The time-window for processing electron spin information (spintronics) in solid-state quantum electronic devices is determined by the spin–lattice and spin–spin relaxation times of electrons. Minimizing the effects of spin–orbit coupling and the local magnetic contributions of neighbouring atoms on spin–lattice and spin–spin relaxation times at room temperature remain substantial challenges to practical spintronics. Here we report conduction electron spin–lattice and spin–spin relaxation times of 175 ns at 300 K in 37±7 nm carbon spheres, which is remarkably long for any conducting solid-state material of comparable size. Following the observation of spin polarization by electron spin resonance, we control the quantum state of the electron spin by applying short bursts of an oscillating magnetic field and observe coherent oscillations of the spin state. These results demonstrate the feasibility of operating electron spins in conducting carbon nanospheres as quantum bits at room temperature.
Electron spin states are an attractive realization of a quantum bit (qubit) as they can undergo a transition between the spin-up and spin-down quantum states1. The most commonly used technique for manipulating electron spin is electron spin resonance (ESR)2. ESR is the physical process, whereby electron spins are polarized in an external magnetic field B0 and rotated by an oscillating magnetic field B1 (perpendicularly to B0, of frequency f), which is resonant with the spin precession frequency in an external magnetic field f=gμBB0/h (μB is the Bohr magneton and g the electron spin g-factor, h is the Planck’s constant). ESR is result of the coherence of the precession of electrons over the spin–lattice and spin–spin relaxation times, T1 and T2, respectively3. T1 is characterized by a number of spin–lattice relaxation process that depend on the spin–orbit coupling to connect the spin of an electron with the lattice vibrational spectrum of the solid. The second important relaxation time T2 is set by the probability of spin–spin relaxation. T2 is concerned with the local magnetic field contribution by one magnetic atom on others and represents the phase coherence of a set of spins. The dominant relaxation time is the shorter of T1 and T2. In magnetically homogenous itinerant systems (for example, metals), the condition T1=T2 is often met and represents the longest period of time that in-phase precessing electron spins and magnetization can propagate as a uniform mode4.
Electron spin states therefore need to be robust against decoherence. The feasibility of applications involving classical or quantum information processing is hence critically dependent on T1 and T2 relaxation times5,6,7,8,9,10,11,12. The prerequisite for T1 and T2 relaxation times is ∼100 ns, as this is the state of the art lower-bound for signal processing times in quantum electronic devices13,14.
Advances in the fields of inorganic15,16 and molecular17,18 quantum dots have made the electron spin system promising for practical application in spintronic and quantum information processing. Current research activities on spin-based qubits are divided into two distinct research directions with limited overlap and are based on the materials employed: inorganic materials, usually semiconducting structures forming quantum dots, and carbon-based molecules. The qubits utilized in these materials are also different: inorganic materials containing localized spins of doped ions or conduction electron spin confined on quantum dots, whereas organic materials utilize localized paramagnetic spins confined on molecules.
Due to the radical differences in the materials and the electron systems employed for spin qubit manipulation, the major challenges to realising devices are also distinct. For solid-state inorganic materials the strong spin–orbit interaction enforced by heavy nuclei in materials like semiconductors10,11,19 and metals12,20,21 strongly requires the pursuit of structural perfection and spin manipulation at low temperatures (40 mK to 100 K). This has resulted in well-defined materials that currently set the benchmark for long T1 relaxation times exceeding seconds9. Unfortunately, at room temperatures a number of intrinsic spin–lattice relaxation processes and phonon modes induce spin decoherence and diminish T1 and T2 (ref. 22). Consequently, for metal nanoparticles21 T1 and T2 shortens to 10–40 ps and for bulk semiconductors23,24 to 1–4 ns.
