Coupling of axion-like particles (ALPs) to photons in the presence of background magnetic field affects propagation of gamma-rays through magnetized environments. This results in modification in the gamma-ray spectra of sources in or behind galaxy clusters. We search for the ALP induced effects in the Fermi/LAT and MAGIC telescope spectra of the radio galaxy NGC 1275 embedded in Perseus galaxy cluster. We report an order-of-magnitude improved upper limit on the ALP-photon coupling constant in the 0.1-10 neV mass range from non-detection of the ALP imprints on the gamma-ray spectra. The improved upper limit extends into the coupling range in which the ALP particles could form the dark matter. We estimate the sensitivity improvements for the ALP search achievable with extension of the measurements to lower and higher energies with e-ASTROGAM and CTA and show that the gamma-ray probe of ALPs with masses in $10^{-11}-10^{-7}$ eV range will be have order-of-magnitude better sensitivity compared to ground-based experiment IAXO.
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