Abstract
The skyrmion racetrack is a promising concept for future information technology. There, binary bits are carried by nanoscale spin swirls–skyrmions–driven along magnetic strips. Stability of the skyrmions is a critical issue for realising this technology. Here we demonstrate that the racetrack skyrmion lifetime can be calculated from first principles as a function of temperature, magnetic field and track width. Our method combines harmonic transition state theory extended to include Goldstone modes, with an atomistic spin Hamiltonian parametrized from density functional theory calculations. We demonstrate that two annihilation mechanisms contribute to the skyrmion stability: At low external magnetic field, escape through the track boundary prevails, but a crossover field exists, above which the collapse in the interior becomes dominant. Considering a Pd/Fe bilayer on an Ir(111) substrate as a well-established model system, the calculated skyrmion lifetime is found to be consistent with reported experimental measurements. Our simulations also show that the Arrhenius pre-exponential factor of escape depends only weakly on the external magnetic field, whereas the pre-exponential factor for collapse is strongly field dependent. Our results open the door for predictive simulations, free from empirical parameters, to aid the design of skyrmion-based information technology.
Highlights
The skyrmion racetrack is a promising concept for future information technology
The celebrated notion of topological protection of a single skyrmion localized in a ferromagnetic ground state of infinite spatial dimensions described in the language of continuum field theory with fixed magnetization length translates to energy barriers, whose heights become finite for physical systems and described in practice by the escape of the skyrmion to the ferromagnetic state by radial collapse, or through the system boundary
At field above 2 T, a field-polarized ferromagnetic phase is observed with isolated skyrmions pinned at atomic defects. This sequence of phases as a function of applied magnetic field can be reproduced by an atomistic spin Hamiltonian parameterized from first principles density functional theory (DFT) calculations[14,15,16,17]
Summary
The skyrmion racetrack is a promising concept for future information technology. There, binary bits are carried by nanoscale spin swirls–skyrmions–driven along magnetic strips. At field above 2 T, a field-polarized ferromagnetic phase is observed with isolated skyrmions pinned at atomic defects (see Fig. 1, panel G in ref.[13]) This sequence of phases as a function of applied magnetic field can be reproduced by an atomistic spin Hamiltonian (see Methods section) parameterized from first principles density functional theory (DFT) calculations[14,15,16,17]. The rare-event problem arises from the fact that in the relevant temperature range, transitions between stable magnetic states induced by thermal fluctuations, e.g. a skyrmion collapsing to the ferromagnetic phase, are typically rare events on the intrinsic time scale of the magnetization dynamics of the system and makes direct simulations of finite temperature spin dynamics[16,20] an intractable approach to evaluate the lifetimes. It is this separation of time scales that makes it possible to apply statistical methods (see Methods section)
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