Electron Spin Components Research Articles

NMR Shift and Relaxation and the Electronic Spin of Superconducting Cuprates

Very recently, by inspecting large sets of data across all families of superconducting cuprates, it became obvious that the prevailing nuclear magnetic resonance (NMR) interpretation of cuprate properties is not adequate, as it does not account for the differences between the families, as well as common characteristics beyond simple temperature dependence. From the most abundant planar Cu shift data, one concludes readily on two electronic spin components with different doping and temperature dependencies. Their uniform response that causes NMR spin shifts consists of a doping-dependent component due to planar O, and another due to spin in the planar copper 3d(x2 − y2) orbital, where the latter points opposite the field direction. Planar Cu relaxation was found to be rather ubiquitous (except for La2−xSrxCuO4), and Fermi liquid-like, i.e., independent of doping and material, apart from the sudden drop at the superconducting transition temperature, Tc. Only the relaxation anisotropy is doping and material dependent. We showed previously that one can understand the shifts within a two-component scenario, but we failed with a model to account for the relaxation. Here, we suggest a slightly different shift scenario, still based on the two components, by introducing different hyperfine couplings, and, importantly, we are able to account for the Cu nuclear relaxation and its anisotropy for all materials, including also La2−xSrxCuO4. The results represent a solid framework for theory.

Properties of the Electronic Fluid of Superconducting Cuprates from 63Cu NMR Shift and Relaxation

Nuclear magnetic resonance (NMR) provides local, bulk information about the electronic properties of materials, and it has been influential for theories of high-temperature superconducting cuprates. NMR reported early that nuclear relaxation is much faster than what one expects from coupling to fermionic excitations above the critical temperature for superconductivity (Tc), i.e., what one estimates from the Knight shift with the Korringa law. As a consequence, special electronic spin fluctuations have been invoked. Here, based on literature relaxation data, it is shown that the electronic excitations, to which the nuclei couple with a material and doping-dependent anisotropy, are rather ubiquitous and Fermi liquid-like, i.e., they are only affected by Tc not the pseudogap. A suppressed NMR spin shift rather than an enhanced relaxation leads to the failure of the Korringa law for most materials. Shift and relaxation below Tc support the view of suppressed shifts, as well. A simple model of two coupled electronic spin components, one with 3d(x2 − y2) orbital symmetry and the other with an isotropic s-like interaction, can explain the data. The coupling between the two components is found to be negative, and it must be related to the pseudogap behavior of the cuprates. We can also explain the negative shift conundrum and the long-standing orbital shift discrepancy for NMR in the cuprates.

Interplay of Electron and Nuclear Spin Noise in n-Type GaAs.

We present spin-noise spectroscopy measurements on an ensemble of donor-bound electrons in ultrapure GaAs:Si covering temporal dynamics over 6 orders of magnitude from milliseconds to nanoseconds. The spin-noise spectra detected at the donor-bound exciton transition show the multifaceted dynamical regime of the ubiquitous mutual electron and nuclear spin interaction typical for III-V-based semiconductor systems. The experiment distinctly reveals the finite Overhauser shift of an electron spin precession at zero external magnetic field and a second contribution around zero frequency stemming from the electron spin components parallel to the nuclear spin fluctuations. Moreover, at very low frequencies, features related with time-dependent nuclear spin fluctuations are clearly resolved making it possible to study the intricate nuclear spin dynamics at zero and low magnetic fields. The findings are in agreement with the developed model of electron and nuclear spin noise.

Ultrafast spin dynamics in II-VI diluted magnetic semiconductors with spin-orbit interaction

We study theoretically the ultrafast spin dynamics of II-VI diluted magnetic semiconductors in the presence of spin-orbit interaction. Our goal is to explore the interplay or competition between the exchange $sd$-coupling and the spin-orbit interaction in both bulk and quantum well systems. For bulk materials we concentrate on Zn$_{1-x}$Mn$_x$Se and take into account the Dresselhaus interaction, while for quantum wells we examine Hg$_{1-x-y}$Mn$_x$Cd$_y$Te systems with a strong Rashba coupling. Our calculations were performed with a recently developed formalism which incorporates electronic correlations beyond mean-field theory originated from the exchange $sd$-coupling. For both bulk and quasi-two-dimensional systems we find that, by varying the system parameters within realistic ranges, both interactions can be chosen to play a dominant role or to compete on an equal footing with each other. The most notable effect of the spin-orbit interaction in both types of systems is the appearance of strong oscillations where the exchange $sd$-coupling by itself only causes an exponential decay of the mean electronic spin components. The mean-field approximation is also studied and it is interpreted analytically why it shows a strong suppression of the spin-orbit-induced dephasing of the spin component parallel to the Mn magnetic field.

