Skyrmion-Antiskyrmion Lattice: A Net-Zero Topological Phase in Low-Symmetry Frustrated Chiral Magnets

TL;DR

The study demonstrates a thermodynamically stable Skyrmion–Antiskyrmion Lattice (Sk–ASkL) with net-zero global topological charge in low-symmetry, frustrated chiral magnets formed as Fe films on GaAs(110) and CdTe(110). By integrating ab initio parameterization (DFT/KKR) with large-scale atomistic spin dynamics, the authors show that symmetry-induced anisotropic exchange and DMI stabilize Sk–ASkL under an applied field, yielding a CySS → Sk–ASkL → CoSS → FM sequence. A minimal $J_1$–$J_3$–$D$ model captures the essential balance between exchange frustration and DMI that favors Sk–ASkL, revealing that anisotropy is crucial for net-zero topology in a single ferromagnetic layer. The work further demonstrates current-driven, Hall-effect-free motion of the Sk–ASkL, highlighting potential for racetrack-like devices exploiting net-zero topologies. Overall, symmetry engineering in TM/SC interfaces opens a new route to stable topological phases with practical spintronic implications.

Abstract

We report the discovery of a thermodynamically stable skyrmion-antiskyrmion lattice in two-dimensional heterostructures, a novel state exhibiting a net-zero global topological charge owing to an equal population of skyrmions and antiskyrmions. This surprising coexistence of oppositely charged solitons remarkably circumvents their anticipated annihilation. We demonstrate the formation and evolution of this phase in Fe films on C1v -symmetric (110) surfaces of GaAs and CdTe semiconductors. Specifically, we reveal a series of magnetic field-induced phase transitions: cycloidal spin-spiral to skyrmion-antiskyrmion lattice to conical spin-spiral to ferromagnet. The remarkable stability of the net-zero lattice is attributed to symmetry-enforced anisotropic magnetic interactions. Lowering interfacial symmetry to C1v thus enables frustrated chiral magnets, uniquely manifesting in thermodynamically stable net-zero topological soliton lattices, as revealed by our findings.

Figures (14)

• Figure 1: Symmetry-dependent Néel-type topological spin configurations in interfacial chiral magnets. Schematic illustrations depict chiral magnetic heterostructures with interfacial symmetries: (a) four-fold ($C_{4v}$), (b) three-fold ($C_{3v}$), and (c) two-fold ($C_{2v}$) and (d) single-fold ($C_{1v}$, the present work). Mirror planes ($\mathcal{M}$) are indicated. For the well-known $C_{4v}$ and $C_{3v}$ systems, symmetry-restricted DM vectors (Moriya rules) lead to stabilize hexagonal SkLs. The $C_{2v}$ interface, exhibiting effective $D_{2d}$ symmetry, stabilizes isolated antiskyrmions. Unlike typical TM/HM heterostructures, we investigate magnetic thin-film interfaced with semiconductor substrates, possessing $C_{1v}$ symmetry. The corresponding magnetic model is described in Eq. \ref{['spin_hamiltonian']}.
• Figure 2: A typical $C_{1v}$ symmetric interface geometry: 2Fe/GaAs(110) slab (a) Side view of the epitaxial Fe double-layer slab, highlighting inequivalent Fe atoms (indexed $\alpha = 1-4$) in surface (L1) and interface (L2) layers. (b) Top-view of L1 and L2, emphasizing asymmetric coordination environments induced by the substrate's low symmetry. A single mirror plane, $\mathcal{M}_x$ (aligned with [001], $x$-axis), governs symmetry constraints. First three neighboring shells illustrate spatially varying intralayer exchange strengths (FM/AFM) due to inequivalent Fe-substrate bonding. (c) Intralayer and (d) interlayer interaction shells near the central Fe atom ($\alpha=1$), mapping exchange constants (color scale: FM = $+$ve, AFM = $-$ve) and DM vectors (arrows). DM interactions within the $\mathcal{M}_x$ plane exhibit purely $y$-axis components (see also SM Secs. III (2Fe/GaAs(110)) and IV (2Fe/CdTe(110)) supp)
• Figure 3: Zero temperature magnetic phases of pristine 2Fe/GaAs(110) in the presence of magnetic field ($B_\perp$). (a) Total energies relative to the CySS state. The competing phases are CySS, CoSS, FM, SkL, and Sk-ASkL. Inset: Zero-field CySS ground state. (b) and (c) Spin textures of the CoSS and Sk-ASkL phases, respectively. (d) Phase stability vs. interlayer exchange ($\tilde{J}^{1\beta}_\alpha$). Reducing the nearest-neighbor exchange parameter by $\sim 25\%$, shifts the transition sequence to CySS$\rightarrow$Sk-ASkL ($Q_\textrm{UC}=0$)$\rightarrow$CoSS$\rightarrow$FM.
• Figure 4: Stability of competing magnetic phases--CySS, Sk-ASkL, SkL, and FM--under $B_\perp$. (a) Relative total energy with respect to the CySS energy. Systems are strained 2Fe/GaAs(110) (solid lines) and pristine 2Fe/CdTe(110) (dashed lines). The red-shaded region's vertical borders indicate critical $B_\perp$ fields for phase transitions. Lower panel: Magnetization discontinuities at critical fields ($M/M_\textrm{s}$, where $M_\textrm{s}$= 2.37 $\mu_\textrm{B}$ and 2.70 $\mu_\textrm{B}$ for 2Fe/GaAs(110) and 2Fe/CdTe(110), respectively). The transition between CoSS and FM phases is marked by the coalescence of energy and magnetization curves at high $B_\perp$ (rightmost figures).
• Figure S5: The relaxed atomic geometries near the interface are shown for (a) the 2Fe/GaAs(110) heterostructure and (b) the 2Fe/CdTe(110) heterostructure. The displacement of the atoms within the plane is indicated by the in-plane arrows. The out-of-plane arrows depict the outward displacement of the atoms from the atoms positioned at the lowest point in the corresponding layer. For example, in L1 and L2, the lowest positions are Fe-4 and Fe-2 atoms, respectively. The length of the arrows is proportional to the magnitude of the displacement.