Finite-temperature stability of skyrmion crystals in frustrated magnets: Role of sixfold anisotropy and uniform spin mode in momentum space

TL;DR

The paper addresses finite-temperature stabilization of skyrmion crystals in frustrated magnets by analyzing the momentum-space exchange $J(\bm{q})$ of a classical $J_1$-$J_2$-$J_3$ Heisenberg model on a triangular lattice. Using parallel-tempering Monte Carlo, it demonstrates that two momentum-space features—the sixfold anisotropy $\Delta$ on the ring $|\bm{q}|=Q^*$ and the uniform-spin energy $J(\bm{0})$—govern SkX stability. Larger $|\Delta|$ strengthens triple-$Q$ locking and expands the SkX region, while larger $J(\bm{0})$ correlates with SkX emergence at finite temperature, with a threshold around $J(\bm{0})/|J_0| \approx 0.02$. These insights link microscopic momentum-space energy landscapes to practical SkX design principles, suggesting routes to engineer robust skyrmion phases in frustrated magnets and related systems.

Abstract

We study the finite-temperature stability of skyrmion crystals in frustrated magnets by analyzing the momentum-space exchange interaction of a classical Heisenberg model on a triangular lattice. Our analysis identifies two key momentum-space features that play a crucial role in stabilizing the skyrmion crystal phase. The first is the sixfold anisotropy in the momentum-space exchange interaction, which acts as a locking potential favoring triple-$Q$ skyrmion crystals. Monte Carlo simulations reveal that a larger anisotropy tends to enhance the stability region of the skyrmion crystal in the temperature--magnetic-field phase diagram. The second factor is the momentum-space energy related to the uniform spin mode, which correlates with the emergence of the skyrmion crystal phase at finite temperatures. These results provide a further understanding of the stabilization mechanism of the skyrmion crystal phase in frustrated magnets and will be useful for the design of skyrmion-hosting materials.

Figures (7)

• Figure 1: (a) Ground-state phase diagram of the $J_1$-$J_2$-$J_3$ Heisenberg model on a triangular lattice in the $(J_2, J_3)$ plane with $J_1=-1$. (b) Color map of the magnitude of the ordering vector $Q^*=|\bm{Q}^*|$ in the Spiral I phase.
• Figure 2: (a)-(c) Color plots of $J(\bm{q})$ in the momentum space for $Q^*=0.6\pi$ with (a) $J_2=-0.5$ ($J_3=3.061$), (b) $J_2=0.5$ ($J_3=1.7845$), and (c) $J_2=1.3$ ($J_3=0.7638$). (d)-(f) Finite-temperature phase diagrams in the plane of temperature $T$ and magnetic field $H$ for the same parameter sets as (a)-(c), respectively. Dotted lines indicate minimum temperatures in simulations.
• Figure 3: Schematic image of the sixfold anisotropy $\Delta$ and the isotropic part $J_0$ of $J(\bm{q})$.
• Figure 4: $J_2$ and $Q^*$ dependence of the sixfold anisotropy $\Delta$ normalized by $|J_0|$. The star symbols indicate the parameter sets used in Fig. \ref{['fig:Jq PhaseDiagram']}, which correspond to $Q^*=0.6\pi$ with $J_2=-0.5, 0.5,$ and $1.3$ that gives $\Delta=1.440$, $0.672$, and $0.050$, respectively.
• Figure 5: (a) Color plot of $J(\bm{0})/|J_0|$ in the $(J_2, Q^*)$ plane. Circles and crosses represent the presence and absence of the SkX phase at finite temperatures, respectively. The star symbols indicate the parameter sets used in Fig. \ref{['fig:J0 T dependence']}, which correspond to $Q^*=11\pi/21$ with $J_2=-0.5, -0.25, 0, 0.25,$ and $0.5$. (b) Relative energy difference between the SkX and spiral states as a function of magnetic field $H$ for $Q^*=11\pi/21$ with various $J_2$.