Electron-phonon correlations on spin texture of gapped helical Dirac fermions

The metallic surface states of a topological insulator support helical Dirac fermions protected by topology with their spin locked perpendicular to their momentum. They can acquire mass through magnetic doping or through hybridization of states on opposite faces of a thin sample. In this case there can be a component of electron spin oriented perpendicular to the surface plane. The electron-phonon interaction renormalizes the dynamics of the charge carriers through their spectral density. It also modifies the gap channel and a second spectral function enters which, not only determines the out of plane spin component, but also comes into in-plane properties. While the out of plane spin component is decreased below the Fermi momentum ($k_F$), the in plane component increases. There are also correlation tails extending well beyond $k_F$. The angular resolved photo-emission line shapes aquire Holstein side bands. The effective gap in the density of states is reduced and the optical conductivity aquires distinct measurable phonon structure even for modest value of the electron-phonon coupling.

The Ising version of the t–J model

The t–J model is analysed in the limit of strong anisotropy, where the transverse components of electron spin are neglected. We propose a slave-particle-type approach that is valid, in contradiction to many of the standard approaches, in the low-doping regime and becomes exact for a half-filled system. We describe an effective method that allows to numerically study the system with the no-double-occupancy constraint rigorously taken into account at each lattice site. Then, we use this approach to demonstrate the destruction of the antiferromagnetic order by increasing the doping and formation of Nagaoka polarons in the strong interaction regime.

High-Resolution Solid-State Oxygen-17 NMR of Actinide-Bearing Compounds: An Insight into the 5f Chemistry

A massive interest has been generated lately by the improvement of solid-state magic-angle spinning (MAS) NMR methods for the study of a broad range of paramagnetic organic and inorganic materials. The open-shell cations at the origin of this paramagnetism can be metals, transition metals, or rare-earth elements. Actinide-bearing compounds and their 5f unpaired electrons remain elusive in this intensive research area due to their well-known high radiotoxicity. A dedicated effort enabling the handling of these highly radioactive materials now allows their analysis using high-resolution MAS NMR (>55 kHz). Here, the study of the local structure of a series of actinide dioxides, namely, ThO2, UO2, NpO2, PuO2, and AmO2, using solid-state (17)O MAS NMR is reported. An important increase of the spectral resolution is found due to the removal of the dipolar broadening proving the efficiency of this technique for structural analysis. The NMR parameters in these systems with numerous and unpaired 5f electrons were interpreted using an empirical approach. Single-ion model calculations were performed for the first time to determine the z component of electron spin on each of the actinide atoms, which is proportional to the shifts. A similar variation thereof was observed only for the heavier actinides of this study.

Electron spin decoherence in diluted magnetic quantum wells

We study electron-spin dynamics in diluted magnetic quantum wells. The electrons are coupled by exchange interaction with randomly distributed magnetic ions polarized by magnetic field $\mathbf{B}$. This coupling leads to both spin relaxation and spin decoherence. We demonstrate that even very small spatial fluctuations of quantum well width dramatically increase rate of decoherence. Depending on the strength of exchange interaction and the amplitude of the fluctuations the decoherence can be homogeneous or inhomogeneous. In the homogeneous regime, the transverse (with respect to $\mathbf{B}$) component of electron spin decays on the short time scale exponentially while the long-time spin dynamics obeys a power law. In the inhomogeneous case, the transverse spin component decays exponentially with the exponent quadratic in time.

