Thin-Film Magnetization Dynamics on the Surface of a Topological Insulator

Abstract

We theoretically study the magnetization dynamics of a thin ferromagnetic film exchange-coupled with a surface of a strong three-dimensional topological insulator. We focus on the role of electronic zero modes imprinted by domain walls (DW's) or other topological textures in the magnetic film. Thermodynamically reciprocal hydrodynamic equations of motion are derived for the DW responding to electronic spin torques, on the one hand, and fictitious electromotive forces in the electronic chiral mode fomented by the DW, on the other. An experimental realization illustrating this physics is proposed based on a ferromagnetic strip, which cuts the topological insulator surface into two gapless regions. In the presence of a ferromagnetic DW, a chiral mode transverse to the magnetic strip acts as a dissipative interconnect, which is itself a dynamic object that controls (and, inversely, responds to) the magnetization dynamics.PACS numbers: 72.15.Gd, Following theoretical predictions [1] and experimental realizations [2] of three-dimensional topological insulators (TI's), vigorous ongoing activities in this burgeoning field are aimed at introducing spontaneous symmetry breaking mechanisms into the system. This could be accomplished by bulk or surface doping to induce magnetism or superconductivity in the parent (essentially free-electron) TI, or by a heterostructure design wherein symmetry breaking is instilled at the TI surface by a quantum proximity effect. We are following the latter route, considering an insulating ferromagnetic layer (MI) capping the bulk TI, such that the TI surface states are exchange coupled to the collective magnetic moment of the MI. Previous theoretical investigations of a similar TI/MI heterostructure were concerned with currentinduced spin torques experienced by a monodomain MI [4], Gilbert damping by a doped TI [4], electric charging of magnetic textures [4], and the rectification of charge pumping by a monodomain precession [4], all in case of a well-defined spatially uniform sign of the time-reversal symmetry breaking gap in the TI. The essential physical ingredient underlying the key ideas in these papers is the axion electrodynamics [3] associated with the TI [8], with a quantized magnetoelectric coupling that is odd under time reversal. In this Letter, we are interested in salient features associated with dynamic magnetic textures that imprint a spatially inhomogeneous gap onto the TI surface states, both in regard to its magnitude and sign. The latter, in particular, engenders electronic chiral modes at the magnetic domain boundaries [1], whose hydrodynamics become intricately coupled with magnetic precession.According to the spin-charge helicity of the TI electronic states, the spin-transfer torques acting on the MI are locked with the self-consistent electronic charge currents in the TI. These currents, in turn, can respond to a combination of electromagnetic fields and fictitious forces induced by MI dynamics, having several distinct contributions: (i) two-dimensional (2D) surface c...

Domain wall motion in junctions of thin-film magnets and topological insulators

“…V is the voltage between both sides of the magnetic strip [14] (see Appendix D). Notice that we reintroduced and e.…”

“…An interesting aspect of the surface states of threedimensional TI is that external magnetic agents can modify their spectrum [9] and electronic transport properties [10], and conversely, the dynamics of magnets coupled to these surface states can be severely modified [11][12][13][14]. Specifically, the question of how the presence of these surface states influences the dynamics of a DW has been recently addressed in the literature [12,14]. We will go further by bringing into * yago.ferreiros@csic.es † alberto.cortijo@csic.es play an out-of-plane magnetic field, and show how magnetic field generated DW velocity can be significantly increased by holding off the appearance of Walker breakdown via an external electric field, and how the macroscopic DW chirality can be controlled by the presence of the TI surface state.…”

Skyrmion-induced anomalous Hall conductivity on topological insulator surfaces

“…Under a finite out-of-plane magnetization, the Dirac point is gapped out and the system acquires a finite Chern number C = ±1 from the momentum-space Berry curvature, leading to the well-known quantum anomalous Hall effect (quantum AHE, QAHE) [19][20][21][22][23][24] . Since the exchange coupling between the local in-plane magnetization and the TI surface electron can be regarded as the emergent gauge field (vector potential) for the conduction electrons 25 , topological magnetic textures on TI surfaces can give rise to even richer electronic properties: vortices and domain walls, for instance, are supposed to host zero modes, leading to electric charging of those textures [26][27][28] . Recent theoretical studies predict that magnetic skyrmions on TI surface can be charged as well 29,30 .…”

Growth and characterization of hybrid insulating ferromagnet-topological insulator heterostructure devices

“…Experiments aimed at observing such phenomena have primarily focused on magnetically doped TIs [3][4][5][6][7]. Complementary to the direct magnetic doping of TIs, several theoretical schemes have proposed explorations of a different sample geometry wherein a patterned ferromagnet (FM) is interfaced with a TI [8][9][10][11]. When the magnetic easy axis of the FM overlayer is out-of-plane, a gap opens in the surface states of the vicinal TI and this massive Dirac Hamiltonian should lead to chiral 1D edge states along FM domain walls where the mass changes sign.…”