  Magnetic skyrmions are topological quasiparticles of great interest for data
storage applications because of their small size, high stability, and ease of
manipulation via electric current. Antiferromagnetic (AF) skyrmions, with new
features and huge benefits (ultra-small skyrmion sizes, no transverse
deflection and efficient manipulation), have recently become the subject of
intense focus. Here we show that a spontaneous antiferromagnetic
skyrmion/antiskyrmion lattice (AF-SkL/ASkL) emerges in the classical Heisenberg
antiferromagnet on the triangular-lattice under magnetic fields, taking only
exchange interactions up to third nearest neighbors ($J_1$-$J_2$-$J_3$). By
means of the Luttinger-Tisza approximation and large scale Monte-Carlo
simulations (combining Parallel-Tempering and overrelaxation with the
Metropolis algorithm), we present a rich $J_2$-$J_3$ magnetic phase diagram
including exotic multiple-q phases, degenerate states and a spontaneous
AF-SkL/ASkL lattice at intermediate magnetic fields. In addition, we show that
at zero magnetic field, exotic spin liquid states with ring-like degeneracy
emerge at intermediate temperatures, which are broken by thermal fluctuations
selecting different multiple-q states. These findings greatly enrich the
research on antiferromagnetic skyrmions in centrosymmetric materials or
lattices including relatively weak Dzyaloshinskii-Moriya interaction.
