Elastic Dislocation-based Skyrmion Traps: Fundamentals and Applications

TL;DR

This work addresses how crystal dislocations couple to topological spin textures, specifically skyrmion tubes, in distorted magnets. It develops a continuum theory combining exchange, bulk DMI, and elastic geometry via a vielbein formalism, then derives a Thiele equation to describe dislocation-induced trapping and current-driven dynamics. It further shows that skyrmion gyrotropic modes can be quantized into bound states with a Landau-level-like spectrum and noncommutative coordinates, including a half-integer orbital angular momentum in 2D. Finally, it proposes practical devices, notably a dislocation-based skyrmion race track memory, controlled by low currents and detectable via the topological Hall effect. The results provide a framework for integrating topological magnetism with topological elasticity for low-power, high-density spintronic applications.

Abstract

Topologically secure spin configurations, such as skyrmions and bimerons, offer a compelling alternative to conventional magnetic domains, potentially enabling high-density, low-power spintronic devices. These pseudo-particles, characterized by their swirling spin textures and nontrivial topological charges, are prevalent and notably influence their electronic, magnetic, and mechanical traits. This paper provides an in-depth overview of the interaction between a screw dislocation within a distorted magnetic lattice, exploring possible coupling mechanisms and establishing a promising link between two disparate topics in materials science: topological magnetism and topological elasticity. We first provide a classical analysis of skyrmion motion that reveals the dislocations as shallow traps on the magnetic texture. Afterwards, we provide an analysis of the quantized motion of the skyrmion and identify its quantum states. We conclude by illustrating how the ideas in our paper can be implemented in simple yet compelling devices based on the shallow traps from an array of dislocations acting as frets in a race-track, controlling the motion with a low current activation mechanism.

Figures (5)

• Figure 1: (a) shows a Néel-type skyrmion, in which $A$ is a real number. (b) corresponds to a Bloch-type skyrmion, where $A$ is a pure imaginary number.
• Figure 2: a) Normalized energy $E/J$ as a function of the skyrmion position $\rho/\ell$, considering $A=i$, $\gamma=\pi/2$, and $J/D=10$. The inset shows the normalized energy $E/J$ for $b/\ell=0.2$ as a function of the skyrmion coordinates $x/\ell$ and $y/\ell$, showing the effect of the phase. b) Normalized energy for $\rho=0$ and $\rho = \rho_{min}$ as a function $b/\ell$. The blue line shows the dependence of the equilibrium radius $\rho_{min}$ on $b/\ell$.
• Figure 3: a) Trajectory of the skyrmion with an initial position larger (white) and smaller (orange) than the equilibrium radii $\rho_{min}$ (dashed green circle). Considering $b/\ell=0.2$, $A=i$, $\gamma=\pi/2$, $\alpha= \beta =0.02$, and $J/D=10$. The surface represents the energy $E$ in the 2D plane. b) Average long-term velocity as a function of the current $u$. A trapping mechanism is revealed where the terminal velocity vanishes for currents up to a critical value. Restoring the S.I. units for the parameters mentioned in the main text, this critical electric current is of the order of $10^{10}$ A/m$^2$, indicating a shallow trap.
• Figure 4: a) Energy $E\times 10^2/J$ as a function of $\rho/\ell$ for $b/\ell = 0.2$ and $\chi=0.5$. The dashed lines represent the confined eigenvalues $E_n$. The inset figure corresponds to a zoom of the curve around the minimum eigenstate $E_{10}$ (black line). b) $n_{GS}$ and $\Delta E= E_{n_{GS}}- E(\rho_{min})$ as a function of $\chi$.
• Figure 5: Density plots of the Wigner function for three energy levels ($n=0$, $n = 11$, and $n = 25$, ordered from left to right). The ground state corresponds to $n = 25$. We use $\chi=0.5$.