Polarization amplification by spin-doping in nanomagnetic/graphene hybrid systems

Tim Anlauf, Marta Prada, Stefan Freercks, Bojan Bosnjak, Robert Frömter, Jonas Sichau, Hans Peter Oepen, Lars Tiemann, and Robert H. Blick

Phys. Rev. Materials 5, 034006 – Published 16 March 2021

Abstract

The generation of nonequilibrium electron spin polarization, spin transport, and spin detection are fundamental in many quantum devices. We demonstrate that a lattice of magnetic nanodots enhances the electron spin polarization in monolayer graphene via carrier exchange. We probed the spin polarization through a resistively detected variant of electron spin resonance and observed resonance amplification mediated by the presence of the nanodots. Each nanodot locally injects a surplus of spin-polarized carriers into the graphene, and the ensemble of all spin hot spots generates a nonequilibrium electron spin polarization in the graphene layer at macroscopic lengths. This occurs whenever the interdot distance is comparable or smaller than the spin diffusion length.

Received 13 August 2020
Revised 27 January 2021
Accepted 5 March 2021

DOI:https://doi.org/10.1103/PhysRevMaterials.5.034006

Physics Subject Headings (PhySH)

Spin polarization Transport phenomena

Graphene Magnetic nanoparticles

Electron spin resonance

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Tim Anlauf¹, Marta Prada², Stefan Freercks¹, Bojan Bosnjak¹, Robert Frömter ¹, Jonas Sichau ¹, Hans Peter Oepen¹, Lars Tiemann ^1,*, and Robert H. Blick¹

¹Center for Hybrid Nanostructures, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
²I. Institute for Theoretical Physics, Universität Hamburg HARBOR, Geb. 610 Luruper Chaussee 149, 22761 Hamburg, Germany

^*Corresponding author: lars.tiemann@physik.uni-hamburg.de

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Issue

Vol. 5, Iss. 3 — March 2021

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Images

Figure 1
Schematic illustration of exemplary spin populations at a finite magnetic field. The center panel shows a section of the Fermi distribution function in comparison to the upper and lower spin bands (red bars). The Fermi energy, $E_{F}$ , dwarves the Zeeman splitting that is of the order of $100 μ eV$ . The red layers above and below are magnifications of the spin bands and their occupations in a system without excess spin polarized carriers (top) and in the presence of additional spin sources (bottom). The resistive detection of ESR is based the small difference in the occupation of the spin-down and spin-up levels which is different in the top and bottom panels.
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Figure 2
Sample B. (a) SEM image of the substrate with prepatterned Pt/Co nanodots. (b) Schematic illustration of the graphene Hall bar sample B on the substrate with nanodots (white dots) and the relative orientations of the microwave field generated by a nearby coil, the external magnetic field ( $B$ ), and the low frequency transport current ( $I$ ). Sample A has the same dimensions but rests on a ${SiO}_{2}$ without nanodots (not shown here).
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Figure 3
Reference sample A (graphene on plain ${SiO}_{2}$ ). Upper panel (a): $ρ_{x x}^{dark}$ measured without microwaves (blue solid line) and $ρ_{x x}^{23 GHz}$ under continuous radiation of 23 GHz/21 dBm (red solid line). The back gate was tuned to the smallest density at the charge neutrality point of approximately $n \approx 2 \times 10^{11} {cm}^{- 2}$ . Thermal activation leads to an overall increase of the conductivity under microwave radiation. Lower panel (a): $Δ ρ_{x x} = ρ_{x x}^{23 GHz} - ρ_{x x}^{dark}$ . The peak centered at $B = 0$ T is resulting from thermal activation in the weak localization regime; the highlighted areas indicate electron spin resonances (see main text). (b) Open circles represent resonance amplitudes in ohms, taken from Lorentzian fits of the resonances that occur around 0.85 T as function of the carrier concentration. The dashed red line shows the estimated resonance amplitudes based on the model in Sec. 2. The black solid line represents the CNP in $ρ_{x x}$ measured at $B = 0$ T (right-hand axis). A discontinuity exists because the density cannot be tuned to be zero for $T >$ 0 K. (c) Spin diffusion length ( $λ_{S}$ ) versus frequency measured at a density of 2 $\times 10^{11} {cm}^{- 2}$ .
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Figure 4
Sample B. (a) Absolute $ρ_{x x}$ shown for two exemplary frequencies, $ν = 27$ GHz and 35 GHz using a power of $+ 21$ dBm, shows strong Zeeman resonance peaks (red highlighted areas) and transitions originating from the existence of an intrinsic band gap (unmarked). Inset: Frequencies vs resonance positions obtained from Lorentzian fits of the resonances [24]. The slope corresponds to a $g$ factor of $1.96 \pm 0.02$ . All measurements were performed with the (intrinsic) hole density of $p_{i} \approx 1.5 \times 10^{13} {cm}^{- 2}$ , which is two orders of magnitude larger as for the data shown in Fig. 3. (b) Ratio of peak heights of $Δ_{A}$ (sample A at $n = 2 \times 10^{11} {cm}^{- 2}$ ) and $Δ_{B}$ (sample B at $p_{i}$ ) vs frequency.
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Figure 5
(a) Simplified schematic illustration of two contrasting diffusive regimes. Blue filled circles represent the nanodots, the red semitransparent areas [enclosed by a dashed circle for clarity] represent the spin diffusion length $λ_{S}$ , $a$ is the interdot distance. For $λ_{S} / a < 1$ (left panel), no excess polarization can build up. For $λ_{S} / a ⩾ 1$ (right panel), a net excess spin polarization is maintained during the transit to the next spin hot spot, where the polarization is refreshed. (b) The predicted enhancement factor of the resonance amplitude for lower carrier concentrations. Inset: exemplary data points for $λ_{S}$ vs $ν$ .
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