Multiband [formula omitted] Riccati equation for electronic structure and transport in type-II heterostructures

An alternative method is proposed and implemented to calculate electronic structure and quantum transport properties of type-II heterojunctions. By deriving a multiband k·p Riccati equation for the envelope function matrix, it is shown how to obtain the reflection matrix through a simple numerical integration of the Riccati equation. Numerical instability, which is usually associated with type-II systems due to the simultaneous presence propagating and evanescent states, is avoided by working with the logarithmic derivative of the envelope function matrix.The theory is implemented numerically for a 6-band k·p matrix Hamiltonian in which the electron spin components have been decoupled. Preliminary results are presented for InAs/GaSb/InAs quantum wells. First, the calculated transmission versus energy curves are compared to those obtained from the microscopic empirical pseudo-potential calculation of Edwards and Inkson [Semicond. Sci. Technol. 9 (1994) 178]. For GaSb layer widths of 18, 55 and 152Å, the transmission spectra agree almost exactly. Minor discrepancies are discussed. Second, the net current density is calculated at room temperature as a function of applied voltage. For a GaSb layer width of 74Å, the self-consistently calculated net current density and peak-to-valley ratios are found to be in semi-quantitative agreement with the experiment of Yu et al. [Appl. Phys. Lett. 57 (1990) 2675].Other than its applications to electron tunneling, which can include spin-dependent tunneling (spintronics), the theory may also be applied to emerging field of multi-channel inverse scattering; in which desired transmission or reflection properties are used as input for designing heterostructure potential profiles.

Electronic relaxation of paramagnetic metal ions and NMR relaxivity in solution: Critical analysis of various approaches and application to a Gd(III)-based contrast agent

The time correlation functions (TCFs) G(alphaalpha(t)[triple bond](Salpha(t)Salpha(0)) (alpha = x,y,z) of the electronic spin components of a complexed paramagnetic metal ion give information about the time fluctuations of its zero-field splitting (ZFS) Hamiltonian due to the random dynamics of the coordination polyhedron. These TCFs reflect the electronic spin relaxation which plays an essential role in the inner- and outer-sphere paramagnetic relaxation enhancements of the various nuclear spins in solution. When a static ZFS Hamiltonian is allowed by symmetry, its modulation by the random rotational motion of the complex has a great influence on the TCFs. We discuss several attempts to describe this mechanism and show that subtle mathematical pitfalls should be avoided in order to obtain a theoretical framework, within which reliable adjustable parameters can be fitted through the interpretation of nuclear-magnetic relaxation dispersion experimental results. We underline the advantage of the numerical simulation of the TCFs, which avoids the above difficulties and allows one to include the effect of the transient ZFS for all the relative magnitudes of the various terms in the electron-spin Hamiltonian and arbitrary correlation times. This method is applied for various values of the magnetic field taken to be along the z direction. At low field, contrary to previous theoretical expectations, if the transient ZFS has negligible influence, the longitudinal TCF GII(t) [triple bond] G(zz)(t) has a monoexponential decay with an electronic relaxation time T1e different from 1/(2D(r)), D(r) being the rotational diffusion coefficient of the complex. At intermediate and high field, the simulation results show that GII (t) still has a monoexponential decay with a characteristic time T1e, which is surprisingly well approximated by a simple analytical expression derived from the Redfield perturbation approximation of the time-independent Zeeman Hamiltonian, even in the case of a strong ZFS where this approximation is expected to fail. These results are illustrated for spins S = 1, 3/2, and 5/2 in axial and rhombic symmetries. Finally, the simulation method is applied to the reinterpretation of the water-proton relaxivity profile due to P760-Gd(III), an efficient blood pool contrast agent for magnetic-resonance imaging.

