Session V35: Focus Session: Spins in Semiconductors -- Carbon-based Systems

Gigahertz dynamics of a strongly-driven single spin in diamond

Fast quantum control is critical to quantum information processing due to the practical need for fault tolerance. Resonant quantum manipulation is typically performed under the rotating wave approximation (RWA) which assumes that the oscillating driving field can be approximated by a rotating field. Here we present experiments probing the spin dynamics of single nitrogen vacancy (NV) centers in diamond driven by a large amplitude oscillating field where this approximation is no longer valid\footnote{G. D. Fuchs, V. V. Dobrovitski, D. M. Toyli, F. J. Heremans, D. D. Awschalom, {\em Science}, 19 November 2009 (10.1126/science.1181193).}. Using lithographic coplanar waveguides on diamond substrates we generate oscillating magnetic fields large enough to produce spin rotations on the same timescale as Larmor precession. In this regime the Rabi oscillations become highly anharmonic due to the influence of both the co- and counter-rotating components of the magnetic driving field. Surprisingly, we find that coherent spin flips can still occur under these conditions. Moreover, they occur on sub-nanosecond timescales -- faster than expected from the RWA. Our results in combination with the recent demonstration of millisecond coherence times in this system suggest that over one million coherent operations can be performed on an NV center at room temperature. Finally, we present ion implantation experiments demonstrating the ability to place NV centers in the diamond lattice near the high-field region of our waveguides with sub-100nm spatial accuracy. This technique is applicable to other experiments requiring precise positioning of NV centers within the diamond host.   

Imaging magnetic field vectors using nitrogen-vacancy centers in diamond

The localized spin triplet state of nitrogen-vacancy (NV) centers in diamond can be used in atomic-scale detection of local magnetic fields. Here we present a technique to image fields around magnetic structures[1]. We extract the magnetic field vector by probing resonant transitions of the four fixed tetrahedral NV orientations. In combination with confocal microscopy techniques, we construct an image of the local magnetic field vectors. Samples consist of patterned permalloy structures with integrated microwave antennas formed by optical lithography on single-crystal diamond substrates with high NV center concentrations. Measurements are done in external fields of less than 50 G at ambient conditions. \\[4pt] [1] B. J. Maertz \textit{et al. }(2009).   

Distance measurement based on electron spin decoherence time (T2)

Magnetic resonance techniques have been used for applications to magnetic imaging sensors with nanometer and sub-nanometer scale and for determination of static and dynamical structure of biological molecules. Among the methods, electron spin resonance (ESR) brings important capabilities which nuclear magnetic resonance (NMR) cannot access to. The examples include a long distance determination up to several nanometers and a fast time resolution with hundreds of nanoseconds. Currently several advanced pulsed and continuous wave (cw) ESR techniques are commonly used to determine distance with low frequency ESR. We have recently demonstrated that high frequency pulsed ESR can well-characterize the strength of magnetic dipolar interaction between electron spins through spin decoherence time (T2) [1]. This result implies that investigation of spin decoherence time by high frequency ESR can be used for distance measurement. We will present a principle of this new distance measurement technique and will determine an average distance of impurities in diamond. In addition, bio-related applications will be discussed.\\[4pt] [1] S. Takahashi et al., \textit{Phys. Rev. Lett.} \textbf{101}, 047601 (2008).   

Contact resistances, transfer lengths, and spin transport in graphene structures

In graphene device structures, electric current is usually injected from a 3-dimensional (3D) metal electrode to a 2D graphene layer. The contact resistance, which is present in structures even without an oxide layer between the electrode and graphene, can be characterized by the transfer length, which measures the length required for a current changes from lateral in graphene to vertical in the electrode. Different transfer lengths with respect to the electrode size can give rise to different spin injection and transport behaviors. Here we study spin transport in nonlocal graphene device structures by solving the spin drift-diffusion equations with boundary conditions that take into account finite spin-dependent transfer lengths. Our theory can consistently explain measured nonlocal resistances and their bias-current dependences in structures with and without an Al$_2$O$_3$ layer between Co electrodes and graphene.   

