Spin-Orbit Qubits of Rare-Earth-Metal Ions in Axially Symmetric Crystal Fields

Contrary to the well known spin qubits, rare-earth qubits are characterized by a strong influence of crystal field due to large spin-orbit coupling. At low temperature and in the presence of resonance microwaves, it is the magnetic moment of the crystal-field ground-state which nutates (for several $\mu$s) and the Rabi frequency $\Omega_R$ is anisotropic. Here, we present a study of the variations of $\Omega_R(\vec{H}_{0})$ with the magnitude and direction of the static magnetic field $\vec{H_{0}}$ for the odd $^{167}$Er isotope in a single crystal CaWO$_4$:Er$^{3+}$. The hyperfine interactions split the $\Omega_R(\vec{H}_{0})$ curve into eight different curves which are fitted numerically and described analytically. These "spin-orbit qubits" should allow detailed studies of decoherence mechanisms which become relevant at high temperature and open new ways for qubit addressing using properly oriented magnetic fields

Decoherence window and electron-nuclear cross-relaxation in the molecular magnet V 15

Rabi oscillations in the V_15 Single Molecule Magnet (SMM) embedded in the surfactant DODA have been studied at different microwave powers. An intense damping peak is observed when the Rabi frequency Omega_R falls in the vicinity of the Larmor frequency of protons w_N, while the damping time t_R of oscillations reaches values 10 times shorter than the phase coherence time t_2 measured at the same temperature. The experiments are interpreted by the N-spin model showing that t_R is directly associated with the decoherence via electronic/nuclear spin cross-relaxation in the rotating reference frame. It is shown that this decoherence is accompanied with energy dissipation in the range of the Rabi frequencies w_N - sigma_e < Omega_R < w_N, where sigma_e is the mean super-hyperfine field (in frequency units) induced by protons at SMMs. Weaker damping without dissipation takes place outside this dissipation window. Simple local field estimations suggest that this rapid cross-relaxation in resonant microwave field observed for the first time in SMMV_15 should take place in other SMMs like Fe_8 and Mn_12 containing protons, too

Crossover from spin accumulation into interface states to spin injection in the germanium conduction band

Electrical spin injection into semiconductors paves the way for exploring new phenomena in the area of spin physics and new generations of spintronic devices. However the exact role of interface states in spin injection mechanism from a magnetic tunnel junction into a semiconductor is still under debate. In this letter, we demonstrate a clear transition from spin accumulation into interface states to spin injection in the conduction band of $n$-Ge. We observe spin signal amplification at low temperature due to spin accumulation into interface states followed by a clear transition towards spin injection in the conduction band from 200 K up to room temperature. In this regime, the spin signal is reduced down to a value compatible with spin diffusion model. More interestingly, we demonstrate in this regime a significant modulation of the spin signal by spin pumping generated by ferromagnetic resonance and also by applying a back-gate voltage which are clear manifestations of spin current and accumulation in the germanium conduction band.Comment: 5 pages, 4 figure

Spin-Orbit qubits of rare-Earth-Metal ions in axially symmetric crystal fields

Contrary to the well-known spin qubits, rare-earth-metal qubits are characterized by a strong influence of crystal field due to large spin-orbit coupling. At low temperature and in the presence of resonance microwaves, it is the magnetic moment of the crystal-field ground state which nutates (for several μs) and the Rabi frequency ΩR is anisotropic. Here, we present a study of the variations of ΩR(H→0) with the magnitude and direction of the static magnetic field H→0 for the odd Er167 isotope in a single crystal CaWO4:Er3+. The hyperfine interactions split the ΩR(H→0) curve into eight different curves which are fitted numerically and described analytically. These "spin-orbit qubits" should allow detailed studies of decoherence mechanisms which become relevant at high temperature and open new ways for qubit addressing using properly oriented magnetic fields. © 2009 The American Physical Society

Quantum simulations and experiments on Rabi oscillations of spin qubits: intrinsic {\sl vs} extrinsic damping

Electron Paramagnetic Resonance experiments show that the decay of Rabi oscillations of ensembles of spin qubits depends noticeably on the microwave power and more precisely on the Rabi frequency, an effect recently called "driven decoherence". By direct numerical solution of the time-dependent Schr\"odinger equation of the associated many-body system, we scrutinize the different mechanisms that may lead to this type of decoherence. Assuming the effects of dissipation to be negligible ($T_1=\infty$), it is shown that a system of dipolar-coupled spins with -- even weak-- random inhomogeneities is sufficient to explain the salient features of the experimental observations. Some experimental examples are given to illustrate the potential of the numerical simulation approach.Comment: Accepted for publication in Physical Review