Nuclear hyperfine structure in the X3Σ + state of 91ZrC

Electronic band systems of zirconium monocarbide, ZrC, in the 16 000–19 000 cm −1 region have been observed following the reaction of laser-ablated Zr atoms with methane under supersonic free-jet conditions. Rotational analyses of high-resolution spectra have shown that the ground state of ZrC is a 3Σ state, with r 0=1.8066 Å and an unexpectedly small spin–spin parameter, λ=0.5139 cm −1. The spectra are dense because of the five naturally occurring isotopes of Zr. Four of these, with mass numbers 90, 92, 94, and 96, have I=0, but the fifth, 91Zr, present in 11.22% abundance, has I=5/2. Lines of 91ZrC can be assigned in some of the strongest bands, and are found to display sizeable hyperfine splittings, with widths of up to 0.2 cm −1. Analysis shows that the largest hyperfine effects are in the ground state, where b=−0.03133±0.00015 cm −1 and c=−0.00123±0.00037 cm −1 (3 σ error limits). The large Fermi contact parameter, b, indicates that an unpaired Zr 5 sσ electron is present, which, taken together with the small value of λ, means that the ground state must be a 3Σ + state, from the electron configuration (Zr 5 sσ) 1 (C 2 pσ) 1. Internal hyperfine perturbations occur between the F 1 and F 3 electron spin components of the ground state in the range N=2–4, producing extra lines in some of the branches; the perturbations are of the type Δ N=0, Δ J=±2, and are a second-order effect arising because the F 1 ( J= N+1) and F 3 ( J= N−1) spin components both interact with the F 2 ( J= N) component through Δ N=0, Δ J=±1 matrix elements of the Fermi contact operator. Second-order perturbations of this type can only occur in states that are very close to case ( b) coupling.

A general approach to the electronic spin relaxation of Gd(III) complexes in solutions. Monte Carlo simulations beyond the Redfield limit

The time correlation functions of the electronic spin components of a metal ion without orbital degeneracy in solution are computed. The approach is based on the numerical solution of the time-dependent Schrödinger equation for a stochastic perturbing Hamiltonian which is simulated by a Monte Carlo algorithm using discrete time steps. The perturbing Hamiltonian is quite general, including the superposition of both the static mean crystal field contribution in the molecular frame and the usual transient ligand field term. The Hamiltonian of the static crystal field can involve the terms of all orders, which are invariant under the local group of the average geometry of the complex. In the laboratory frame, the random rotation of the complex is the only source of modulation of this Hamiltonian, whereas an additional Ornstein–Uhlenbeck process is needed to describe the time fluctuations of the Hamiltonian of the transient crystal field. A numerical procedure for computing the electronic paramagnetic resonance (EPR) spectra is proposed and discussed. For the [Gd(H2O)8]3+ octa-aqua ion and the [Gd(DOTA)(H2O)]− complex [DOTA=1,4,7,10-tetrakis(carboxymethyl)-1,4,7,10-tetraazacyclo dodecane] in water, the predictions of the Redfield relaxation theory are compared with those of the Monte Carlo approach. The Redfield approximation is shown to be accurate for all temperatures and for electronic resonance frequencies at and above X-band, justifying the previous interpretations of EPR spectra. At lower frequencies the transverse and longitudinal relaxation functions derived from the Redfield approximation display significantly faster decays than the corresponding simulated functions. The practical interest of this simulation approach is underlined.

Far-Infrared Rotational Spectra of ZnH and ZnD in theX2Σ+(v= 0) State

Several rotational transitions of zinc hydride and deuteride within thev= 0 level of theX2Σ+state have been measured in both electron spin components over the rangesN″ = 2 to 10 for ZnH andN″ = 9 to 21 for ZnD. A least-squares fit to these data in combination with low-Nmicrowave data measured by other workers has resulted in improved values of the rotational, fine, and hyperfine structure constants. The values of the proton hyperfine constants are discussed in the context of a molecular orbital analysis of zinc hydride.

Reanalysis and extension of the MnH A7Π- X7Σ + (0, 0) band: Fine structure and hyperfine-induced rotational branches

