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Quantum collapse of a small skyrmion in a thin magnetic film with Dzyalishinskii-Moriya (DMI) interaction has been studied. The energy of the skyrmion and the stability threshold determined by the DMI, the external magnetic field, and the underlying atomic lattice are investigated analytically and numerically. The Lagrangian describing the coupled dynamics of the skyrmion size and the chirality angle is derived. Equations of motion possess an instanton solution that corresponds to the skyrmion underbarrier contraction via quantum tunneling with subsequent collapse and decay of the topological charge. The tunneling rate is computed and the conditions needed to observe quantum collapse of a skyrmion in a magnetic film are discussed.
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Thermal collapse of an isolated skyrmion on a two-dimensional spin lattice has been investigated. The method is based upon solution of the system of stochastic Landau-Lifshitz-Gilbert equations for up $10^4$ spins. Recently developed pulse-noise algorithm has been used for the stochastic component of the equations. The collapse rate follows the Arrhenius law. Analytical formulas derived within a continuous spin-field model support numerically-obtained values of the energy barrier and the pre-exponential factor, and their dependence on the magnetic field. Our findings agree with experiments, as well as with recent numerical results obtained by other methods.
We investigate the quantum depinning of a weakly driven skyrmion out of an impurity potential in a mesoscopic magnetic insulator. For small barrier height, the Magnus force dynamics dominates over the inertial one, and the problem is reduced to a massless charged particle in a strong magnetic field. The universal form of the WKB exponent, the rate of tunneling, and the crossover temperature between thermal and quantum tunneling is provided, independently of the detailed form of the pinning potential. The results are discussed in terms of macroscopic parameters of the insulator Cu2OSeO3 and various skyrmion radii. We demonstrate that small enough magnetic skyrmions, with a radius of ~ 10 lattice sites, consisting of some thousands of spins, can behave as quantum objects at low temperatures in the mK regime.
Within a microscopic theory, we study the quantum Brownian motion of a skyrmion in a magnetic insulator coupled to a bath of magnon-like quantum excitations. The intrinsic skyrmion-bath coupling gives rise to damping terms for the skyrmion center-of-mass, which remain finite down to zero temperature due to the quantum nature of the magnon bath. We show that the quantum version of the fluctuation-dissipation theorem acquires a non-trivial temperature dependence. As a consequence, the skyrmion mean square displacement is finite at zero temperature and has a fast thermal activation that scales quadratically with temperature, contrary to the linear increase predicted by the classical phenomenological theory. The effects of an external oscillating drive which couples directly on the magnon bath are investigated. We generalize the standard quantum theory of dissipation and we show explicitly that additional time-dependent dissipation terms are generated by the external drive. From these we emphasize a friction and a topological charge renormalization term, which are absent in the static limit. The skyrmion response function inherits the time periodicity of the driving field and it is thus enhanced and lowered over a driving cycle. Finally, we provide a generalized version of the nonequilibrium fluctuation-dissipation theorem valid for weakly driven baths.
We consider a magnetic skyrmion crystal formed at the surface of a topological insulator. Incorporating the exchange interaction between the helical Dirac surface states and the periodic Neel or Bloch skyrmion texture, we obtain the resulting electronic band structures. We discuss the properties of the reconstructed skyrmion bands, namely the impact of symmetries on the energies and Berry curvature. We find substantive qualitative differences between the Neel and Bloch cases, with the latter generically permitting a low-energy tight-binding representation whose parameters are tightly constrained by symmetries. We explicitly construct the associated Wannier orbitals, which resemble the ring-like chiral bound states of helical Dirac fermions coupled to a single skyrmion in a ferromagnetic background. We construct a two-band tight-binding model with complex nearest-neighbor hoppings which captures the salient topological features of the low-energy bands. Our results are relevant to magnetic topological insulators (TIs), as well as to TI-magnetic thin film heterostructures, in which skyrmion crystals may be stabilized.
Magnetic skyrmions are of considerable interest for low-power memory and logic devices because of high speed at low current and high stability due to topological protection. We propose a skyrmion field-effect transistor based on a gate-controlled Dzyaloshinskii-Moriya interaction. A key working principle of the proposed skyrmion field-effect transistor is a large transverse motion of skyrmion, caused by an effective equilibrium damping-like spin-orbit torque due to spatially inhomogeneous Dzyaloshinskii-Moriya interaction. This large transverse motion can be categorized as the skyrmion Hall effect, but has been unrecognized previously. The propose device is capable of multi-bit operation and Boolean functions, and thus is expected to serve as a low-power logic device based on the magnetic solitons.
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