  We investigate the existence and stability of skyrmions in a frustrated
chiral ferromagnet by considering the competition between ferromagnetic (FM)
nearest-neighbour (NN) interaction ($J_1$) and antiferromagnetic (AFM)
next-nearest-neighbour (NNN) interaction ($J_2$). Contrary to the general
wisdom that long-range ferromagnetic order is not energy preferable under
frustration, the skyrmion lattice not only exists but is even stable for a
large field range when $J_2 \leq J_1$ compared with frustration-free systems.
We defend that the enlargement of stability window of skyrmions is a
consequence of the reduced effective exchange interaction caused by the
frustration. A multi-sublattice helical state is found below the skyrmion
phase, which results from the competition between AFM coupling that favors a
two-sublattice N\'{e}el state and the chiral interaction that prefers a helix.
As a byproduct, the hysteresis loop of the frustrated chiral system shrinks as
the magnetization goes to zero and then opens up again, known as wasp-waist
hysteresis loop. The critical field that separates the narrow and wide part of
the wasp-waist loop depends exponentially on the strength of NNN coupling. By
measuring the critical field, it is possible to determine the strength of NNN
coupling.
