Abstract
Transition-metal interfaces and multilayers are a 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 large effect on the energy barrier preventing skyrmion and antiskyrmion collapse into the ferromagnetic state. Our work opens perspectives to stabilize topological spin structures even in the absence of Dzyaloshinskii-Moriya interaction.
Highlights
Transition-metal interfaces and multilayers are a promising class of systems to realize nanometer-sized, stable magnetic skyrmions for future spintronic devices
We describe the magnetic state of an ultrathin film by a set of classical magnetic moments {Mi} localized on each atom site i of a hexagonal lattice and their dynamics is governed by the following Hamiltonian: X
We neglect the dipole-dipole interaction since it is small in ultrathin films, which is of the order of 0.1 meV per atom, and it can be effectively included into the MAE44,45
Summary
Transition-metal interfaces and multilayers are a promising class of systems to realize nanometer-sized, stable magnetic skyrmions for future spintronic devices. Due to the possibility of varying film composition and structure, these systems allow to modify magnetic interactions and thereby the properties of skyrmions At such transition-metal interfaces, individual magnetic skyrmions with diameters ranging from a few 100 nanometers down to a few nanometers have been realized as a metastable state in the field-polarized ferromagnetic background[8,10,11,12,13,14,15,16] as needed for applications. The exchange interactions are long-range in itinerant magnets such as 3d transition-metals This can lead to a competition between exchange interactions from different shells of atoms resulting in an enhanced skyrmion stability[16,22] even in the absence of DMI23. Based on the spin-1/2 Hubbard model, it has been shown that the higher-order exchange interactions (HOI)
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