Standard tunnel junctions for graphene spintronics

Graphene, whereas in sole or few layers, has aroused a considerable interest for spintronics. This is mainly due to its high mobility and long spin diffusion length expected up to room temperature. In line with the early results of spintronics, conventional tunneling barriers of MgO or alumina have been used in order to inject spins into the graphene/graphite layer up to now.We studied the influence of both spin dependent barriers on the exfoliated graphene properties. We will first present the results of a Raman study on the chemical compatibility of graphene with spin-dependant tunnel barrier (MgO, Al2O3). In the case of alumina, a 0.6nm Al film is deposited and then oxidized in pure O2. In the case of MgO, the sputtering is done directly from a MgO polycristaline target. This will be followed by a presentation of transport properties.   

Enhanced Spin Injection into Graphene with MgO Tunnel Barriers

Graphene is an attractive material for spintronics due to its tunable carrier concentration and polarity, weak spin-orbit coupling, and the prediction of novel spin-dependent behavior. We investigate the spin dependent properties in single layer graphene (SLG) spin valves via nonlocal magnetoresistance (MR) measurements. We compare two types of SLG spin valves: with transparent contacts (Co/SLG) and with tunneling contacts (Co/MgO/SLG) It is shown that with MgO tunnel barrier, the nonlocal MR is increased and the spin injection efficiency is greatly enhanced. Temperature dependence of the SLG spin valves is studied. Also, our results show that the nonlocal MR is dependent on the gate voltage and DC bias current.   

Spin relaxation in graphene quantum dots

With its low concentration of nuclear spins and relatively weak spin-orbit coupling, graphene is a promising host material for electron spin qubits. We have calculated the spin relaxation time $T_1$ of a single spin in graphene quantum dots [1,2] as a function of the externally applied magnetic field $B$. We find that in quantum dots without coupling between the valleys $K$ and $K'$ in the graphene band structure, there is an effective time-reversal symmetry breaking which prevents the Van Fleck cancellation at $B=0$ known from semiconductor quantum dots. In combination with the lower dimensionality of the phonons in graphene, this leads to a distinct value of the exponent $\alpha$ in the power law $T_1 \propto B^\alpha$ which can be different from the value for semiconductor quantum dots. \\[4pt] [1] B. Trauzettel, D.V. Bulaev, D. Loss, and G. Burkard, Nature Phys.\ {\bf 3}, 192 (2007).\\[0pt] [2] P. Recher, J. Nilsson, G. Burkard, and B. Trauzettel, Phys.\ Rev.\ B {\bf 79}, 085407 (2009).   

Is Coulomb scattering important for spin relaxation in graphene

Due to the low intrinsic spin-orbit and hyperfine couplings, graphene is expected to have long spin lifetime up to $\mu $s regime. Even though spin transport in graphene has been demonstrated at room temperature, the reported spin lifetime has never achieved over one nano-second. Because recent experiments find that the primary source of spin relaxation is momentum scattering and the dominant source of momentum scattering is believed to be the charged impurity scattering, it is reasonable to assume that charge impurity scattering is an important factor for spin relaxation. To study this unexpected short spin lifetime, we investigate the effects of charged impurity scattering on spin relaxation by systematically introducing gold impurities onto graphene spin valves. We find that Au impurities on graphene do not generate the dominant spin relaxation. In addition, Au impurities are found to slightly enhance the spin lifetime ($\sim $10{\%}). This result suggests a new direction to study the spin relaxation in graphene.   

Giant Tunneling Magnetoresistance (TMR) in Graphene Patches

Graphene-based field effect devices based on graphene flakes and nanoislands have attracted a great deal of attention due to their unique physical properties and potential for nanoelectronic applications. The emergence of magnetism[1,2] in nanometer graphene patches terminated by zigzag edges along with the low intrinsic spin-orbit interaction opens a new research venue for spintronics, such as tunneling magnetoresistance, spin filter, and quantum computing. We have employed density functional theory and the nonequilibrium Green's functions approach to study the charge and spin transport in tunnel junctions comprising of one and two zigzag-terminated graphene triangular flakes connected to reconstructed zigzag-terminated graphene ribbons. We will present results of (1) the interplay between gate voltage and its incidence on the selection of the filtered spin channel and (2) the effect of the relative orientation of the magnetizations of the two graphene nanoflakes on the transport of the tunnel junctions. The calculations demonstrate the possibility of engineering such graphene patches as magnetic tunneling junctions that exhibit giant TMR. [1] J. Fernandez-Rossier et al., Physical Review Letters \textbf{99} (2007). [2] W. L. Wang et al., Nano Letters \textbf{8}, 241 (2008).   

