  We show existence of strong negative correlation between the temporal
variations of magnetic field toroidal component of the solar tachocline (the
bottom of convective zone) and the Earth magnetic field (Y-component). The
possibility that hypothetical solar axions, which can transform into photons in
external electric or magnetic fields (the inverse Primakoff effect), can be the
instrument by which the magnetic field of convective zone of the Sun modulates
the magnetic field of the Earth is considered. We propose the axion mechanism
of "solar dynamo-geodynamo" connection, where an energy of axions, which form
in the Sun core, is modulated at first by the magnetic field of the solar
tachocline zone (due to the inverse coherent Primakoff effect) and after that
is absorbed in the liquid core of the Earth under influence of the terrestrial
magnetic field, thereby playing the role of an energy source and a modulator of
the Earth magnetic field. Within the framework of this mechanism new
estimations of the strength of an axion coupling to a photon (ga_gamma about
5*10^-9 GeV^-1) and the axion mass (ma ~ 30 eV) have been obtained.
