Electron Spin Correlation Research Articles

Electron Spin Correlations: Probabilistic Description and Geometric Representation

The electron spin correlation is shown to be expressible in terms of a bona fide probability distribution function with an associated geometric representation. With this aim, an analysis is presented of the probabilistic features of the spin correlation within the quantum formalism, which helps clarify the concepts of contextuality and measurement dependence. The dependence of the spin correlation on conditional probabilities allows for a clear separation between system state and measurement context; the latter determines how the probability space should be partitioned in calculating the correlation. A probability distribution function is then proposed, which reproduces the quantum correlation for a pair of single-particle spin projections and is amenable to a simple geometric representation that gives meaning to the variable . The same procedure is shown to be applicable to the bipartite system in the singlet spin state. This endows the spin correlation with a clear probabilistic meaning and leaves the door open for a possible physical picture of the electron spin, as discussed at the end of the paper.

Superconducting-like and magnetic transitions in oxygen-implanted diamond-like and amorphous carbon films, and in highly oriented pyrolytic graphite

In our previously published work, we have reported colossal magnetoresistance, Andreev oscillations, ferromagnetism, and granular superconductivity in oxygen-implanted carbon fibers, graphite foils, and highly oriented pyrolytic graphite (HOPG). In this follow-up research, more results on these oxygen-implanted graphite samples are presented. We show results from transport measurements on oxygen-implanted diamond-like carbon thin coatings, amorphous carbon films, and HOPG. Significantly, a three-order magnitude drop in the electrical resistance of the oxygen-implanted diamond-like carbon films is observed at the 50 K temperature that we have previously reported for the transition to the superconducting state. Below 50 K, the films’ resistance oscillates between the high and low resistance states, less when the sample is under a transverse magnetic field. This metastability between the insulating and superconducting-like states possibly reflects the evolution of the amplitude for the superconducting order parameter also known as the longitudinal Higgs mode. Transitions to low resistance state and metastability are also observed for amorphous carbon films. Finally, the HOPG samples’ resistance have a thermally activated term that can be understood on the basis of the Langer–Ambegaokar–McCumber–Halperin model applied to narrow SC channels in which thermal fluctuations can cause phase slips. We also find that in oxygen-implanted carbon materials, the electron charge and spin correlations do not compete and their interplay rather facilitates the emergence of high-temperature superconductivity, and thus, additional unexpected effects like Heisenberg spin waves and magneto-structural transitions are observed.

Bottom-up nano-integration route for modified carbon nanotube spintronic device fabrication

This study is focused on a bottom-up nano-integration route for the production of carbon based spintronic devices. In order to enhance magnetic interactions along nanotube walls a controlled synthetic chemical technique is utilized, this method is based on a two-step method which firstly looks at the functionalization of nanotubes (carbonyl groups) and subsequently the attachment of an organo-metallic complex to the carbonyl group. The system is then characterized in bulk, including magnetometry analysis as well as transport at low temperatures. Mesoscopic electron-spin correlations have been observed as well as a clear crossover from superparamagnetism to weakly ferromagnetic depending on the functionalization technique. We then demonstrate a novel fabrication technique based on nano-integration utilizing a nano-tweezer created from a memory metal alloy. The devices envisioned include quantum rings, crossed junction as well as fine network structures that can be manipulated using nano-probes. As the carbon nanotubes have been functionalized with nanoscale magnetic molecules, such devices are interesting for novel spintronic applications.

Coherent transfer of electron spin correlations assisted by dephasing noise

Quantum coherence of superposed states, especially of entangled states, is indispensable for many quantum technologies. However, it is vulnerable to environmental noises, posing a fundamental challenge in solid-state systems including spin qubits. Here we show a scheme of entanglement engineering where pure dephasing assists the generation of quantum entanglement at distant sites in a chain of electron spins confined in semiconductor quantum dots. One party of an entangled spin pair, prepared at a single site, is transferred to the next site and then adiabatically swapped with a third spin using a transition across a multi-level avoided crossing. This process is accelerated by the noise-induced dephasing through a variant of the quantum Zeno effect, without sacrificing the coherence of the entangled state. Our finding brings insight into the spin dynamics in open quantum systems coupled to noisy environments, opening an avenue to quantum state manipulation utilizing decoherence effects.