Molecular qubits can be produced on an industrial scale and are readily processed18. These spin-bearing organic molecules often have low spin–orbit coupling, possess many non-degenerate spin transitions, and can be chemically modified. These attributes have led to the potential of molecular compounds for both spintronics and quantum information processing. However, the dipole–dipole interactions between molecules and the hyperfine interaction of the molecule requires diluting the spin containing molecules and isotope engineering of the host system to reduce magnetic inhomogeneity. It also needs low temperatures (<100 K) for spin manipulation to dampen molecular vibrations that cause spin decoherence.
Attempts to combine the advantages of inorganic and molecular qubit materials have led to electronically insulating systems like nitrogen-vacancy (N-V) centre nanodiamonds25 and N@C60 (refs 14, 26). Long microsecond T1 and T2 of localized electrons in these materials can be achieved and manipulated at ambient conditions. Magnetic inhomogeneity in these materials is accounted for by isotopic engineering constituent 13C and 14,15N nuclei, however, the localized electron spins themselves generate fluctuating magnetic fields, posing limitations on the qubit density. This limitation is specific to localized electron systems and it is absent for conduction electrons where the motional narrowing process negates this effect27.
Carbon nanotube-based quantum dots have been prepared with an electron spin dephasing time of ∼3 ns at millikelvin temperature28. The shortening of T2 in these carbon nanotubes is attributed to an increase in the spin–orbit coupling induced by the high curvature of the carbon sheets29. Graphene on the other hand is comprised entirely from a single-atom thick crystalline layer of carbon, is flat (or at best not curved), and conducting30,31. Experiments on single- and few-layer graphene have demonstrated T1=T2 of 1–4 ns at room temperature32. However, this value is still far below expectations for practical use and possibly limited by physisorption and chemisorption of molecular oxygen or other species onto the unprotected carbon surface33. Non-carbon-based materials have also been developed, including heterometallic molecular nanomagnets comprising of isotopically engineered and diamagnetically diluted Cr7M (M=Ni, Mn, Zn) that demonstrate the prerequisite for quantum processing applications at low temperature (5 K) (ref. 34).
These possible solutions demonstrate that there are clear and established trade-offs to be considered regarding the feasibility of applying a qubit material system: a conducting material of light atomic weight constituents that meets the prerequisite T1 and T2 at room temperature would permit real spintronics and quantum processing applications. Such a material would combine the best aspects of both inorganic and molecular spin qubit schemes.
Here we report the observation of T1=T2=175 ns at room temperature (300 K) in conducting metallic-like carbon nanospheres via ESR. Furthermore, we could coherently control the quantum state of the electron spin confined on the carbon nanospheres at 300 K. This remarkable result can be put in context by comparing it with other promising systems, which could carry the quantum bit: N@C60, N-V centre in nanodiamond or P-doped Si (Fig. 1). In the carbon nanospheres, the electron spins are highly delocalized and polarizable (Pauli-paramagnetic) over the volume of the nanosphere, rather than highly confined to a small path on the order of the electron orbit, as would be the case for a localized electron system. This has the advantages that there is no need for isotopic engineering of the carbon nuclei to suppress magnetic inhomogeneity, and an absence of fluctuations in local magnetic fields of localized spins. The material thus allows a higher density packing of qubits to be, in principle, achieved over other promising qubits.
The structural and chemical properties of the carbon nanospheres are inherently key to the observation of the long T1=T2. Transmission electron microscopy (TEM) images show the extensive formation of spherical carbon spanning micron scales (Fig. 2a and Supplementary Fig. 1). The as-prepared carbon nanospheres are a conglomeration of spherical bodies and after sonication in suspension they could appear as individual particles (Fig. 2b). In comparison with other nanoparticle quantum dots used as qubits, for example, Mn-doped PbS (ref. 35), the carbon nanospheres are relatively uniform with a size distribution of 37±7 nm estimated from TEM images (Supplementary Fig. 2).
