Skyrmions and multi-sublattice helical states in a frustrated chiral magnet

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.