Annihilation of topological solitons in magnetism with spin-wave burst finale: Role of nonequilibrium electrons causing nonlocal damping and spin pumping over ultrabroadband frequency range

Letter

Annihilation of topological solitons in magnetism with spin-wave burst finale: Role of nonequilibrium electrons causing nonlocal damping and spin pumping over ultrabroadband frequency range

Marko D. Petrović, Utkarsh Bajpai, Petr Plecháč, and Branislav K. Nikolić

Phys. Rev. B 104, L020407 – Published 14 July 2021

Abstract

We not only reproduce a burst of short-wavelength spin waves (SWs) observed in a recent experiment [S. Woo et al., Nat. Phys. 13, 448 (2017)] on magnetic-field-driven annihilation of two magnetic domain walls (DWs) but, furthermore, we predict that this setup additionally generates highly unusual pumping of electronic spin currents in the absence of any bias voltage. Prior to the instant of annihilation, their power spectrum is ultrabroadband, so they can be converted into rapidly changing in time charge currents, via the inverse spin Hall effect, as a source of THz radiation of bandwidth $≃ 27$ THz where the lowest frequency is controlled by the applied magnetic field. The spin pumping stems from time-dependent fields introduced into the quantum Hamiltonian of electrons by the classical dynamics of localized magnetic moments (LMMs) comprising the domains. The pumped currents carry spin-polarized electrons which, in turn, exert backaction on LMMs in the form of nonlocal damping which is more than twice as large as conventional local Gilbert damping. The nonlocal damping can substantially modify the spectrum of emitted SWs when compared to widely used micromagnetic simulations where conduction electrons are completely absent. Since we use a fully microscopic (i.e., Hamiltonian-based) framework, self-consistently combining time-dependent electronic nonequilibrium Green functions with the Landau-Lifshitz-Gilbert equation, we also demonstrate that previously derived phenomenological formulas miss ultrabroadband spin pumping while underestimating the magnitude of nonlocal damping due to nonequilibrium electrons.

Received 9 August 2019
Revised 17 June 2021
Accepted 21 June 2021

DOI:https://doi.org/10.1103/PhysRevB.104.L020407

Physics Subject Headings (PhySH)

Domain walls Quantum transport Spin dynamics Spin pumping Spin torque Spin waves

Multiple time scale dynamics Nanowires Noncollinear magnets Nonequilibrium systems Solitons

Green's function methods Landau-Lifschitz-Gilbert equation Quantum master equation

Nonlinear DynamicsCondensed Matter, Materials & Applied PhysicsStatistical Physics & Thermodynamics

Authors & Affiliations

Marko D. Petrović ¹, Utkarsh Bajpai¹, Petr Plecháč², and Branislav K. Nikolić ^1,*

¹Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716, USA
²Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716, USA

^*bnikolic@udel.edu

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 104, Iss. 2 — 1 July 2021

Reuse & Permissions

Access Options

Article Available via CHORUS

Download Accepted Manuscript

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Schematic view of a ferromagnetic nanowire modeled as a 1D tight-binding chain whose sites host classical LMMs (red arrows) interacting with spins (blue arrow) of conduction electrons. The nanowire is attached to two NM leads terminating into the macroscopic reservoirs kept at the same chemical potential. The two DWs within the nanowire carry opposite topological charge [8], $Q_{L} = - 1$ for the L one and $Q_{R} = + 1$ for the R one. They collide with the opposite velocities $V_{DW}^{L}$ and $V_{DW}^{R}$ and annihilate, upon application of an external magnetic field $B_{ext}$ parallel to the nanowire, thereby mimicking the setup of the experiment in Ref. [20].
Reuse & Permissions
Figure 2
(a) Sequence of snapshots of two DWs, in the course of their collision and annihilation in the setup of Fig. 1; and (b) the corresponding time dependence of the $z$ component of LMMs where blue and orange lines mark $t = 6.9$ ps (when two DWs start vanishing) and $t = 7.2$ ps (when all LMMs become nearly parallel to the $x$ axis) from panel (a). A movie animating panels (a) and (b) is provided in the Supplemental Material [58]. Spatiotemporal profile of: (c) angle $δ_{i}^{eq}$ and (d) “nonadiabaticity” angle $δ_{i}^{neq} - δ_{i}^{eq}$ , with the meaning of $δ_{i}^{neq}$ and $δ_{i}^{eq}$ illustrated in the inset above panel (c); (e) DL STT [Eq. (3)] as electronic backaction on LMMs; (f) ratio of DL STT to conventional local Gilbert damping [Eq. (2)]; and (g) ratio of the sum of DL STT to the sum of conventional local Gilbert damping over all LMMs.
Reuse & Permissions
Figure 3
Time dependence of: (a)–(c) electronic spin currents pumped into the right NM lead during DW collision and annihilation; (e)–(g) SW-generated contribution to spin currents in panels (a)–(c), respectively, after spin current carried by SW from Fig. 2 is stopped at the magnetic-nanowire/nonmagnetic-NM-lead interface and converted (as observed experimentally [20, 61]) into electronic spin current in the right NM lead. Vertical dashed lines mark times $t = 6.9$ ps and $t = 7.2$ ps whose snapshots of LMMs are shown in Fig. 2. For easy comparison, gray curves in panels (f) and (g) are the same as the signal in panels (b) and (c), respectively, for postannihilation times $t \geq 7.2$ ps. Panels (d) and (h) plot FFT power spectrum of signals in panels (c) and (g), respectively, before (red curve) and after (brown curves) completed annihilation at $t = 7.2$ ps.
Reuse & Permissions
Figure 4
Spatial profile at $t = 6.9$ ps of: (a) locally pumped spin current $I_{i \to j}^{S_{x}}$ [47] between sites $i$ and $j$ ; and nonlocal damping due to backaction of nonequilibrium electrons. Solid lines in (a) and (b) are obtained from $TDNEGF + LLG$ calculations, and dashed lines are obtained from SMF theory phenomenological formulas [32, 33, 69]. (c)–(e) FFT power spectra [22] of $M_{i}^{z} (t)$ where (c) and (d) are $TDNEGF + LLG$ -computed with $λ = 0.01$ and $λ = 0$ , respectively, while (e) is LLG-computed with backaction of nonequilibrium electrons removed, $T_{i} [M_{i} (t)] \equiv 0$ , in Eq. (2). The dashed horizontal lines in panels (c)–(e) mark frequencies of peaks in Fig. 3.
Reuse & Permissions

Physical Review B

covering condensed matter and materials physics