By means of TEM tomography, a number of carbon nanospheres are also observed to have an asymmetric shape, which also results from the formation of joint graphitic layers of contacting particles (Fig. 2c–e), with the accretion of layers between nanospheres generally forming within a region of ca. 5 nm of the outer layers (Supplementary Fig. 3). High-resolution TEM revealed the short graphitic fragments that comprise the carbon nanospheres are graphitic fragments that follow the curvature of a sphere, creating many open edges (Fig. 2f–h). The individual graphitic fragments in the carbon nanospheres are not curved and do not resemble the curvature in nanotubes or fullerenes. Rather, the fragments exhibit an intricate array of interplanar bonding all the way to the centre of the nanosphere even when heated to temperatures of 583 K. The carbon nanospheres are not hollow and show a continuation of the closed cage structure towards the centre.
X-ray photoelectron spectroscopy (XPS), thermogravimetric analysis (TGA), and Raman experiments were also performed and are found in Supplementary Figs 4–9 and Supplementary Notes 1–3. XPS indicated that the chemical structure is predominately conducting graphitic carbon (90.2 wt%) containing surface bound oxygen (9.8 wt%), and there was no inclusion of metals and other heavy atoms. TGA experiments confirmed the carbon nanosphere material did not contain residual precursor polyaromatic hydrocarbons and remained chemically and thermally stable even up to temperatures of 883 K. Valence band XPS revealed the presence of non-bonding π and σ orbitals as a result of fragmented sheets that contained carbon arranged in a distorted hexagonal network.
The carbon nanospheres are easily synthesized36 and readily processable (Fig. 3), yielding a homogenous material that is structurally highly non-crystalline (Fig. 2). Thus the carbon nanospheres can be reliably employed for spintronics applications with minimal processing and without the need for fabricating a well-defined crystal structure to achieve long T1 and T2. Furthermore, in a conducting carbon nanosphere qubit system, the rich chemistry of carbon can, in future experiments, allow for a myriad of non-covalent and covalent interactions to connect the nanospheres to conducting electronic device surfaces37,38. Finally, the carbon nanospheres are of a size that can be isolated on a surface from the ‘top-down’ using micromanipulator probe tips (Fig. 3d), and this in future experiments can allow for building qubit ensembles39.
Here we develop in more detail our key observations obtained by ESR. At 300 K and at 9.4 GHz frequency the continuous-wave ESR line width (peak-to-peak) is ΔH=0.056 mT (inset Fig. 4a and Supplementary Fig. 10) and the g-value is 2.00225 (inset Fig. 4b). This is a remarkably narrow conduction-electron spin ESR line testifying the long spin-relaxation times. The observed spectra had, to a high precision, homogeneously broadened Lorentzian line shapes and the deviation from the Lorentzian line shape in the entire spectra was <5%, (see Supplementary Fig. 10 as an example), which reveals the itinerant nature of the spins. The observed linewidth determined by continuous-wave ESR is identical within the experimental error with the T2-derived Lorentzian width. Note that the size distribution of the carbon nanospheres has a negligible effect on the linewidth at 9.4 GHz because of the motional narrowing of conduction electrons (Supplementary Fig. 11). The hyperfine ESR lines of 13C were also absent (which are readily observable for localized spins14,25,26) due to motional narrowing of conduction electrons27. The g-factor is characteristic to conduction electrons of carbon, and it does not originate from metallic inclusions (in agreement with our chemical analysis) or from localized paramagnetic ‘dangling’ bonds of carbon (commonly with g=2.00282) (ref. 40).
In addition to the continuous-wave ESR experiment, where detection and spin rotation occur at the same time, we extended our experiments to probe the spin relaxation dynamics of T1 and T2 independently using pulsed ESR (Fig. 4a). At 9.5 GHz frequency and 300 K, with good approximation we found that the intrinsic T1=T2=175 ns. Pulsed ESR therefore simultaneously validated our continuous-wave ESR results and verified that the line-shape obtained by continuous-wave ESR was indeed homogenous as expected for itinerant electrons.