Long-time coherence in fourth-order spin correlation functions

We study the long-time decay of fourth-order electron spin correlation functions for an isolated singly charged semi-conductor quantum dot. The electron spin dynamics is governed by the applied external magnetic field as well as the hyperfine interaction. While the long-time coherent oscillations in the correlation functions can be understood within an semi-classical approach treating the Overhauser field as frozen, the field dependent decay of its amplitude reported in different experiments cannot be explained by the central-spin model indicating the insufficiency of such a description. By incorporating the nuclear Zeeman splitting and the strain induced nuclear-electric quadrupolar interaction, we find the correct crossover from a fast decay in small magnetic fields to a slow exponential asymptotic in large magnetic fields. It originates from a competition between the quadrupolar interaction inducing an enhanced spin decay and the nuclear Zeeman term that suppressed the spin-flip processes. We are able to explain the magnetic field dependency of the characteristic long-time decay time $T_2$ depending on the experimental setups. The calculated asymptotic values of $T_2 = 3 -4\,\mu$s agree qualitatively well with the experimental data.

Ground state and low-energy magnetic dynamics in the frustrated magnetCoAl2O4as revealed by local spin probes

We report a combined experimental study of magnetic properties of a single crystal of the frustrated diamond lattice antiferromagnet ${\text{CoAl}}_{2}{\text{O}}_{4}$ with ${\text{Co}}^{2+}$ electron spin resonance, $^{27}\mathrm{Al}$ nuclear magnetic resonance, and muon spin rotation/relaxation techniques. With our local probes, we show that the frustration of spin interactions and the Co/Al site disorder strongly affect the spin dynamics. The experimental results evidence inhomogeneous and slow magnetic fluctuations and the occurrence of short-range electron spin correlations far above a characteristic temperature ${T}^{*}=8$ K at which the spin system turns into in a quasistatic state. Our data indicate that this spin order is likely short range and unconventional with spin fluctuations persistent even at $T\ensuremath{\ll}{T}^{*}$. The results of three spectroscopy techniques highlight a nontrivial role of structural disorder for the magnetism of a frustrated diamond spin lattice at the proximity to the critical point.

Effect of electronic correlations on magnetotransport through a parallel double quantum dot

We theoretically investigate the effects of electronic correlations (including spin and Coulomb correlations) on the magnetotransport through a parallel double quantum dot (DQD) coupled to ferromagnetic leads. Two dots couple coherently through electron correlations, rather than tunneling directly between two dots, and each dot is coupled to two semi-infinite ferromagnetic leads. We assume that the intradot Coulomb repulsion is much larger than the interdot Coulomb repulsion U. Thus, only the zero, one and two-particle DQD states are relevant to transport. Because of interdot electron correlation, the I-V characteristics of each dot is sensitive to the change in the state of the other dot. This work focuses on the effects of electron spin correlation and electron Coulomb correlation on magnetotransport through this system. In order to determine the transport properties of the system, we use the generalized master equation method. This method is based on the reduced density operator defined by averaging the statistical operator of the total system over the states of all leads. With the framework of the generalized master equation and the sequential tunneling approximation, we calculate the current, differential conductance and tunnel magnetoresistance (TMR) in the dot 1 as a function of bias for different spin correlations and Coulomb correlations. Our results reveal that the magnetotransport through this system is more sensitive to Coulomb correlation than to spin correlation; when Coulomb correlation equals zero, the spin correlation can induce a giant tunnel magnetoresistance, which is further larger than the Jullieres value of TMR; when Coulomb correlation occurs, the giant tunnel magnetoresistance disappears; when Coulomb correlation is equal to or larger than spin correlation, Coulomb correlation can suppress spin correlation; while the coexistence of Coulomb correlation and asymmetry of the DQD system can result in dynamical channel blockade, which can lead to the occurrence of negative tunnel magetoresistance and negative differential conductance. These novel properties lead to the potential applications in nanoelectronics, and relevant underlying physics of this problem is discussed.

Non-equilibrium STLS approach to transport properties of single impurity Anderson model

In this work, using the non-equilibrium Keldysh formalism, we study the effects of the electron–electron interaction and the electron-spin correlation on the non-equilibrium Kondo effect and the transport properties of the symmetric single impurity Anderson model (SIAM) at zero temperature by generalizing the self-consistent method of Singwi, Tosi, Land, and Sjolander (STLS) for a single-band tight-binding model with Hubbard type interaction to out of equilibrium steady-states. We at first determine in a self-consistent manner the non-equilibrium spin correlation function, the effective Hubbard interaction, and the double-occupancy at the impurity site. Then, using the non-equilibrium STLS spin polarization function in the non-equilibrium formalism of the iterative perturbation theory (IPT) of Yosida and Yamada, and Horvatic and Zlatic, we compute the spectral density, the current–voltage characteristics and the differential conductance as functions of the applied bias and the strength of on-site Hubbard interaction. We compare our spectral densities at zero bias with the results of numerical renormalization group (NRG) and depict the effects of the electron–electron interaction and electron-spin correlation at the impurity site on the aforementioned properties by comparing our numerical result with the order U2 IPT. Finally, we show that the obtained numerical results on the differential conductance have a quadratic universal scaling behavior and the resulting Kondo temperature shows an exponential behavior.

