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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.
Highlights
Skyrmions were proposed [1,2] long ago, there has been a strong rise in interest in recent years spurred by experimental observations of Skyrmionic phases in various magnetic thin films [3,4,5]
Magnetic Skyrmions are attractive candidates for magnetic storage of classical information [8,9] because they are topologically stable in the sense that no continuous local deformation in the magnetic texture can remove a Skyrmion, and they can be manipulated at high speed with relatively low current densities [8,10,11]
The dynamic properties of Skyrmions can be considerably simplified by considering the motion of the average magnetic texture [16], which reduces to an equation of motion for the Skyrmion’s centerof-mass coordinate, known as Thiele’s equation
Summary
Skyrmions were proposed [1,2] long ago, there has been a strong rise in interest in recent years spurred by experimental observations of Skyrmionic phases in various magnetic thin films [3,4,5]. The dynamic properties of Skyrmions can be considerably simplified by considering the motion of the average magnetic texture [16], which reduces to an equation of motion for the Skyrmion’s centerof-mass coordinate, known as Thiele’s equation This Skyrmion coordinate behaves as a massless particle under a Magnus force proportional to Q [17], and a possible damping is parametrized by a phenomenological velocitydependent term that is induced by the coupling of the Skyrmion motion to other degrees of freedom in the system such as electrons, phonons, magnons, etc.; the microscopic details of this coupling are typically left unspecified.
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