The temperature-dependent properties of the ESR spectra (Fig. 4 and see also Supplementary Fig. 12) support that conduction electrons are confined within the carbon nanospheres. The g-factor was temperature independent (Fig. 4d), which is in good agreement with general observations in metals with weak spin–orbit coupling and in graphitic nanoparticles41. The resulting spin susceptibility is temperature dependent, following a Curie–Weiss dependence, as one may expect for nanoparticles of metals (Fig. 4b)21,42.
Multi-frequency ESR in the 4–420 GHz frequency and 2–300 K temperature range also confirmed that conduction electrons are confined within the carbon nanoparticles (Fig. 4 and Supplementary Fig. 12)43,44. The ESR linewidth revealed a linear increase with increasing magnetic field at 300 K (Fig. 4c and see also Supplementary Fig. 12). Note that in the case of bulk metals, ΔH is solely determined by spin–orbit coupling thus it is independent of the magnetic field21,45. However, the behaviour observed when the carbon nanospheres experience a variation in external magnetic field is characteristic to conduction electrons enclosed in nanoparticles where T1 and T2 are determined by both the spin–orbit interaction and electron confinement21. This broadening of ΔH for itinerant electrons confined on small particles follows46:
where EZ=hνZ is the Zeeman energy, δ is the average electronic energy level spacing and γe is the electron gyromagnetic ratio46. Using the measured T1=T2=175 ns, we can extract a δ=1 meV for the average electronic energy level spacing (linear line of best fit in Fig. 4c). From this value one can calculate back the size of the carbon spheres by following Kubo’s calculations for a small, almost spherical, metallic particle42:
where me is the free electron mass, vF=106 ms−1 is a typical Fermi velocity for graphene, and n=2.3 g cm−3 is the atomic density of the carbon nanospheres. These values yield an effective linear particle size of L=40 nm. This particle size is in good agreement with that obtained from TEM images. Furthermore, the increase in T1 and T2 as the temperature is decreased (Fig. 4a and see also Supplementary Fig. 12) is characteristic to metals21,41,45, where electron–phonon scattering due to spin–orbit interaction is responsible for the temperature-induced shortening of T1 and T2 (refs 42, 45, 46).
As the temperature was decreased, T2 reached 300 ns at 4 K while T1 reached 450 ns (Fig. 4a). There is a deviation from the T1=T2 dependence below ∼100 K. During the delineation of T1 and T2 below ∼100 K, T1 and T2 nevertheless continue to increase at different rates. The electron spin dynamics of T1 is directly related to phonon dampening in disordered graphitic sheets27,41 and the existence of Wallis-type47 local phonon modes. Future studies have to show if further localization at specific defect sites occurs at very low temperatures. As the temperature is increased, the calculations of Andersson et al.41 indicate that the observed shortening of T1 and T2 is caused by the scattering of conduction electrons by the potentials of peripheral atoms having edge-inherited electronic and lattice dynamical features and the excitation of low-energy phonons.
From our structural, chemical and electronic characterization we propose that the non-bonding orbitals associated to the structural imperfections induce conduction electrons to the system and significantly enhance the electron density of states. This is in agreement with theoretical works41,48 that predict the presence of an additional band superimposed upon the bonding π and the anti-bonding π* bands around the Fermi energy in nanometre size disordered graphitic fragments, and our observations of the changes in the pz wave functions in the p–π band evolutions with temperature near the Fermi energy level (Supplementary Fig. 5).
The carbon nanospheres also contain covalently bonded oxygen that contributes to the disorder within the graphitic lattices (Fig. 3f–h; Supplementary Table 1; Supplementary Fig. 9). We note that the removal of oxygen groups by thermal decomposition introduces non-bonding π and σ orbitals (Supplementary Figs 4 and 5). In future experiments, greater robustness against spin decoherence may be achieved by the removal of adatoms to enhance the electronic density of states33.
