We investigate the stability of a zero-field skyrmion crystal with skyrmion number two in a centrosymmetric distorted square-lattice magnet. By using an effective spin model in momentum space and simulated annealing, we examine the effects of biquadratic interactions, higher-harmonic wave-vector couplings, uniaxial anisotropy, and an in-plane magnetic field. Within the present effective model, the SkX occupies the widest stability region at intermediate biquadratic interaction, where the primary and higher-harmonic wave-vector channels are effectively balanced. Increasing uniaxial anisotropy destabilizes the skyrmion crystal and induces transitions to topologically trivial double-Q and single-Q states. We also show that an in-plane magnetic field drives the zero-field skyrmion crystal into topologically trivial multiple-Q states, single-Q states, and eventually a fully polarized state. These results clarify how anisotropic perturbations control high-topological-number skyrmion crystals in centrosymmetric magnets and provide insight into the stability of topological magnetic textures in distorted square-lattice systems.
The permeability and low temperature magnetization of soft magnetic ribbons Fe_76Si_19.4Nb_2.7Cu_1.7P_0.2 prepared by single-roller cooling method has been investigated. The average crystallite size increases with annealed temperature increasing. The minimum in the real part of the permeability in ribbon annealed at 873 K induced by the competition of domain-wall displacement and domain rotation has been observed. At the annealing temperature of 773 K and 823 K, the ribbons exhibit minimum in the imaginary part of the permeability, excellent energy storage performance at a certain frequency and higher energy storage efficiency. The saturation magnetizations of both as-cast and annealed ribbons decrease as the temperature of measurement increases from 5 K to 240 K. The saturation magnetization of annealed ribbon is smaller than the as-cast ribbon probably because the ribbon contains a small amount of P and the heat treatment process was not carried out under a magnetic field.
