Platform for zero-field isolated skyrmions: 4$d$/Co atomic bilayers on Re(0001)

TL;DR

This study demonstrates that 4d/Co bilayers on Re(0001) can host stable, zero-field isolated skyrmions due to complex magnetic interactions, offering a promising platform for nanoscale magnetic applications.

Contribution

It introduces a comprehensive first-principles and atomistic spin simulation approach to predict zero-field skyrmions in 4d/Co bilayers on Re(0001), including higher-order exchange interactions.

Findings

Skyrmions emerge spontaneously without external magnetic fields.

Skyrmion sizes are approximately 6 nm in Rh/Co and 12 nm in Pd/Co bilayers.

Energy barriers protecting skyrmions are around 150 meV, indicating stability at low temperatures.

Abstract

Using first-principles density functional theory (DFT) combined with atomistic spin simulations, we explore the possibility of realizing zero-field isolated skyrmions in three 4$d$/Co atomic bilayers -- Rh/Co, Pd/Co, and Ru/Co -- grown on the Re(0001) surface. Our investigation employs an extended atomistic spin model, which goes beyond the standard model by including the multi-spin higher-order exchange interactions (HOI) in addition to the Heisenberg pairwise exchange interaction, Dzyaloshinskii-Moriya interaction (DMI), and magnetocrystalline anisotropy energy (MAE). All magnetic interactions of the extended spin model are calculated using DFT. The phase diagram obtained from atomistic spin simulations based on this spin model for Rh/Co and Pd/Co on Re(0001) reveals that isolated skyrmions emerge spontaneously on the ferromagnetic background even in the absence of an external magnetic field. The radius of zero-field isolated skyrmions in Rh/Co/Re(0001) is around 6 nm, whereas the radius of those skyrmions in Pd/Co/Re(0001) is about 12 nm. Transition-state theory calculations show that the skyrmions are protected by substantial energy barriers, approximately 150 meV, which predominantly arise from DMI, with a small contribution from the HOI interactions. The height of the barriers suggests that skyrmions could be observed in low-temperature experiments. Based on this work, we propose 4$d$/Co bilayers on Re(0001) as a new platform to realize nanoscale zero-field isolated skyrmions.