  We identify a new resonance, axion magnetic resonance (AMR), that can greatly
enhance the conversion rate between axions and photons. A series of axion
search experiments rely on converting them into photons inside a constant
magnetic field background. A common bottleneck of such experiments is the
conversion amplitude being suppressed by the axion mass when $m_a \gtrsim
10^{-4}~$eV. We point out that a spatial or temporal variation in the magnetic
field can cancel the difference between the photon dispersion relation and that
of the axion, hence greatly enhancing the conversion probability. We
demonstrate that the enhancement can be achieved by both a helical magnetic
field profile and a harmonic oscillation of the magnitude. Our approach can
extend the projected ALPS II reach in the axion-photon coupling ($g_{a\gamma}$)
by two orders of magnitude at $m_a = 10^{-3}\;\mathrm{eV}$ with moderate
assumptions.
