Spin polarised quantised transport via one-dimensional nanowire-graphene contacts

TL;DR

This work addresses the challenge of achieving ballistic spin transport in graphene spintronics by introducing fully encapsulated graphene channels with nanoscale 1D ferromagnetic nanowire contacts that form edge quantum point contacts (e-QPCs). The authors demonstrate zero-field quantised conductance through these e-QPCs and quantify the transmission through Landauer analysis, yielding $T \in [0.08,0.30]$ with an effective constriction width $W_c \approx 220-240$ nm. Spin transport measurements reveal non-local spin signals with $\lambda_s \approx 7.9\ \mu$m and $P \approx 4.8\%$, confirming ballistic spin injection and diffusion over several micrometers, while bias spectroscopy and a quantum Hall transition further corroborate the ballistic, edge-confinement picture. Collectively, these results establish a scalable pathway to ballistic graphene spintronic devices without physical constrictions in the graphene channel, potentially enabling low-power, high-coherence spin information processing.

Abstract

Graphene spintronics offers a promising route to achieve low power 2D electronics for next generation classical and quantum computation. As device length scales are reduced to the limit of the electron mean free path, the transport mechanism crosses over to the ballistic regime. However, ballistic transport has yet to be shown in a graphene spintronic device, a necessary step towards realising ballistic spintronics. Here, we report ballistic injection of spin polarised carriers via one-dimensional contacts between magnetic nanowires and a high mobility graphene channel. The nanowire-graphene interface defines an effective constriction that confines charge carriers over a length scale smaller than that of their mean free path. This is evidenced by the observation of quantised conductance through the contacts with no applied magnetic field and a transition into the quantum Hall regime with increasing field strength. These effects occur in the absence of any constriction in the graphene itself and occur across several devices with transmission probability in the range T = 0.08 - 0.30.

Figures (4)

• Figure 1: Device and 1D contact architecture. (a) Optical microscope image of a representative graphene spintronic device (D3) on SiO$_2$ substrate. Vertical blue strip is the hBN-encapsulated graphene channel, pale yellow bars are ferromagnetic cobalt (Co) electrodes and bright yellow bars are gold (Cr/Au) reference contacts. $W_{\text{c}}$ is contact width, $W_{\text{ch}}$ is channel width, and $L_{\text{ch}}$ is channel length (i.e. distance between adjacent contacts). Note $W_{\text{c}}$ is varied throughout the device such that each contact has a different magnetic coercivity. Scale bar (bottom left) is 10 $\mu$m. (b) Illustration of the nanowire-graphene interface. Red colouring within the dashed white line represents $n-$doping relative to the rest of the channel, due to charge transfer from the Co nanowire. The doping length scale, $l_{\text{pn}}$, is less than the mean free path of injected charge carriers, $\ell_{\text{mfp}}$. Edge termination in this illustration does not reflect that of real devices, which have disordered edges. (c) Breakdown of device length scales indicating where transport can be considered ballistic. $\lambda_{\text{s}}$ is the spin diffusion length. (d) Side profile view of the bottom hBN (b-hBN)/single layer graphene (SLG)/top hBN (t-hBN) stack. (e) Conductivity of device D1 vs carrier density in the channel at room temperature (300 K) and low temperature (20 K). Dashed cyan lines are linear fits to the conductivity, used to estimate the field-effect mobility of the channel.
• Figure 2: Zero field quantised conductance via e-QPCs (device D2). (a) Hole and (b) electron conductance as a function of bias voltage, $V_\text{Bias}$, applied between the magnetic electrode and the graphene channel. Each black line represents a bias sweep at a different fixed back gate voltage $V_{\text{BG}}$; the conductance minimum for this e-QPC occurs at $6.6 {V_{\text{BG}}}$. Blue squares in (a) highlight zero bias hole subbands ($h_{1,2,3})$. Likewise, purple squares in (b) show zero bias electron subbands, ($e_{1,2}$), while green triangles highlight finite bias plateaus ($e_{1-,1+}$). (c) Conductance vs $k_{\text{F}}$ ($k_{\text{F}} = \sqrt{\pi n_{\text{c}}})$. This data represents a separate measurement, but can be thought of as a trace of the conductance along $V_{\text{Bias}}=0$ in the spectroscopy data. Arrows indicate electron and hole subbands (corresponding to squares in panels (a) and (b)). Inset shows a schematic of the 3-terminal measurement configuration. (d) Spectroscopy data for electron doping (panel (b)), plotted as a 2D map of transconductance against $V_{\text{Bias}}$ and $V_{\text{BG}}$. Plateaus occur where $\text{dG}/\text{dV} = 0$, which is represented in white. Black boxes represent the area fit with a 2D Lorentzian function, to find the local minima and quantify the position of the finite bias plateaus ($e_{1+,1-}$).
• Figure 3: Spin transport, device D1. (a) Spin valve, at a channel density of $n=1.5\times 10^{12}$ cm$^{-2}$, taken by sweeping magnetic field along the easy axis of the contacts. Trace implies $B$ is swept from negative to positive, while retrace implies the opposite direction. The magnitude of the spin signal, $\Delta R_{\text{NL}}$, is indicated by the black arrow. (b) Hanle spin precession measurement, at a channel density of $n=1.5\times 10^{12}$ cm$^{-2}$, taken by sweeping a magnetic field out of plane. The line shape signifies spin moments have almost fully precessed within 200 mT. Dashed red line indicates a fit to the data using the solutions to the 1D Bloch equation. Inset shows schematic of non-local configuration used for spin transport measurements. (c) Evolution of $\Delta R_{\text{NL}}$ with increasing $V_{\text{BG}}$ (black line, left axis), superimposed with conductance through the injector (red line, right axis), for electron transport only. Dotted red lines indicate plateaus in the conductance that correspond to energy subbands.
• Figure 4: Landau fan diagram for D1, symmetrised with respect to $B_\perp$. (a) 2D map of transconductance for a single e-QPC as a function of contact carrier density, $n_{\text{c}}$, and perpendicular magnetic field strength, $|B_\perp|$. White regions imply conductance plateaus (dG/dVBG = 0), occurring due to confinement at low $B$ (dotted black lines), or quantum Hall transport at high $B$ (dashed black lines, labelled by filling factor $\nu$). Solid black line plotted with Equation \ref{['eq:critB']}. (b) Evolution of $G$ vs $n$, with increasing $|B_\perp|$. Dotted black lines indicate positions of low field plateaus and correspond to those seen in panel (a).