Critical behaviors of helimagnetic ordering systems relating to skyrmion

Abstract

Study of critical phenomena plays a key role in developing the theory of phase transition. In this article, we mainly review some new experimental results about the critical phenomena reported recently in the helimagentic ordering materials. These materials exhibit a kind of a vortex-like spin texture so-called skyrmion phase. The skyrmion phase has great potential applications in the new spin-based storage due to the topologically protected stability, nanometric size, and current-driven motion. Generally, the skyrmion state exists in a helimagentic system due to the DzyaloshinskiiMoriya (DM) interaction which forms in the crystal structure without inversion symmetry. It usually emerges just below the helimagentic phase transition temperature TC under a certain temperature and magnetic field. In this review article, firstly, we introduce some basic concepts about the phase transition, such as critical phenomenon, critical exponents, scaling law, and universality. Secondly, we discuss two different methods which can help us to obtain the critical exponents, i.e., the iteration method based on the isothermal dc-magnetization and the fitting technique based on the magnetic entropy change. Both methods are extensively used in the current study of critical phenomena Thirdly, we analyze and outline some latest studies of critical behaviors and critical exponents for several typical helimagnetic systems with skyrmion state, such as MnSi, FeGe, Cu2OSeO3, Fe1-xCoxSi, and Fe1.5-xCoxRh0.5MoN. The B20 compound MnSi is a typical skyrmion material, which undergoes a paramagnetic-to-helimagnetic phase transition at ~30.5 K and the skyrmion phase appears just below TC as an appropriate external magnetic field is applied. Investigations show that critical exponents of MnSi belong in the universality class of a tricritical mean-field model, implying the existence of a long-rang magnetic interaction in this system. The critical behavior of MnSi reveals that its first-order phase transition can be driven into a second-order phase transition by the action of external magnetic field, where a field-induced tricritical point is found among the helimagnetic, conical, and paramagnetic phases in MnSi system. Unlike MnSi, the critical exponent of the near-room-temperature skyrmion system FeGe, which undergoes a helimagentic phase transition at 278 K, belong to the three-dimensional Heisenberg model. The critical behavior of Cu2OSeO3 is similar to that of FeGe, which indicates that the magnetic interactions in these two systems are dominated by the short-range nearestneighbor isotropic magnetic coupling. In addition, studies revealed that magnetic interaction and critical behavior of the skyrmion system can be effectively modulated by doping. The critical exponents of Fe1-xCoxSi and the newly founded skyrmion system of Fe1.5-xCoxRh0.5MoN indicated that the doping concentration of Co can change and affect their critical behaviors. In addition, it was demonstrated that the doping of Co enhanced the anisotropic magnetic coupling in Fe1-xCoxSi while it suppressed that in Fe1.5-xCoxRh0.5MoN. Fourthly, according to the universality and the scaling equations, we proposed a method to construct the detailed H-T phase diagram around the phase transition temperature in the system exhibiting field-induced phase transition. Finally, we make a brief summary and suggest our perspectives of the study of critical phenomena in helimagentic system. The results of critical behaviors indicate that although all these helimagentic systems exhibit a similar skyrmion phase, their essential magnetic interactions belong in different universality classes, indicating different types of magnetic coupling in these systems. Furthermore, the results also suggest that magnetic coupling can also be effectively tuned by the external modulation.