  The solar surface is a continuous source of internal gravity waves (IGWs).
IGWs are believed to supply the bulk of the wave energy for the lower solar
atmosphere, but their existence and role for the energy balance of the upper
layers is still unclear, largely due to the lack of knowledge about the
influence of the Sun's magnetic fields on their propagation. In this work, we
look at naturally excited IGWs in realistic models of the solar atmosphere and
study the effect of different magnetic field topographies on their propagation.
We carry out radiation-magnetohydrodynamic (R-MHD) simulations of a magnetic
field free and two magnetic models -- one with an initial, homogeneous,
vertical field of 100 G magnetic flux density and one with an initial
horizontal field of 100 G flux density. The propagation properties of IGWs are
studied by examining the phase-difference and coherence spectra in the
$k_{h}$-$\omega$ diagnostic diagram. We find that IGWs in the upper solar
atmosphere show upward propagation in the model with predominantly horizontal
field similar to the model without magnetic field. In contrast to that the
model with predominantly vertical fields show downward propagation. This
crucial difference in the propagation direction is also revealed in the
difference in energy transported by waves for heights below 0.8 Mm. Higher up,
the propagation properties show a peculiar behaviour, which require further
study. Our analysis suggests that IGWs may play a significant role in the
heating of the chromospheric layers of the internetwork region where horizontal
fields are thought to be prevalent.
