  We present $ab$ $initio$ study of the electronic stopping power of protons
and helium ions in an insulating material, HfO$_{2}$. The calculations are
carried out in channeling conditions with different impact parameters by
employing Ehrenfest dynamics and real--time, time--dependent density functional
theory. The satisfactory comparison with available experiments demonstrates
that this approach provides an accurate description of electronic stopping
power. The velocity-proportional stopping power is predicted for protons and
helium ions in the low energy region, which conforms the linear response
theory. Due to the existence of wide band gap, a threshold effect in extremely
low velocity regime below excitation is expected. For protons, the threshold
velocity is observable, while it does not appear in helium ions case. This
indicates the existence of extra energy loss channels beyond the electron--hole
pair excitation when helium ions are moving through the crystal. To analyze it,
we checked the charge state of the moving projectiles and an explicit charge
exchange behavior between the ions and host atoms is found. The missing
threshold effect for helium ions is attributed to the charge transfer, which
also contributes to energy loss of the ion.