Although the carbon nanospheres are highly defective, the intrinsically weak spin−orbit interaction of carbon has allowed for long T1 and T2 to persist even at 300 K. In nanotubes and fullerenes, an increase in spin−orbit coupling due to graphene sheet curvature may contribute to the shortening of T1 and T2 (refs 28, 29), however the individual graphitic flakes in the carbon nanospheres are not curved. The T1=T2 in the carbon nanospheres is remarkably a two orders of magnitude enhancement over that found in conducting crystalline graphene32. We attribute part of this increase in T1 and T2 to quantum confinement effects readily observed in conducting nanostructures9,11,12,21.
Following our observations of magnetically induced spin polarization, we coherently rotated the electron spin at 300 K by applying microwave power bursts of increasing duration and with variable power (Fig. 5a). We observed that the magnetization of the carbon nanospheres oscillates periodically with pulse duration, the oscillation frequency being proportional to the square root of the microwave power. This oscillation indicates that we have performed deliberate and coherent electron spin rotations (driving of electron spins between two Zeeman-split energy levels), or Rabi oscillations. This is the sign that one can manipulate spins both for spintronics and quantum information processing (see also Supplementary Note 4)1,49. Fourier-transformed Rabi oscillation signals show a single-component characteristic to electron spin-1/2 qubit (Fig. 5b). A key characteristic of the Rabi process is a linear dependence of the Rabi frequency on the microwave field strength B1 (fRabi=gμBB1/h). We verify this by extracting the Rabi frequency from a fit of the Fourier-transformed signal of Fig. 5b with a Gaussian line, which gives the expected linear behaviour that is proportional to B1 (Fig. 5c). This demonstrated the capacity to rotate the spin qubits on the carbon nanospheres arbitrarily to any point on the Bloch sphere3 at temperatures as high as 300 K. Rabi oscillations can be observed for ∼400 ns, consistent with decoherence by T2. The increase in linewidth of the Fourier-transformed oscillations with microwave power (Fig. 5b) is caused by microwave field inhomogeneity.
We have demonstrated that a long itinerant electron spin lifetime in a magnetically homogenous conducting material can be achieved at room temperature. Through the controlled polarization of coherent electron spins in these carbon nanospheres, we have showed that this electron spin lifetime exceeds the prerequisite for applications in spintronics and quantum information processing. This is possible through electron confinement to nanometre-sized, non-crystalline yet metallic-like carbon spheres. This work effectively bridges the disparate research directions in the fields of inorganic and molecular materials for electron spin qubits and has broad applicability: spin qubits can now be manipulated at room temperature without the need for isotopically engineering a host material, diluting the spin-carrying molecule, cryogenic temperatures, the preparation of well-defined crystal structures, or the use of metals. The facile preparation of a carbon material using common laboratory reagents, combined with the use of well-established electron spin manipulation measurements at room temperature, effectively reduces many of the technological barriers to realising practical quantum computing and spintronics using solid-state materials.
The spin-manipulation experiments described here were performed on a large number of carbon nanospheres. Although the material can be readily chemically processed, it is prepared in a form suitable for device processing: we have demonstrated that the conducting nanospheres can be isolated on a silicon surface by physically manipulating individual nanospheres. In principal, this may provide an initial avenue to high-density qubit arrays of nanospheres that are integrated onto existing silicon technologies or thin-film-based electronics.
The preparation of the carbon nanospheres is described in detail elsewhere36 and can be summarized as the soot product resulting from the partial combustion of naphthalene in air, which is collected and heated at 473 K under dynamic vacuum for 72 h. Approximately 100 mg was prepared for all experimental procedures.
