Abstract
We study the quantum propagation of a Skyrmion in chiral magnetic insulators by generalizing the micromagnetic equations of motion to a finite-temperature path integral formalism, using field theoretic tools. Promoting the center of the Skyrmion to a dynamic quantity, the fluctuations around the Skyrmionic configuration give rise to a time-dependent damping of the Skyrmion motion. From the frequency dependence of the damping kernel, we are able to identify the Skyrmion mass, thus providing a microscopic description of the kinematic properties of Skyrmions. When defects are present or a magnetic trap is applied, the Skyrmion mass acquires a finite value proportional to the effective spin, even at vanishingly small temperature. We demonstrate that a Skyrmion in a confined geometry provided by a magnetic trap behaves as a massive particle owing to its quasi-one-dimensional confinement. An additional quantum mass term is predicted, independent of the effective spin, with an explicit temperature dependence which remains finite even at zero temperature.
- Received 13 December 2016
DOI:https://doi.org/10.1103/PhysRevX.7.041045
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
Magnetic Skyrmions—pointlike regions of reversed magnetization within a uniform magnet—are attractive candidates for the storage and transport of information. These quasiparticles are topologically stable, which means they persevere even in the presence of local deformities, and they can be manipulated at high speed with relatively low current densities. The behavior of Skyrmions in conventional superconductors also suggests a way forward in implementing a robust type of quantum computer. For the nanometer-sized Skyrmions that are relevant to these applications, quantum fluctuations are expected to strongly influence their behavior. At this scale, the classical equations that traditionally describe their dynamics break down. Our goal is to provide a fully quantum mathematical description of Skyrmions, specifically in an insulating magnetic film.
The backaction of magnonlike modes on a Skyrmion strongly affects its dynamics by giving rise to microscopic damping terms in the equation of motion that are nonlocal in time. As a striking consequence, we find that the Skyrmion can acquire an inertial mass not only at finite temperatures but also at absolute zero because of nonuniform magnetic terms that break translational invariance such as defects, magnetic traps, or variations of the exchange constants. In particular, we have discovered that the Skyrmion dynamics become fully massive in a quantum confined geometry such as a quasi-one-dimensional wire, similar to linear tracks used for magnetic memory devices.
Our work shows that Skyrmions are promising candidates for the study of macroscopic quantum effects involving the collective motion of tens of thousands of spins.