Spin-pumping into surface states of topological insulator {\alpha}-Sn, spin to charge conversion at room temperature

We present experimental results on the conversion of a spin current into a charge current by spin pumping into the Dirac cone with helical spin polarization of the elemental topological insulator (TI) {\alpha}-Sn[1-3]. By angle-resolved photoelectron spectroscopy (ARPES) we first confirm that the Dirac cone at the surface of {\alpha}-Sn (0 0 1) layers subsists after covering with Ag. Then we show that resonant spin pumping at room temperature from Fe through Ag into {\alpha}-Sn layers induces a lateral charge current that can be ascribed to the Inverse Edelstein Effect[4-5]. Our observation of an Inverse Edelstein Effect length[5-6] much longer than for Rashba interfaces[5-10] demonstrates the potential of the TI for conversion between spin and charge in spintronic devices. By comparing our results with data on the relaxation time of TI free surface states from time-resolved ARPES, we can anticipate the ultimate potential of TI for spin to charge conversion and the conditions to reach it.Comment: 14 pages, 5 figure

Decoherence window and electron-nuclear cross relaxation in the molecular magnet V 15

Rabi oscillations in the V 15 single molecule magnet embedded in the surfactant (CH 3) 2[CH 3(CH 2) 16CH 2] 2N + have been studied at different microwave powers. An intense damping peak is observed when the Rabi frequency Ω R falls in the vicinity of the Larmor frequency of protons ω N. The experiments are interpreted by a model showing that the damping (or Rabi) time τ R is directly associated with decoherence caused by electron-nuclear cross relaxation in the rotating reference frame. This decoherence induces energy dissipation in the range ω N-σ e<Ω R<ω N, where σ e is the mean superhyperfine field induced by protons at V 15. Weaker decoherence without dissipation takes place outside this window. Specific estimations suggest that this rapid cross relaxation in a resonant microwave field, observed for the first time in V 15, should also take place, e.g., in Fe 8 and Mn 12. © 2012 American Physical Society

Am empirical comparison of the performance of classical power indices

Power indices are general measures of the relative voting power of individual members of a voting body. They are useful in helping understand and design voting bodies particularly those which employ weighted voting, in which different members having different numbers of votes. It is well known that in such bodies a member's voting power, in the sense of their capacity to affect the outcomes of votes called, rarely corresponds to the actual number of votes allocated to him. Many voting bodies for which this is an important consideration exist: examples include international organisations (notably the World Bank, the IMF, the European Union), the US presidential Electoral College and corporations in which votes are proportionate to stockholdings. Two classical power indices dominate the literature: the Shapley-Shubik index and the Banzhaf index (also known by other names). Both are based on the idea that a member's power depends on the relative number of times they can change a coalition from losing to winning by joining it and adding their vote. They may be defined in probabilistic terms as the probability of being able to swing the result of a vote, where all possible outcomes are taken as equiprobable. The indices differ however in the way they count voting coalitions. In probabilistic terms they use different coalition models and therefore differ in precisely what is meant by equiprobable outcomes. The indices have been used in a number of empirical applications but their relative performance has remained an open question for many years, a factor, which has hindered the wider acceptance of the approach. Where both the indices have been used for the same case, they have often given different results, sometimes substantially so, and theoretical studies of their properties have not been conclusive. There is therefore a need for comparative testing of their relative performance in practical contexts. Very little work of this type has been done however for a number of reasons: lack of independent indicators of power in actual voting bodies with which to compare them, difficulties in obtaining consistent data on a voting body over time with sufficient variation in the disposition of votes among members of actual legislatures and the lack of independent criteria against which the results of the indices may be judged. It has also been hampered to some extent by lack of easily available algorithms for computing the indices in large games. This paper assesses the indices against a set of reasonable criteria in terms of shareholder voting power and the control of the corporation in a large cross section of British companies. Each company is a separate voting body and there is much variation in the distribution of voting shares among them. Moreover reasonable criteria exist against which to judge the indices. New algorithms for the Shapley-Shubik and Banzhaf indices are applied to detailed data on beneficial ownership of 444 large UK companies without majority control. Because some of the data is missing, both finite and oceanic games of shareholder voting are studied to overcome this problem. The results, judged against these criteria, are unfavorable to the Shapley-Shubik index and suggest that the Banzhaf index much better reflects the variations in the power of shareholders between companies as the weights of shareholder blocks vary