  Convection in the liquid outer core of the Earth is driven by thermal and
chemical perturbations. The main purpose of this study is to examine the impact
of double-diffusive convection on magnetic field generation by means of 3D
global geodynamo models, in the so-called "top-heavy" regime of
double-diffusive convection, when both thermal and compositional background
gradients are destabilizing. Using a linear eigensolver, we begin by confirming
that, compared to the standard single-diffusive configuration, the onset of
convection is facilitated by the addition of a second buoyancy source. We next
carry out a systematic parameter survey by performing $79$ numerical dynamo
simulations. We show that a good agreement between simulated magnetic fields
and the geomagnetic field can be attained for any partitioning of the
convective input power between its thermal and chemical components. On the
contrary, the transition between dipole-dominated and multipolar dynamos is
found to strongly depend on the nature of the buoyancy forcing. Classical
parameters expected to govern this transition, such as the local Rossby number
or the degree of equatorial symmetry of the flow, fail to capture the dipole
breakdown. A scale-dependent analysis of the force balance instead reveals that
the transition occurs when the ratio of inertial to Lorentz forces at the
dominant length scale reaches $0.5$, regardless of the partitioning of the
buoyancy power. The ratio of integrated kinetic to magnetic energy $E_k/E_m$
provides a reasonable proxy of this force ratio. Given that $E_k/E_m \ll 1$ in
the Earth's core, the geodynamo is expected to operate far from the
dipole-multipole transition. It hence appears that the occurrence of
geomagnetic reversals is unlikely related to dramatic and punctual changes of
the amplitude of inertial forces in the Earth's core, and that another
mechanism must be sought.
