Quantum Dynamics of Skyrmions in Chiral Magnets

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.Comment: 14 pages, 10 figure

Intrinsic spin Nernst effect of magnons in a noncollinear antiferromagnet

“…We now write a general theory applicable to bosonic systems where the Bloch wave function corresponding to the band dispersion ε n,k is given by |ψ n,k = e ik·r |u n,k . We can then introduce a notation [42]…”

Quantum Brownian motion of a magnetic skyrmion

“…We next address the stochastic dynamics of the skyrmion described by the classical fields Φ 0 and Θ 0 in contact with the bath of magnetic excitations at finite temperature driven by an external magnetic field that oscillates in time. This is achieved by first promoting the skyrmion center-of-mass to a dynamical variable R(t), then treating the magnetic excitations as quantum fluctuations around the classical field, and finally obtaining an effective functional [1,39,40,60] by integrating out the magnon degrees of freedom. At the same time, the real-time dynamics of the external field as well as the stochastic effects of the magnon bath at finite T are captured by replacing the time integration by an integration over the Keldysh contour which consists of two branches.…”

“…Magnetic excitations are defined as fluctuations around the classical skyrmion solution through a consistent separation between collective (center-of-mass) and intrinsic (magnetic excitations) degrees of freedom. A description of the dynamics of one-dimensional (1D) domain walls [39] and 2D magnetic skyrmions [40] in a magnetic insulator beyond the classical framework, demonstrated that the dissipation arising from the magnetic excitations is generally non-Markovian with a damping kernel that is nonlocal in time. The quantum nature of the magnetic bath, naturally incorporated within this approach, becomes evident in the nontrivial temperature T dependence of the damping kernel which remains finite even for vanishingly small T .…”

Magnonic analog of the Edelstein effect in antiferromagnetic insulators

“…The transformation matrix satisfies the paraunitary normalization relations, T † k σ 3 T k = σ 3 and T k σ 3 T † k = σ 3 , where here and henceforth σ i (i = 1, 2, 3) stands for the Pauli matrices acting in the particle-hole space. The particlehole space Hamiltonian can be regarded as a pseudo-Hermitian Hamiltonian, with the eigenequation [55] σ 3 H k |u n,k =ε n,k |u n,k ,…”