Lifetime of racetrack skyrmions

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.

Figure 1

Mechanisms of the skyrmion annihilation in a fcc-Pd/Fe/Ir(111) racetrack. Energy variation along the MEPs for radial collapse of the skyrmion in the interior of the strip (a) and escape of the skyrmion through the boundary (b), shown for four values of applied magnetic field. The filled circles show position of the intermediate states along the annihilation paths, while crosses indicate energy maxima along the MEPs. Variation of the absolute value of the topological charge along the MEPs is represented by a purple line for B = 3.5 T. The reaction coordinate is defined as the normalized displacement along the MEP. The starting- and end-points of the reaction coordinate are the skyrmion and ferromagnetic states, respectively. The encircled numbers label the states for which spin configurations are shown in the lower panel (c). The background color indicates the value of the out-of-plane component of the magnetic vectors (red ↔ up, blue ↔ down). Black solid lines show the contour where the out-of-plane component of magnetization vanishes.

Figure 2

Energy barriers for skyrmion annihilation in a Pd/Fe/Ir(111) racetrack. Energy barrier for the skyrmion annihilation and nucleation (inset) in the interior (red curve, triangles) and at the boundary (purple curve, squares) of the Pd/Fe strip as a function of applied magnetic field strength, shown for the fcc (a) and hcp (b) stacking of the Pd layer. The curves intersect at the crossover field, B_c.

Figure 3

Lifetime of a skyrmion in a Pd/Fe/Ir(111) racetrack. Contour plot of the calculated lifetime of an isolated skyrmion in a 23.5 nm wide strip as a function of applied magnetic field strength and temperature, shown for the fcc (a) and hcp (b) stacking of the Pd layer. White contour lines have a characteristic cusp due to the crossover between collapse and escape mechanism indicated by the cyan line. Above the crossover line, the skyrmion lifetime is mostly defined by the collapse mechanism, but the escape mechanism dominates below the crossover line. White dashed lines indicate isochronal contours of the collapse and escape lifetimes. Insets show the cut of the contour plot at T = 15 K (a) and T = 10 K (b); in the insets, annihilation time due to collapse in the interior, escape through the boundary and total skyrmion lifetime are shown with red, purple and black curves, respectively.