An improved semiclassical theory of radical pair recombination reactions

We present a practical semiclassical method for computing the electron spin dynamics of a radical in which the electron spin is hyperfine coupled to a large number of nuclear spins. This can be used to calculate the singlet and triplet survival probabilities and quantum yields of radical recombination reactions in the presence of magnetic fields. Our method differs from the early semiclassical theory of Schulten and Wolynes [J. Chem. Phys. 68, 3292 (1978)] in allowing each individual nuclear spin to precess around the electron spin, rather than assuming that the hyperfine coupling-weighted sum of nuclear spin vectors is fixed in space. The downside of removing this assumption is that one can no longer obtain a simple closed-form expression for the electron spin correlation tensor: our method requires a numerical calculation. However, the computational effort increases only linearly with the number of nuclear spins, rather than exponentially as in an exact quantum mechanical calculation. The method is therefore applicable to arbitrarily large radicals. Moreover, it approaches quantitative agreement with quantum mechanics as the number of nuclear spins increases and the environment of the electron spin becomes more complex, owing to the rapid quantum decoherence in complex systems. Unlike the Schulten-Wolynes theory, the present semiclassical theory predicts the correct long-time behaviour of the electron spin correlation tensor, and it therefore correctly captures the low magnetic field effect in the singlet yield of a radical recombination reaction with a slow recombination rate.

Double exchange model on triangular lattice: Non-coplanar spin configuration and phase transition near quarter filling

Unconventional anomalous Hall effect in frustrated pyrochlore oxides is originated from spin chirality of non-coplanar localized spins, which can also be induced by the competition between ferromagnetic (FM) double exchange interaction JH and antiferromagnetic superexchange interaction JAF. Here truncated polynomial expansion method and Monte Carlo simulation are adopted to investigate the above model on two-dimensional triangular lattice. We discuss the influence of the range of FM-type spin–spin correlation and strong electron–spin correlation on the truncation error of spin–spin correlation near quarter filling. Two peaks of the probability distribution of spin–spin correlation in non-coplanar spin configuration clearly show that non-coplanar spin configuration is an intermediate phase between FM and 120° spin phase. Near quarter filling, there is a phase transition from FM into non-coplanar and further into 120° spin phase when JAF continually increases. Finally the effect of temperature on the magnetic structure is discussed.

Magneto-optic studies of rare earth containing sodium silicate glasses and semiconductor quantum dots in glass composites: Nonlinear effects

Faraday rotation has been measured at room temperature and at magnetic field strengths up to 2.57T for II–VI type semi-conductor nano-crystals (CdS and CdSe) in the form of quantum dots (QDs) and for rare earth containing sodium silicate glasses. The graph of Faraday rotation versus field strength for all quantum dots showed “kinks” (abrupt slope changes) which is evidence for a non-linear Faraday effect. Given the inverse linearity seen in dot size versus magnetic field, possible causes such as exciton coulomb interactions were considered as a mechanism for the enhanced Faraday rotation. The rare earth containing glasses also showed a non-linearity in the Faraday rotation as a function of magnetic field strength. However, a single crystal NaCl sample exhibited no kinks up to 2.57T. Various mechanisms will be put forth and evaluated as to the feasibility of using these processes to explain the observed effects. We consider Landau levels, resonance effects, shape and piezo-electric effects, electron-spin correlation for the quantum dot composites; and intermediate range order (IRO) for the rare earth containing glass matrix itself and try to interpret how each of these mechanisms may or may not have an effect on the Faraday rotation behavior.

