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Dark matter may consist of axion-like particles (ALPs). When polarized electromagnetic radiation passes through the dark-matter media, interaction with background ALPs affects the polarization of photons. The condensate of axionic dark matter experiences periodic oscillations, and the period of the oscillations is of order of years for ultra-light dark matter. This would result in observable periodic changes in the polarization plane, determined by the phases of the ALP field at the Earth and at the source. In this paper, we use recent polarimetric observations of the HL Tauri protoplanetary disk performed in different years to demonstrate the lack of changes of polarization angles, and hence to constrain masses and photon couplings of the hypothetical axion-like ultralight dark matter.