Is there hope for spintronics in one dimensional realistic systems?

The use of the electron spin as the ultimate logic bit can lead to a novel way of thinking about information flow. At the same time graphene, a gapless semiconductor, has been the subject of intense research due to its fundamental properties and its potential application in electronics. Defects are usually seen as having deleterious effects on the spin polarization of devices and thus they would tend to hinder the applicability of spintronics in realistic devices. Here we use a ab initio methods to simulate the electronic transport properties of graphene nanoribbons up to 450 nm long containing a large number of randomly distributed impurities. We will demonstrate that it is possible to obtain perfect spin selectivity in these nanoribbons which can be explained in terms of different localization lengths for each spin channel. This together with the well know exponential dependence of the conductance on the length of the device leads to a new mechanism for the spin filtering effect that is in fact driven by disorder. Furthermore, we demonstrate that this is an effect that does not depend on the underlying system itself and could be observed in carbon nanotubes and nanowires or any other one-dimensional device.   

Spin relaxation for a confined electron in a buried carbon nanotube

The problem of spin relaxation in carbon nanotube quantum dots has recently been studied in theory [1,2] and experiment [3]. The existing theoretical work [1] focuses on a suspended tube, while many experimental studies are done in nanotubes buried under a dielectric. Here we consider the effect of bulk phonon modes of the substrate and/or dielectric coupled to a buried nanotube and investigate influence of the bulk dispersion and dimensionality on spin relaxation for an electron confined in a carbon nanotube quantum dot. \\[4pt] [1] D. V. Bulaev, B. Trauzettel, D. Loss, Phys. Rev. B 77 235301 (2008).\\[0pt] [2] B. Bezanson and X. Hu, in preparation.\\[0pt] [3] H. O. H. Churchill et al, Phys. Rev. Lett. 102, 166802 (2009)   

Temperature Dependence of Electron Spin Dynamics in Oxygen-Free Single-Walled Carbon Nanotubes

Using electron spin resonance (ESR), we have measured the spin susceptibility and coherence time of electron spins in bulk powder single-walled carbon nanotubes (SWNTs) before and after removing oxygen via annealing. Removal of oxygen resulted in an increase of the spin susceptibility by roughly two orders of magnitude. In addition, the spin susceptibility was found to increase with decreasing temperature, both in the as-prepared and oxygen-free SWNTs, indicating localization at low temperatures. However, the temperature dependence does not exhibit a standard Curie law (i.e., a $\frac{1}{T}$ trend); deviation from this behavior may be due to strong electron-electron correlations. Furthermore, through the temperature dependence of the ESR lineshape, linewidth, and conductivity, we demonstrate quasi-one-dimensional variable range hopping between nanotubes in the oxygen-free sample. Specifically, the hopping conduction produced a motional narrowing of the ESR linewidth at elevated temperatures, resulting in an estimated hopping frequency on the order of 100~GHz.   

Electron spin relaxation in carbon nanotubes: Dyakonov-Perel mechanism

The long standing problem of unaccountable short spin relaxation in carbon nanotubes (CNT) meets a disclosure in terms of curvature-mediated spin-orbital interaction that leads to spin fluctuating precession analogous to Dyakonov-Perel mechanism. Strong anisotropy imposed by arbitrary directed magnetic field has been taken into account in terms of extended Bloch equations. Especially, stationary spin current through CNT can be controlled by spin-flip processes with relaxation time as less as 150 ps, the rate of transversal polarization (i.e. decoherence) runs up to 1/(70 ps) at room temperature while spin interference of the electrons related to different valleys can be responsible for shorter spin dephasing. Dependencies of spin-relaxation parameters on magnetic field strength and orientation, CNT curvature and chirality have been analyzed.