Doping Effect of Nb5+ on the Microstructure and Defects of LiFePO4

An Nb5+-doped cathodic material, Li1−xNbx+yFe1−yPO4, was synthesized via the high-temperature solid-state method. The crystal structure, micro-defects and doping ion occupancy of doped LiFePO4 have been studied via the Rietveld crystal structure refinement, HRTEM, EPR and positron annihilation lifetime spectroscopy (PALS) methods. The effect of ion doping on the electrochemical properties was studied by measuring the changes in the electronic localization and structural defects. The results of the Rietveld crystal structure refinement showed that Nb5+ occupied positions on both Li and Fe in [Li0.99−xNbx][Fe1−yNby]PO4, with an occupancy rate on Fe approximately six times greater than that in the Li position. The HRTEM results indicated that, when Nb5+ was doped into the lattice well, there were no other phases on the grain surface. Furthermore, the EPR results indicated that Nb5+ occupying the Fe position broke the Fe2+-O-Fe2+ electron spin correlation, which distorted the crystal ligand field around Fe2+. The PALS investigation showed that Nb5+ could be doped into the internal LiFePO4 lattice to produce cation vacancy defects. The internal defects and outer electron energy of the cations in the lattice were changed because of the Nb5+ doping, which could improve the electrochemical performance of the material.

Distinguishing Polymorphs of the Semiconducting Pigment Copper Phthalocyanine by Solid-State NMR and Raman Spectroscopy

Cu(II)(phthalocyanine) (CuPc) is broadly utilized as an archetypal molecular semiconductor and is the most widely used blue printing pigment. CuPc crystallizes in six different forms; the chemical and physical properties are substantially modulated by its molecular packing among these polymorphs. Despite the growing importance of this system, spectroscopic identification of different polymorphs for CuPc has posed difficulties. This study presents the first example of spectroscopic distinction of alpha- and beta-forms of CuPc, the most widely used polymorphs, by solid-state NMR (SSNMR) and Raman spectroscopy. (13)C high-resolution SSNMR spectra of alpha- and beta-CuPc using very-fast magic angle spinning (VFMAS) at 20 kHz show that hyperfine shifts sensitively reflect polymorphs of CuPc. The experimental results were confirmed by ab initio chemical shift calculations. (13)C and (1)H SSNMR relaxation times of alpha- and beta-CuPc under VFMAS also showed marked differences, presumably because of the difference in electronic spin correlation times in the two forms. Raman spectroscopy also provided another reliable method of differentiation between the two polymorphs.

Electron spin relaxation at low field

The low field ESR lineshape and the electron spin-lattice relaxation correlation function are calculated using the stochastic Liouville theory for an effective electron spin quantum number S = 1. When an axially symmetric permanent zero field splitting provides the dominant relaxation mechanism, and when it is much larger than the rotational diffusion constant, it is shown that both electron spin correlation functions S(0)S(t) (n = 0,1) are characterized by the same relaxation time tau(S) = (4D(R))(-1). This confirms the conjectures made by Schaefle and Sharp, J. Chem. Phys., 2004, 121, 5287 and by Fries and Belorizky, J. Chem. Phys., 2005, 123, 124510, based on numerical results using a different formalism. The stochastic Liouville approach also gives the paramagnetically enhanced nuclear spin relaxation time constants, T(1) and T(2), and the ESR lineshape function I(omega). In particular, the L-band (B(0) = 0.035 T) ESR spectrum of a low symmetry Ni(ii)-complex with a cylindrical ZFS tensor is shown to be detectable at sufficiently slowly reorientation of the complex. The analysis shows that the L-band spectrum becomes similar to the zero-field spectrum with a electron spin relaxation time tau(S) = (4D(R))(-1).

Electron-spin dephasing via hyperfine interaction in a quantum dot: An equation-of-motion calculation of electron-spin correlation functions

In this paper we develop an equation-of-motion (EOM) approach to study the non-Markovian single-electron-spin dynamics due to its inhomogeneous hyperfine coupling to the surrounding nuclei in a quantum dot. In particular, we identify an electron-spin correlation function that fully represents the electron-spin quantum coherence. Using the EOM method, we recover the exact solution of electron-spin decoherence for the case of a fully polarized nuclear reservoir. By considering nuclear-spin flip-flops mediated by virtual electron flips, which generate fluctuations in the Overhauser field (the nuclear field) for the electron spin, we find that the free-induction decay of the electron-spin correlation function for partially polarized and unpolarized nuclear-spin configurations is of the order unity instead of $O(1/N)$ ($N$ being the number of nuclei in the dot) obtained in previous studies. We show that the complete amplitude decay corresponds to the spectral broadening of the correlation function near the electron-spin Rabi frequency induced by nuclear-spin flip-flops. Our results show that a 90% nuclear-spin polarization can enhance the electron-spin coherence time by more than 1 order of magnitude. In the long-time limit, the envelope of the transverse electron-spin correlation function has a nonexponential $1/{t}^{2}$ decay in the presence of both polarized and unpolarized nuclei.

