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Axion production due to photon-axion mixing in tangled magnetic field(s)prior to recombination epoch and magnetic field damping can generate cosmicmicrowave background (CMB) spectral distortions. In particular, contribution ofboth processes to CMB $\mu$ distortion in the case of resonant photon-axionmixing is studied. Assuming that magnetic field power spectrum is approximatedby a power law $P_B(k)\propto k^n$ with spectral index $n$, it is shown thatfor magnetic field cut-off scales $172.5$ pc $\leq \lambda_B\leq 4\times 10^3$pc, axion contribution to CMB $\mu$ distortion is subdominant in comparisonwith magnetic field damping in the cosmological plasma. Using COBE upper limiton $\mu$ and for magnetic field scale $\lambda_B\simeq 415$ pc, weaker limit incomparison with other studies on the magnetic field strength ($B_0\leq8.5\times 10^{-8}$ G) up to a factor 10 for the DFSZ axion model and axion mass$m_a\geq 2.6\times 10^{-6}$ eV is found. A forecast for the expectedsensitivity of PIXIE/PRISM on $\mu$ is also presented.

Axion production and CMB spectral distortion in cosmological tangled magnetic field