Zero-field skyrmion crystal with skyrmion number two driven by four-spin interactions on a centrosymmetric square lattice

We investigate the stabilization of a skyrmion crystal in a centrosymmetric square-lattice magnet under zero magnetic field. By constructing an effective spin model in momentum space, we examine the roles of bond-dependent magnetic anisotropy, higher-harmonic wave-vector interactions, and two distinct types of four-spin interactions. Using simulated annealing, we obtain a low-temperature phase diagram that includes a skyrmion crystal with skyrmion number two, three topologically trivial double- Q states, and a single- Q state. The zero-field skyrmion crystal is characterized by a noncoplanar multiple- Q texture composed of sinusoidal modulations at the primary and higher-harmonic ordering wave vectors. We show that the cooperative effect of the conventional biquadratic interaction and the sinusoidal-wave–selective four-spin interaction is essential for activating the higher-harmonic components and stabilizing the topological phase. We also demonstrate that an out-of-plane magnetic field drives the skyrmion crystal into a topologically trivial double- Q state by suppressing the scalar spin chirality and higher-harmonic wave vector components, while a trivial double- Q state remains topologically trivial under magnetic fields. Our results provide a microscopic route to zero-field skyrmion crystals with high skyrmion number in centrosymmetric square-lattice magnets.