Purely Dynamic Skyrmion Phase discovered

The study of dynamic evolution pattern away from equilibrium in large-scale interacting systems is a crucially relevant aspect of science, given that stable and repetitive pattern as well as transitions between them are present in widely varying areas such as climate dynamics, brain activity and laser emission. Hereby, the more specific study of non-equilibrium dynamic phenomena under periodic excitation is a main scientific focus. Its detailed understanding relies crucially on simplified, but sufficient model descriptions, such as the kinetic Ising Model, which can exhibit qualitatively different types of dynamic spin behavior as well as dynamic phase transitions, despite its formal simplicity. Such models have been successfully investigated for decades and much of their dynamic state complexity has also been verified by experiments on thin magnetic films. However, virtually all theoretical and experimental work so far has been conducted on systems that exhibit a uniform magnetic ground state, and accordingly the complex dynamics of non-uniform phases has been essentially overlooked to date. The now published work by Z. Demir Vatansever et al. [1] rectifies this most relevant limitation of prior work, given that uniform magnetic ground states represent only a small sub-class of magnetically ordered states. Furthermore, leading data storage technologies are based on non-uniform magnetization states, so that the dynamic evolution of such complex magnetic states under excitation is also a most relevant applied scientific issue.

In their novel study [1], the authors have now utilized a Hamiltonian, in which collinear Heisenberg-type exchange coupling and asymmetric Dzyaloshinskii-Moriya-type exchange coupling are both present, which leads to non-uniform skyrmion-type equilibrium states for certain model parameters and applied field strengths, as previously reported. The main novelty of [1] is the in-depth study and analysis of non-equilibrium pattern and phases in the presence of oscillating magnetic fields by means of large-scale Monte-Carlo simulations, for which a set of suitable order parameters were identified to describe the dynamic phases. Specifically, the time-averaged magnetization Q in conjunction with the time-averaged skyrmion density turn out to be especially meaningful, given that they provide complimentary information.

The core observation made in [1] is the discovery of a dynamic skyrmion phase that has no equivalent in equilibrium. The specifics can be seen in the figure below, where both characteristic state parameters Q and  are shown respectively for the same dynamic phase space, defined by the oscillatory field amplitude h₀ and the additionally applied bias field h_b. While Q displays a rather conventional transition from low values in the high h₀/low h_b region to high values in the low h₀/high h_b region, the behavior within the same phase space is far more complex. Instead of simply vanishing for sufficiently high h₀ or h_b values, the skyrmion density  inverts, meaning that the corresponding microscopic state exhibits an inverted skyrmion lattice (yellow area in sub-figure b). So, instead of simply suppressing the skyrmion phase for seemingly unfavorable field characteristics, the system exhibits first an inverted re-entrant skyrmion phase that does not exist in the equilibrium phase diagram. 

[1] Z. Demir Vatansever, E. Vatansever, A. Vasilopoulos, N. G. Fytas and A. Berger, Phys. Rev. Lett. 137, 026703 (2026).