The A 7Π- X 7Σ + (0, 0) band of MnH at 568 nm has been recorded by laser fluorescence excitation spectroscopy. The original rotational analysis of Nevin [ Proc. R. Irish Acad. 48A, 1–45 (1942); 50A, 123–137 (1945)] has been extended with some corrections at low J. Systematic internal hyperfine perturbations in the X 7Σ + state, caused by the Δ N = 0, Δ J = ±1 matrix elements of the 55Mn hyperfine term in the Hamiltonian, have been observed in all seven electron spin components over the entire range of N″ studied. These perturbations destroy the “goodness” of J″ as a quantum number, giving rise to hyperfine-induced Δ J = ±2 rotational branches and to observable energy shifts of the most severely affected levels. The A 7Π state, with A = 40.5 cm −1 and B = 6.35 cm −1, evolves rapidly from Hund's case ( a) to case ( b) coupling, which produces anomalous branch patterns at low J. A total of 156 rotational branches have been identified and fitted by least squares to an effective Hamiltonian, providing precise values for the rotational and fine structure constants. Values of the principal constants determined in the fit are (1σ errors in units of the last digit are listed in parentheses): The fine structures of the A 7Π and X 7Σ + states confirm the assignment of the A ← X transition as Mn 4 pπ ← 4 sσ in the presence of a spectator, nonbonding Mn 3 d 5 ( 6 S) open core.

Elucidation of electronic structure by the analysis of hyperfine interactions: The MnH A 7Π–X 7Σ+ (0,0) band

We present a complete analysis of the hyperfine structure of the MnH A 7Π–X 7Σ+ (0,0) band near 5680 Å, studied with sub-Doppler resolution by intermodulated fluorescence spectroscopy. Magnetic hyperfine interactions involving both the 55Mn (I=5/2) and 1H (I=1/2) nuclear spins are observed as well as 55Mn electric quadrupole effects. The manganese Fermi contact interaction in the X 7Σ+ state is the dominant contributor to the observed hyperfine splittings; the ΔF=0, ΔN=0, ΔJ=±1 matrix elements of this interaction mix the electron spin components of the ground state quite strongly at low N, destroying the ‘‘goodness’’ of J as a quantum number and inducing rotationally forbidden, ΔJ=±2 and ±3 transitions. The hyperfine splittings of over 50 rotational transitions covering all 7 spin components of both states were analyzed and fitted by least squares, allowing the accurate determination of 14 different hyperfine parameters. Using single electronic configurations to describe the A 7Π and X 7Σ+ states and Herman–Skillman atomic radial wave functions to represent the molecular orbitals, we calculated a priori values for the 55Mn and 1H hyperfine parameters which agree closely with experiment. We show that the five high-spin coupled Mn 3d electrons do not contribute to the manganese hyperfine structure but are responsible for the observed proton magnetic dipolar couplings. Furthermore, the results suggest that the Mn 3d electrons are not significantly involved in bonding and demonstrate that the molecular hyperfine interactions may be quantitatively understood using simple physical interpretations.

Anomalous structure in the A 6Σ +-X 6Σ + transition of MnO caused by interference between two internal hyperfine perturbations

Sub-Doppler spectra of the A 6Σ +-X 6Σ + electronic transition of gaseous MnO are reported. It is found that both electronic states contain “internal hyperfine perturbations” where the hyperfine levels of different electron spin components interact through matrix elements of the hyperfine Hamiltonian off-diagonal in the quantum number J. The ν=0 level of the A 6Σ + state is severely perturbed by another electronic state so that its internal hyperfine perturbations are overwhelmed; in consequence the A-X (0, 0) band shows a characteristic pattern of line doublings, resulting from the internal perturbations of the X 6Σ + state alone. The A 6Σ +, ν=1 level is less perturbed than the ν=0 level, so that the A-X (1, 0) band shows the effects of the internal perturbations in both electronic states. By chance, these occur at corresponding places in the level structure, between the F 3 and F 4 electron spin components. Since the correspondence is fairly exact, the effects of the two internal perturbations partly cancel. No extra lines are induced, even though the hyperfine patterns are highly anomalous. Detailed calculations of the hyperfine line strengths confirm that the extra lines should be vanishingly weak in this case. The criteria for the appearance of internal hyperfine perturbations, and their value, are discussed.

Cytochrome electron spin resonance line shapes, ligand fields, and components stoichiometry in ubiquinol-cytochrome c oxidoreductase.