Kondo screening cloud in a one-dimensional wire: Numerical renormalization group study

We study the Kondo model --a magnetic impurity coupled to a one dimensional wire via exchange coupling-- by using Wilson's numerical renormalization group (NRG) technique. By applying an approach similar to which was used to compute the two impurity problem we managed to improve the bad spatial resolution of the numerical renormalization group method. In this way we have calculated the impurity spin - conduction electron spin correlation function which is a measure of the Kondo compensation cloud whose existence has been a long standing problem in solid state physics. We also present results on the temperature dependence of the Kondo correlations.

High Field NMR Study of Yb0.9Y0.1InCu4 up to 30 T

NMR measurements of 115 In in Yb 0.9 Y 0.1 InCu 4 were performed at 4.2 K up to 30 T with a hybrid magnet installed in National Institute for Materials Science (NIMS). Fourier-transformed (FT) spectrum at a constant magnetic field was obtained by summing a set of FT spectra with shifting the transient frequency. A first-order valence transition was observed at 22 T. Coexistence of the valence-fluctuating phase and the field-induced phase was confirmed. It was found that the proportion of the field-induced phase continues to increase even at 30 T. The effect of 4 f -electron spin correlations in the field-induced phase on the spin–spin relaxation time T 2 was discussed.

Analytical solution of electron spin decoherence through hyperfine interaction in a quantum dot

We analytically solve the non-Markovian single-electron spin dynamics due to hyperfine interaction with surrounding nuclei in a quantum dot. We use the equation-of-motion method assisted with a large field expansion, and find that virtual nuclear spin flip-flops mediated by the electron contribute significantly to a complete decoherence of the transverse electron spin correlation function. Our results show that a 90% nuclear polarization can enhance the electron spin time ${T}_{2}$ by almost two orders of magnitude. In the long time limit, the electron spin correlation function has a nonexponential $1∕{t}^{2}$ decay in the presence of both polarized and unpolarized nuclei.

Effects of electron-electron interaction and electron spin correlations on the exchange coupling in mesoscopic rings

Using the formalism of Lobo, Singwi, and Tosi (LST), we study the effect of electron-electron interaction and electron spin correlations on the indirect exchange interaction between two nuclear spins embedded in a mesoscopic metallic ring, threaded by an Aharonov-Bohm magnetic flux. We first calculate the spin local field correction and the spin-density response function of the ring in a self-consistent manner. Then, we employ the Ruderman-Kittel-Kasuga-Yosida (RKKY) theory to determine the variation of the exchange coupling as a function of the magnetic flux and the angular distance between the two nuclear spins. The LST approach predicts a reach behavior for the exchange coupling as a function of the magnetic flux. Our numerical results show that due to the electron-electron interaction and the electron spin-correlations the exchange coupling can change sign as a function of the magnetic flux, contrary to the prediction of the random phase approximation. Furthermore, the exchange coupling beside its usual oscillatory behavior acquires an oscillatory envelope which brings about strong RKKY interaction between the two nuclear spins even at far distances on the ring.

Magnetic versus non-magnetic doping effectsin the Haldane chain compound PbNi2V2O8

Study of an impurity-driven phase transition into a magnetically ordered state in the spin-liquid Haldane chain compound PbNi2V2O8 is presented. Both macroscopic magnetization as well as 15V nuclear magnetic resonance (NMR) measurements reveal that the magnetic nature of dopants has a crucial role in determining the stability of the induced long-range magnetic order. In the case of non-magnetic (Mg2+ doping at the Ni2+ sites (S = 1), a metamagnetic transition is observed in relatively low magnetic fields. On the other hand, the magnetic order in magnetically (Co2+) doped compounds survives at much higher magnetic fields and temperatures. We attribute this feature to a significant anisotropic impurity–host magnetic interaction. The NMR measurements confirm that the staggered magnetic moments liberated next to the impurity sites, are the reason for the magnetic ordering. In addition, differences in the broadening of NMR spectra and the increase of nuclear spin-lattice relaxation in doped samples indicate an impurity-dependent character for the dominant electron-spin correlations; the latter begin to develop at rather high temperatures with respect to the antiferromagnetic phase-transition temperature.