A single region, e.g. a recollimation shock, might dominate the jet emission downstream of the jet launching region. We detect a sign change in the observed RMs of CTA 102 on a time scale of $approx$1 month, which might be related to new superluminal components emerging from its core undergoing acceleration/deceleration and/or bending. We see indication for quasars having higher core RMs than BL Lac objects, which could be due to denser inflows/outflows in quasars.
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