Nonlinear magnetic dynamics in a nanomagnet--topological insulator heterostructure

Nonlinear magnetic dynamics in a nanomagnet–topological insulator heterostructure

Xiaopeng Duan, Xi-Lai Li, Yuriy G. Semenov, and Ki Wook Kim

Phys. Rev. B 92, 115429 – Published 18 September 2015

Abstract

Magnetization dynamics of a nanomagnet, when strongly coupled with a topological insulator (TI) via the proximity interaction, is examined theoretically in the presence of electrical current on the TI surface under realistic transport conditions. Due to the spin-momentum interlock, the magnetic state and TI electron transport depend significantly on each other. Such an interdependence leads to a variety of nonlinear dynamical responses in all transport regimes including the scattering dominant diffusive cases. Generation of the anomalous Hall current, in particular, is found to be a key to the unique features that have not been observed previously. For instance, the anomalous Hall current can result in antiparallel alignment of the final magnetization state in reference to the effective driving magnetic field by inducing an extra term that counters the damping effect. Similarly the calculation also reveals steady oscillation of the magnetization under a broad range of conditions, offering a robust mechanism for highly efficient magnetization reversal and/or spin wave excitation under a dc bias.

Received 23 June 2015
Revised 11 August 2015

DOI:https://doi.org/10.1103/PhysRevB.92.115429

Authors & Affiliations

Xiaopeng Duan¹, Xi-Lai Li¹, Yuriy G. Semenov¹, and Ki Wook Kim^1,2,*

¹Department of Electrical and Computer Engineering, North Carolina State University, Raleigh, North Carolina 27695, USA
²Department of Physics, North Carolina State University, Raleigh, North Carolina 27695, USA

^*kwk@ncsu.edu

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Vol. 92, Iss. 11 — 15 September 2015

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Images

Figure 1
(a) Schematic illustration of the TI-magnet structure under investigation. An insulating nanomagnet (FMI) is placed on top of a TI surface, where two electrodes are used to inject the current through the TI-FMI interface region. The red arrow ( $\vec{m}$ ) denotes the magnetization of the magnet. (b) and (c) show the mechanisms for the transverse current (i.e., the anomalous Hall effect) due to the in-plane and the out-of-plane magnetization, respectively. The thick arrows (yellow) represents the electron flow while the thin arrows (red) denote the corresponding spin polarization. The inset in (b) illustrates the shift of the iso-energy contour in the momentum space (TI) due to the in-plane magnetization (FMI).
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Figure 2
Dynamical response of the magnetization from the initial state $m_{x} = - 1$ calculated under diffusive transport conditions (i.e., $β_{x} = 0$ ) with $β_{z} = 0.06$ at different driving voltages $V$ and damping constants $α$ : (a) $V = 0.25$ V, $α = 0.08$ ; (b) $V = 0.25$ V, $α = 0.01$ ; (d) $V = 0.2$ V, $α = 0.03$ ; (e) $V = 0.15$ V, $α = 0.07$ . (c) and (f) show the corresponding trajectories in the magnetization space. The blue (dark) and orange (light) curves in (c) represent the results of (a) and (b), respectively. Similarly in (f), they are for (e) (blue) and (d) (orange). The red dot marks the initial state. The length $L$ of 90 nm and the TI chemical potential $u_{0}$ of 50 meV are assumed in all cases.
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Figure 3
Magnetization dynamics mapped on the $V - α$ parameter space. As in Fig. 2, the diffusive electron transport is considered with $β_{z}$ fixed at 0.06. The solid lines separate the different dynamical regimes. The dashed lines in the flip-flop region indicate the smeared nature of the boundaries between the two final states ( $+ x$ or $- x$ ) after the precession. The background color provides the corresponding frequency of the magnetization rotation. AO stands for auto (or sustained) oscillations.
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Figure 4
Phase diagram of the magnetization dynamics with (a) a reversed bias ( $V < 0$ ), (b) a different TI chemical potential $u_{0}$ , and (c) a negative $β_{z}$ . The rest of the conditions and the notations are the same as in Fig. 3.
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Figure 5
(a) Magnetization dynamics calculated under ballistic but non-coherent transport conditions with $β_{z} = 0.06$ and $β_{x} = 0.6$ . (b) and (c) examine hypothetical cases with the specified conditions for reference. The rest of the parameters and the notations remain the same as in Fig. 3.
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