Role of higher-order exchange interactions for skyrmion stability

Abstract: Transition-metal interfaces and multilayers are a very promising class of systems to realize nanometer-sized, stable magnetic skyrmions for future spintronic devices. For room temperature applications it is crucial to understand the interactions which control the stability of isolated skyrmions. Typically, skyrmion properties are explained by the interplay of pair-wise exchange interactions, the Dzyaloshinskii-Moriya interaction and the magnetocrystalline anisotropy energy. Here, we demonstrate that higher-order exchange interactions -- which have so far been neglected -- can play a key role for the stability of skyrmions. We use an atomistic spin model parametrized from first-principles and compare three different ultrathin film systems. We consider all fourth order exchange interactions and show that in particular the four-site four spin interaction has a giant effect on the energy barrier preventing skyrmion and antiskyrmion collapse into the ferromagnetic state. Our work opens new perspectives to enhance the stability of topological spin structures.

• The paper shows that higher-order (four-site four spin) interactions significantly increase energy barriers, enhancing skyrmion lifetimes.
• It employs an atomistic spin model with DFT-derived parameters to analyze phase diagrams of Pd/Fe/Rh(111) films.
• Findings indicate that tuning higher-order interactions can stabilize skyrmions, paving the way for robust spintronic device applications.

Role of Higher-Order Exchange Interactions for Skyrmion Stability

Introduction

The study examines the impact of higher-order exchange interactions (HOI) on the stability of magnetic skyrmions within transition-metal interfaces, exploring their potential use in spintronic devices for robust data storage solutions. Using an atomistic spin model complemented with parameters derived from first-principles, this research challenges the conventional focus on pair-wise interactions and demonstrates the vital role of higher-order terms, particularly the four-site four spin interaction, in modifying the energy barriers and lifetimes of skyrmions.

Atomistic Spin Model and Higher-Order Interactions

The magnetic properties of transition-metal interfaces are modeled through a Hamiltonian incorporating both traditional pair-wise interactions and HOI. Calculated via density functional theory (DFT), the key parameters include exchange constants, Dzyaloshinskii-Moriya interaction (DMI), and magnetocrystalline anisotropy energy (MAE). The four-site four spin interaction significantly alters the energy landscape, affecting the stability and collapse mechanisms of skyrmions.

Figure 1: Higher-order exchange interactions and multi-Q states illustrate the complex interactions beyond pair-wise terms.

Phase Diagrams and Skyrmion Stability

The study evaluates the phase diagrams of Pd/Fe/Rh(111) films, identifying pronounced changes due to HOI (Figure 2). The interplay between various interactions affects the boundaries of stable skyrmion lattices, highlighting the diminished skyrmion lattice phase and the expansion of spin spiral and ferromagnetic phases. The skyrmion and antiskyrmion lifetimes exhibit substantial increases when HOI are considered, driven primarily by changes in energy barriers.

Figure 2: Phase diagram, radius, and barrier heights of Pd/Fe/Rh(111), showing the significant influence of HOIs.

Analysis of Skyrmion Collapse Mechanisms

The geodesic nudged elastic band (GNEB) method reveals distinct collapse mechanisms for skyrmions, with HOIs notably affecting the chimera and radial collapse paths. The four-site four spin interaction emerges as the predominant driver of these changes, demonstrating a localized energy increase at saddle points along the minimum energy paths, which consequentially affects skyrmion stability.

Figure 3: Minimum energy paths of skyrmion and antiskyrmion collapse show significant changes in collapse mechanisms due to HOIs.

Discussion on the Four-Site Four Spin Interaction

A detailed examination of the four-site four spin interaction reveals its linear scaling effect on energy barriers, with implications for skyrmion and antiskyrmion stabilization in the absence of DMI. This implies a new avenue for controlling topological spin structures solely through HOI, offering notable potential for device applications, allowing for skyrmion stabilization at room temperature.

Figure 4: Atomic-site resolved energy contributions of the four-site four spin interaction at saddle points.

Conclusion

This paper underscores the critical importance of including higher-order exchange terms in modeling skyrmion behavior at transition-metal interfaces. The substantial energy barrier variations due to the four-site four spin interaction suggest that these terms can no longer be dismissed in theoretical frameworks. Consequently, this opens opportunities for enhancing skyrmion stability purely through material engineering, promising advancements in data storage technologies.

Figure 5: Variation of energy barriers with four-site four spin constant, showing the linear relationship and its impact.

The research marks a significant advancement in comprehending skyrmion stability dynamics, offering pathways to innovate spintronic applications without dependency on traditional interactions such as DMI. Future investigations focusing on material-specific tuning of HOI could unlock further potential in skyrmion-based technologies.