Spontaneous antiferromagnetic skyrmion/antiskyrmion lattice and spiral spin liquid states in the frustrated triangular lattice

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.