  Using density functional theory (DFT), we study how the stability of
individual magnetic skyrmions in an ultrathin transition-metal film can be
controlled via the external electric fields. For applied electric fields of
$\mathcal{E}$= $\pm 0.5$ V/{\AA}, we find changes from 8 to 30$\%$ of the
Heisenberg exchange, the Dzyaloshinskii-Moriya interaction, the
magnetocrystalline anisotropy energy, and the higher-order exchange
interactions. Based on atomistic spin simulations using the DFT parameters, we
find that the energy barriers for electric field assisted skyrmion writing and
deleting can vary by up to a factor of three more than the variations of the
interactions. This unexpected result originates from the electric field induced
shifts of the critical magnetic field, marking the onset of the field-polarized
phase, which exhibits metastable skyrmions. The shift leads to an electric
field dependent change of the skyrmion radius at a fixed magnetic field and
explains the enhanced energy barrier variations.