The EPR spectra of the cytochromes in ubiquinol-cytochrome c oxidoreductase (Complex III) have peaks at g = 3.78 (cytochrome b566) g = 3.45 (cytochrome b562) and g = 3.35 (cytochrome c1). The highly asymmetric peak of cytochrome b566 has been simulated using an arbitrary gaussian distribution of crystal field parameters. The asymmetry is due to the nonlinear relationship between field position and crystal field. The results suggest that the b cytochromes have bis-imidazole ligation. The gz peak of cytochrome c1 was also found to be asymmetric; simulations suggest histidine-methionine ligation. No other important cytochrome components were needed to simulate the spectrum of the oxidized complex; these results are consistent with 1:1:1 stoichiometry of components. These results argue against any asymmetric dimer model for Complex III.

Laser spectroscopy of VO: Analysis of the rotational and hyperfine structure of the C4Σ −- X4Σ − (0, 0) band

The (0, 0) band of the C 4Σ −- X 4Σ − electronic transition of VO was recorded by intermodulated laser-induced fluorescence at a resolution of about 100 MHz over the range 17 300–17 427 cm −1. The hyperfine structure caused by the 51V nucleus ( I = 7 2 ) is almost completely resolved, and provides good examples of case ( b βJ ) coupling in both electronic states. Internal hyperfine perturbations between the F 2 and F 3 electron spin components (where N = J − 1 2 and J + 1 2 , respectively) occur in both electronic states; these are caused by hyperfine matrix elements of the type Δ J = ±1, and induce hundreds of extra hyperfine lines which permit the courses of the electron spin and hyperfine levels to be followed in detail. In the band center observations of Q lines, center dips and transitions with Δ F ≠ Δ J have allowed the hyperfine and electron spin constants for the two electronic states to be determined separately despite the parallel polarization of the electronic transition. Numerous local electronic-rotational perturbations occur in the C 4Σ − state, which have required that the line positions be corrected for their effects before meaningful centrifugal distortion constants could be obtained. The C 4Σ − state also suffers from large spin-orbit perturbations by distant electronic states, for which it has been necessary to introduce a second spin-rotation parameter, γ S , following the formalism of Brown and Milton. The corresponding isotropic hyperfine parameter b S is also required. Both γ S and b S result from third-order cross-terms involving the spin-orbit interaction; given sufficient resolution they are always needed in a full description of electronic states of quartet and higher multiplicity.

Resolved hyperfine structure in the C–X electronic transition of VO. An internal hyperfine perturbation in the C4Σ− state

New grating and laser excitation spectra of VO show resolved nuclear hyperfine structure in the lines of the F1 and F4 electron spin components in the C4Σ−–X4Σ−electronic transition. It is shown that the C4Σ− state has a sizeable hyperfine structure, with the Fermi contact parameter bF (the coefficient of I∙S in the magnetic hyperfine Hamiltonian) equal to −0.00773 cm−1. Another internal hyperfine perturbation, of the type described by Richards and Barrow for the ground state, occurs in the C4Σ−state near N = 5; the line doublings are consistent with the Fermi contact parameter derived from the F1 and F4 lines.

Rotational and hyperfine structure in the A6Σ+–X6Σ+ electronic transition of MnO

The (0,0), (0,1), and (1,0) bands of the A6Σ+–X6Σ+ transition of MnO near 5500 Å have been photographed at high dispersion, and partial rotational analyses carried out. The spectrum is unusually complicated because of the high electron multiplicity, the manganese hyperfine structure, and extensive rotational perturbations. It is found that hyperfine perturbations frequently accompany the rotational perturbations. These are a new type of perturbation, resulting from a mixing of the F3 and F4 electron spin components in the upper state through hyperfine matrix elements of the type ΔN = 0, ΔJ ± 1, ΔF = 0 as a result of rotational perturbations. Extra lines, obeying the selection rules ΔJ = 0, ± 2, are induced: these give the energy separations of the F3 and F4 electron spin components of the ground state. As a result it has been possible to determine the electron spin fine structure parameters for the two states despite the parallel polarization of the electronic transition. The reason for the great complexity of the A6Σ+ ν = 0 level is the occurrence of a large avoided crossing near N = 26 with a level which is possibly a highly excited vibrational level of the ground state. The ground state Mn—O bond length is r0 = 1.6477 Å, and ΔG1/2(X6Σ+) = 832.41 cm−1.