Faraday tomography of polarimetric observations at low frequency is a unique tool to study the structure of the magneto-ionic interstellar medium (ISM) based on Faraday depth. LOFAR data below 200 MHz revealed a plethora of features in polarization, whose origin remains unknown. Previous studies highlighted the remarkable association of such features to tracers of the magnetized-neutral ISM, as interstellar dust and atomic hydrogen (HI). However, the physical conditions responsible for the correlation between magneto-ionic and neutral media are yet to be clarified. In this letter we investigate further the correlation between LOFAR data and HI observations at 21cm from the Effelsberg-Bonn HI Survey (EBHIS). We focus on the multiphase properties of the HI gas. We present the first statistical study on the morphological correlation between LOFAR tomographic data and the cold (CNM), luke-warm (LNM), and warm (WNM) HI phases, separately. We use the Regularized Optimization for Hyper-Spectral Analysis (ROHSA) approach to decompose the HI phases based on the Gaussian decomposition of the HI spectra. In at least two fields of view -- Fields 3C196 and A -- out of four -- Fields B and C -- we find a significant correlation between LOFAR and EBHIS data using the Histograms of Oriented Gradients (HOG). The absence of correlation in Fields B and C is caused by low signal-to-noise ratio in polarization. The observed HOG correlation in Fields 3C196 and A is associated with all HI phases and it is surprisingly dominant in the CNM and LNM phases. We discuss possible mechanisms that would explain the correlation between CNM, LNM, and WNM, with polarized emission at Faraday depths up to 10 rad m$^{-2}$. Our results show how the complex structure of the ionic medium seen by LOFAR data is tightly related to phase transition in the diffuse and magnetized neutral ISM traced by HI spectroscopic data.
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