Positional Stability of Skyrmions via Pinning Sites in a Racetrack Memory

Abstract

Magnetic skyrmions are topologically protected chiral spin textures stabilized by the Dzyaloshinskii–Moriya interactions (DMI) in systems lacking inversion symmetry. The attractive features of skyrmions, such as ultra-small size, solitonic nature, and easy mobility with small electrical currents, make them promising as information-carrying bits in low power high-density memory and logic applications [1, 2]. In a skyrmion-based boolean racetrack memory, information can be encoded by the presence (bit “1”) and absence (bit “0”) of skyrmions at a particular position in the track. For an unconventional use of skyrmion racetrack, such as for native temporal memory [1], the information is encoded into the spatial coordinates of the skyrmions, which then can be translated into the timing information needed for race logic operations. The thermal stability of skyrmions is a critical issue for both of these applications, as a randomly displaced skyrmion can alter the sequence of the “0" and “1" bits in a Boolean memory application. Similarly, for race logic applications, the displacement of skyrmions would change the spatial coordinates of the skyrmion and hence the encoded analog timings. For reliable information extraction, it is essential to guarantee the positional stability of skyrmions for a certain amount of time. For example, for a long-term memory application it would require positional stability of years, while for cache memory, hours would be sufficient. In an ideal racetrack, skyrmions are susceptible to thermal fluctuations and exhibit Brownian motion that leads to the diffusive displacement of skyrmions [3]. Moreover, skyrmions show inertia driven drift shortly after a current pulse is removed, rather than stopping immediately. One way to control such undesirable motion is by engineering confinement barriers such as point defects with a different anisotropy, or notches etched into the racetrack (missing materials), which ensure the pinning of skyrmions. If the required unpinning current is too large, it will destabilize the skyrmions, which can cause annihilation of the skyrmions. In addition, high currents have been shown to randomly nucleate unwanted skyrmions as well [4]. This would mean that the energy barrier height needs to be optimized in such a way that it can hold the skyrmions for a long enough time and yet requires a modest current to unpin them. Using micromagnetic simulations [5], we present a quantitative analysis of racetrack geometries with different types of notches to calculate the minimum energy barriers associated with them. To calculate the energy barrier, we use the string method to find the minimum energy path (MEP) for the skyrmion to go over the notch [6]. We vary material parameters, specifically, the DMI, anisotropy ratio between the pinning sites and the rest of the magnetic material, and the geometry of the notches, in order to get the optimal barrier height. Furthermore, we investigate the effects of topology in the unpinning process by comparing the unpinning behavior of a ferrimagnetic vs a ferromagnetic skyrmion. We find a range of energy barriers (up to ~ 45 kBT) that can provide a long enough positional lifetime (years) of skyrmions for long-term memory applications while requiring a moderate amount of current (~ 1010 - 1011 A/m2) to move the skyrmions. Our results open up possibilities to design practical skyrmion-based racetrack geometries for spintronic applications. **