Axion production due to photon–axion mixing in tangled magnetic fields prior to the recombination epoch and magnetic field damping can generate cosmic microwave background (CMB) spectral distortions. In particular, the contribution of both processes to the CMB μ\documentclass[12pt]{minimal}
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\begin{document}$$\mu $$\end{document} distortion in the case of resonant photon–axion mixing is studied. Assuming that the magnetic field power spectrum is approximated by a power law, PB(k)∝kn\documentclass[12pt]{minimal}
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\begin{document}$$P_B(k)\propto k^n$$\end{document} with spectral index n, it is shown that for magnetic field cut-off scales 172.5 pc ≤λB≤4×103\documentclass[12pt]{minimal}
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\begin{document}$$\le \lambda _B\le 4\times 10^3$$\end{document} pc, the axion contribution to the CMB μ\documentclass[12pt]{minimal}
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\begin{document}$$\mu $$\end{document} distortion is subdominant in comparison with magnetic field damping in the cosmological plasma. Using the COBE upper limit on μ\documentclass[12pt]{minimal}
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\begin{document}$$\mu $$\end{document} and for the magnetic field scale λB≃415\documentclass[12pt]{minimal}
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\begin{document}$$\lambda _B\simeq 415$$\end{document} pc, a weaker limit in comparison with other studies on the magnetic field strength (B0≤8.5×10-8\documentclass[12pt]{minimal}
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\begin{document}$$B_0\le 8.5\times 10^{-8}$$\end{document} G) up to a factor 10 for the DFSZ axion model and axion mass ma≥2.6×10-6\documentclass[12pt]{minimal}
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\begin{document}$$m_a\ge 2.6\times 10^{-6}$$\end{document} eV is found. A forecast for the expected sensitivity of PIXIE/PRISM on μ\documentclass[12pt]{minimal}
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\begin{document}$$\mu $$\end{document} is also presented.