Transmission electron microscopy
Samples were analysed using a field emission JEOL3000F operated at 300 kV. Particle-size distribution and topography image analysis was performed using freely available ImageJ 1.48v software (http://imagej.nih.gov/ij). Energy-filtered tomography images were obtained using a JEOL JEM 2200FS Field Emission Microscope operated at 200 kV using a high-tilt holder, with an in-column omega filter and objective aperture applied. JEOL recorder software v184.108.40.206 was used to collect the topography images. JEOL Composer and JEOL Visualizer-kai programs were used to reconstruct the tomography images.
Scanning electron microscopy
Scanning electron microscopy was performed using a Zeiss Ultra Plus.
X-ray photoelectron spectroscopy
Measurements were conducted using an ESCALAB250Xi instrument manufactured by Thermo Scientific, UK. The background vacuum was better than 2 × 10−9 mbar. A monochromated Al Kα (energy hν=1,486.68 eV) was used with a spot size of 500 μm. The fine carbon powder was manually pressed onto indium foil for analysis or pressed into a disc prior to in situ heating experiments. Curve fitting was performed using the Scienta ESCA300 data-system software. Binding energy reference was C 1s=285.0 eV for adventitious carbon.
Raman spectroscopy was performed using Argon 514 nm excitation laser on a Renishaw Raman inVia Reflex with a notch and edge filter cutoff of 100 cm−1.
Modulated thermogravimetric analysis
Modulated thermogravimetric analysis measurements were obtained using a TA HiRes Discovery TGA in modulated TGA mode with a heating profile of 2 °C min−1 under the flow of 20 ml min−1 high-purity N2 with sinusoidal temperature amplitude of 4 °C and period of 200 s. A 100-μl alumina pan was used. Evolved gas analysis (TGA GC–MS) was performed using a Perkin Elmer Thermogravimetric Analyzer Pyris 1 coupled to a Perkin Elmer Gas Chromatograph Clarus 680 and Mass Spectrometer Clarus SQ 8 C.
Experiments were performed on a home built quasi-optical spectrometer operated in the 55–420 GHz frequency range in a corresponding 0–16 T field range43,44. At low frequencies of 4, 9.4 and 34 GHz, a Bruker elexsys E500 spectrometer was used. For a typical experiment, about 1 mg of the carbon sample was weighed and then sealed in a quartz ESR tube after being heated at 500 K under dynamic vacuum overnight. For temperature- and frequency-dependent experiments, the magnetic field modulation amplitude was smaller than 0.01 mT and the microwave power was set to 0.2 μW to avoid signal distortion. For g-factor reference, a polycrystalline KC60 powder was used with g=2.0006.
Experiments were performed at 9.4 and 34 GHz using Bruker ElexSys 580 and 680 spectrometers. For T2 determination we used a simple 2-pulse sequence, invoking a first π/2 pulse of 16 ns, and an initial delay of the second pulse of 300 ns. The resulting echo was integrated over 175 ns. For T1, a 3-pulse sequence was used. An initial π pulse of 32 ns was followed after 300 ns delay by a 2-pulse echo sequence with 200 ns initial pulse delay for monitoring the inversion recovery. For Rabi experiments, a single π/2 pulse was used. Its length was incremented by 2 or 4 ns. After a delay of ∼84 ns with respect to the pulse ending, the signal was observed with a short integrating time of 16 ns.
The data that support the findings of this study are available from the corresponding authors upon request.
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We acknowledge the financial support of Swiss National Science Foundation (snsf 200021_144419) and ERC advanced grant (PICOPROP#670918). We acknowledge the support of the group of Professor R Bittl (FU Berlin) in pulsed ESR. M.C. acknowledges financial support from the University of Sydney and the technical support from the Australian Centre for Microscopy and Microanalysis and from the Mark Wainwright Analytical Centre.
The authors declare no competing financial interests.
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Náfrádi, B., Choucair, M., Dinse, KP. et al. Room temperature manipulation of long lifetime spins in metallic-like carbon nanospheres. Nat Commun 7, 12232 (2016). https://doi.org/10.1038/ncomms12232
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