Nonlinear Analog Spintronics with van der Waals Heterostructures

S. Omar, M. Gurram, K. Watanabe, T. Taniguchi, M.H.D. Guimarães, and B.J. van Wees

Phys. Rev. Applied 14, 064053 – Published 17 December 2020

Abstract

The existence of nonlinearity in a spintronic device is indispensable for spin-based complex signal-processing operations. Here we measure the presence of electron-spin-dependent nonlinearity in a van der Waals heterostructure spintronic device. We further demonstrate its application for basic analog operations such as essential elements of amplitude modulation and frequency sum (heterodyne detection) on pure spin signals, by exploiting the second-harmonic generation of the spin signal due to nonlinear spin injection. Furthermore, we show that the presence of nonlinearity in the spin signal has an amplifying effect on the energy-dependent conductivity-induced nonlinear spin-to-charge conversion effect. The interaction of the two spin-dependent nonlinear effects in the spin-transport channel leads to a highly efficient modulation of the spin-to-charge conversion effect, which in principle can also be measured without using a ferromagnetic detector. These effects are measured both at room and low temperatures, and are suitable for their applications as nonlinear circuit elements in the fields of advanced spintronics and spin-based neuromorphic computing.

Received 26 July 2020
Revised 24 October 2020
Accepted 16 November 2020

DOI:https://doi.org/10.1103/PhysRevApplied.14.064053

Physics Subject Headings (PhySH)

Spin current Spin injection Spin polarization Transport phenomena

Graphene Monolayer films Spin valves Van der Waals systems

Nonlinear DynamicsCondensed Matter, Materials & Applied Physics

Authors & Affiliations

S. Omar ^1,*, M. Gurram¹, K. Watanabe ², T. Taniguchi², M.H.D. Guimarães ¹, and B.J. van Wees¹

¹The Zernike Institute for Advanced Materials, University of Groningen, Nijenborgh 4, Groningen 9747 AG, Netherlands
²National Institute for Material Science, 1-1 Namiki, Tsukuba 305-044, Japan

^*s.omar@rug.nl

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 14, Iss. 6 — December 2020

Subject Areas

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
(a) Graphene encapsulated between a thick $h$ -BN at the bottom and a 3L– $h$ -BN tunnel barrier on the top. The cobalt (inner) injector electrode $C 1$ is located on top of the tunnel barrier and the (inner) detector electrode $C 2$ is directly in contact with the graphene flake. The outer injector and detector electrodes (transparent orange) are far enough to be spin sensitive, and serve as reference electrodes. A charge current $i + I$ is applied across $C 1$ for spin injection and a nonlocal ac voltage $v_{nl}$ is measured at $C 2$ via the lock-in detection method. (b) An optical image of the stack with the actual positions of electrodes drawn schematically. The $h$ -BN tunnel barrier is highlighted with false blue color. (c) An ac charge current $i = 50$ nA ( $20 μ A$ ) at $f = 6$ Hz is applied at $C 1$ ( $C 2$ ) and the Fourier transform of the nonlocal signal measured at $C 2$ ( $C 1$ ) is plotted in blue (red). In the inset, $I$ - $V$ characteristics of the tunnel contact $C 1$ (blue) and the transparent contact $C 2$ (red). These measurements are performed at room temperature. (d) The concept of nonlinearity is presented schematically via a circuit diagram. A sinusoidal charge current $i$ along with a dc current $I$ is applied at the input of a nonlinear element (inside the triangle) and a distorted nonsinusoidal spin signal is measured at the output. The harmonic components, which construct the output signal are also shown. The equivalent circuit representing the bias-dependent spin injection [ $p_{inj} = f (I)$ ] and spin transport ( $R_{s}$ ) is highlighted in pink.
Reuse & Permissions
Figure 2
(a) First-, (b) second-, and (c) third-harmonic spin-valve measurements. Here, a constant background offset (approximately $100 μ V$ for first, and approximately $μ V$ for second and third harmonic) is subtracted from the signal, for a clear representation. (d) First-, (e) second-, and (f) third-harmonic spin signal $v_{s}$ (in orange) is plotted at the left $y$ axis, and nonlocal signal $v_{nl}$ is plotted at the right $y$ axis, as a function of $I$ applied at $C 1$ , using the measurement geometry in Fig. 1. The ac injection current $i$ is kept fixed at 50 nA. $v_{nl}^{p}$ (red) and $v_{nl}^{ap}$ (blue) are the nonlocal signal $v_{nl}$ measured at the parallel and antiparallel magnetization configurations of the injector-detector electrodes, respectively. (g) First-, (h) second-, and (i) third-harmonic Hanle spin signal $v_{s}$ as a function of out-of-plane magnetic field $B_{⊥}$ . Hanle data is symmetrized in order to remove the linear background and is offset to zero. SV measurements in (a)–(f) are performed at room temperature, and Hanle curves in (g)–(h) are measured at 4 K.
Reuse & Permissions
Figure 3
A sum signal of the message signal with frequency $f_{m}$ and the carrier signal with frequency $f_{ref}$ is prepared outside the device and fed at the input terminal. (a) Amplitude modulation (AM) scheme. (b) AM measurement of the spin signal $v_{s}$ for $i_{m} << i_{ref}$ and the linear fit (black) (c) $i_{m} \geq i_{ref}$ and the nonlinear fit (fourth-order polynomial). (d) Heterodyne detection scheme (e) for $i_{m} = 0$ no spin signal is present at the frequency $f$ and $3 f$ . The spin-valve signal at $2 f$ is present because of second-harmonic generation due to nonlinear spin injection. (f) For $i_{m} \neq 0$ , due to the frequency shifting of the signal present at $2 f$ to $f$ and $3 f$ , equal strength signal appears at both frequencies. Both measurements are performed at room temperature. SV measurements in (e),(f) are offset to zero for clear representation.
Reuse & Permissions
Figure 4
Second-harmonic Hanle measurements in the parallel (green) and antiparallel (red) configuration for $i_{a c}$ = (a) 100 nA, (b) 300 nA, and (c) 400 nA. The enhancement in the spin-accumulation-induced charge signal $v_{c}$ with $i$ is visible in the asymmetry between $v_{nl}^{p}$ and $v_{nl}^{ap}$ with respect to the spin-independent background (dashed black line). The measured data is symmetrized in order to remove the spin-independent linear component present in the data and is offset to zero. All measurements are performed at 4 K. Second-harmonic Hanle spin-precession measurements of (d) the spin signal $v_{s}$ and (e) the spin-accumulation-induced charge signal $v_{c}$ . Both data are obtained from (a) for $i = 100$ nA and fitted with the solution to the Bloch equation. From the fit in (d), (e), we obtain $λ_{s} \sim 4 μ m$ and $1.8 μ m$ for the spin and charge signal, respectively. (f) $v_{c} - i$ dependence for the second-harmonic data is fitted (blue curve) with a fourth-order polynomial function. The dark (light) gray dashed line is the calculated magnitude of second-harmonic component of $v_{c}$ due to the nonlinear (linear) spin injection.
Reuse & Permissions

Physical Review Applied