Skyrmion Crystal in a Microwave Field

TL;DR

We analyze a 2D skyrmion lattice stabilized by Dzyaloshinskii–Moriya interaction under a microwave field, focusing on the resonance spectrum and damping of the three uniform modes and the melting dynamics under resonant pumping. A classical-spin lattice model with exchange $J$, DMI $A$, and Zeeman field $H$, driven by ac field ${\bf h}(t)$, is solved with a configurational-temperature–based thermal dynamics and an energy-correction scheme to stabilize the temperature. We identify three uniform modes—the breathing mode and two precession modes LF and HF—with frequencies that depend on temperature and field; resonant pumping of the LF mode induces Rabi-like magnetization oscillations and, at sufficient drive, a one-stage, nonthermal melting of the skyrmion lattice, accompanied by loss of translational and orientational order. The results illuminate microwave control of SkL and suggest experimental tests of single-stage melting in skyrmion systems.

Abstract

Temperature and field dependences of the frequencies of uniform modes of the skyrmion lattice in a 2D ferromagnetic film with Dzyaloshinskii-Moriya interaction, as well as their damping, are computed within the model of classical spins. We show that the magnetization of the film exhibits Rabi-like oscillations when subjected to the microwave field at resonance with the low-frequency mode. Melting of the skyrmion lattice by resonant microwaves is investigated in terms of the time dependence of the orientational and translational order parameters. A distinct single-stage melting transition has been observed.

Figures (12)

• Figure 1: Hexagonal skyrmion lattice at $T=0$ obtained by the relaxation of the initial state of topological bubbles defining the topological charge $Q$ of the system. Spin components are color coded: $s_{z}=-1$ green, $s_{z}=1$ orange. White arrows show the in-plane spin components $s_{x}$ and $s_{y}$. The latter are directed in the circular direction (depending on the sign of $A$) around skyrmion centers for the Bloch-type DMI which was used in Eq. (\ref{['Ham']}). For the Néel-type DMI, $s_{x}$ and $s_{y}$ are directed in the radial direction away or toward the skyrmions centers, depending on the sigh of $A$.
• Figure 2: Thermalized SkL at $T/J=0.11$, cf. Fig. \ref{['Fig_SkL']}.
• Figure 3: Power-absorption spectra of the skyrmion lattice of $116\times132$ spins containing 12 skyrmions for our main set of parameters. Upper: $T/J=0.03$; Lower: $T/J=0.16$. Note the temperature dependence of the modes' frequencies and damping constants.
• Figure 4: The temperature dependence of the frequency and intrinsic damping of the breathing and LF modes for the system of $384\times400$ spins containing 120 skyrmions. Upper: frequencies; Lower: damping.
• Figure 5: Field dependence of the SkL modes' frequencies at nearly zero temperature for our main SkL and an SkL with a larger density of skyrmions. In the latter, all three modes stiffen.