Time-dependent Spin Research Articles

Correlation effects and the high-frequency spin susceptibility of an electron liquid: Exact limits

Spin correlations in an interacting electron liquid are studied in the high-frequency limit and in both two and three dimensions. The third-moment sum rule is evaluated and is used to derive exact limiting forms (at both long and short wavelengths) for the spin-antisymmetric local-field factor, ${limop}_{\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\omega}}\ensuremath{\infty}}{G}_{\ensuremath{-}}(\mathbf{q},\ensuremath{\omega}).$ In two dimensions ${limop}_{\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\omega}}\ensuremath{\infty}}{G}_{\ensuremath{-}}(\mathbf{q},\ensuremath{\omega})$ is found to diverge as $1/q$ at long wavelengths, and the spin-antisymmetric exchange-correlation kernel of time-dependent spin density functional theory diverges as ${1/q}^{2}$ in both two and three dimensions. These signal a failure of the local-density approximation, one that can be redressed by alternative approaches.

Time-dependent spin interaction and switching in quantum dot molecule under the adiabatic approximation

We study a two-electron quantum dot molecule subjected to an uniform magnetic field and in a time-dependent electric field under the adiabatic approximation. The time-dependent spin exchange energy J( t) provides a possible realization for logic gates in quantum computer. Switching between the states is best achieved by the time. As the exchange coupling is tuned by changing the time-dependent electric field, thermal or other types of fluctuations in the experimental environment of system will lead to fluctuations in the exchange, thus causing error in the exchange-based swap gate, which is crucial for two qubit operations. We study the fluctuation effects on the exchange.

On Lagrangian stochastic modelling of material transport in oceanic gyres

The introduction of ‘spin’ into second-order Lagrangian stochastic models (LSM) for stationary turbulence with broken reflectional symmetry is shown to result in the prediction of super-diffusive transport at intermediate times and the occurrence of anomalously large normal diffusion at later times. These characteristic features of material transport in oceanic gyres cannot be reproduced by two-dimensional first-order LSM. A correspondence is established between high-dimensional, low-order LSM and lower-dimensional, higher-order LSM. It is found that time-dependent spin statistics allow for the coexistence of rotating particle trajectories and non-oscillatory Lagrangian velocity autocorrelation functions.

Spin dynamics from time-dependent spin-density-functional theory.

We derive the spin-wave dynamics of a magnetic material from the time-dependent spin-density-functional theory in the linear response regime. The equation of motion for the magnetization includes, besides the static spin stiffness, a "Berry curvature" correction and a damping term. A gradient expansion scheme based on the homogeneous spin-polarized electron gas is proposed for the latter two quantities, and the first few coefficients of the expansion are calculated to second order in the Coulomb interaction.

New approach for the spectroscopy of an isolated hydrogen-like atom in semiconductors by μSR under laser irradiation

Recently, μSR under pulsed laser excitation has been developed at KEK-MSL. By applying this powerful new technique to the muonium (as an isolated hydrogen analog) in non-doped GaAs, significant changes in time-dependent longitudinal muon spin relaxation were observed. Muonium located around Ga–As bond center is established to be a recombination center. On the other hand, muonium at tetrahedral site in GaAs behaves as a spectator to photoexcited carrier at low temperature (∼90 K). Direct evidence was also obtained for the secondary propagation of the local excitation into the bulk by the photon recycling mechanism for the first time.

Spin picture of the one-dimensional Hubbard model: Two-fluid structure and phase dynamics

We propose a scheme for investigating the quantum dynamics of interacting electron models by means of a time-dependent variational principle and spin coherent states of space lattice operators. We apply such a scheme to the one-dimensional Hubbard model, and solve the resulting equations in different regimes. In particular, we find that at low densities the dynamics is mapped into two coupled nonlinear Schr\"odinger equations, whereas near half-filling the model is described by two coupled Josephson-junction arrays. Focusing then to the case in which only the phases of the spin variables are dynamically active, we examine a number of different solutions corresponding to the excitations of few macroscopic modes. Based on fixed-point equations of the simpler among them, we show that the standard one-band ground-state phase space is found.

Cold neutron spin interferometry and its application to modified spin echo methods

We propose three kinds of modified neutron spin echo methods using cold neutron spin interferometry, which is based on the coherent superposition principle of the neutron spin. Two kinds of the modified methods are based on a novel quantum precession of neutron spin by multilayer spin splitters and another method on time dependent spin interferometry using RF flippers. The performances of the last type are discussed and the firmer two methods are described in other proceedings.

Spin dynamics in Co/Pd multilayers by varying the number of repeats

The spin reversal of nanostructured Co/Pd multilayers by varying the number of repeats has been investigated quantitatively. The magnetization viscosity measurement and the direct observation of the time-dependent spin reversal patterns showed that their reversal behavior gradually changed from wall-motion dominant to nucleation dominant by increasing the number of repeats. Both the wall-motion speed V and the nucleation rate R of the samples were determined by a quantitative analysis of the time-dependent domain patterns. It was found that V was significantly decreased and R was increased by increasing the number of repeats, and the ratio of V/R was an important parameter of different spin reversal behavior.

Heteronuclear relaxation in time-dependent spin systems: (15)N-T1 (rho) dispersion during adiabatic fast passage.

A novel NMR experiment comprising adiabatic fast passage techniques for the measurement of heteronuclear self-relaxation rates in fully 15N-enriched proteins is described. Heteronuclear self-relaxation is monitored by performing adiabatic fast passage (AFP) experiments at variable adiabaticity (e.g., variation of RF spin-lock field intensity). The experiment encompasses gradient- selection and sensitivity-enhancement. It is shown that transverse relaxation rates derived with this method are in good agreement with the ones measured by the classical Carr-Purcell-Meiboom-Gill (CPMG) sequences. An application of this method to the study of the carboxyl-terminal LIM domain of quail cysteine and glycine-rich protein qCRP2(LIM2) is presented.

Paramagnetically induced nuclear magnetic resonance relaxation in solutions containing S⩾1 ions: A molecular-frame theoretical and physical model

The enhancement of nuclear magnetic resonance (NMR) relaxation rates produced by paramagnetic solutes is physically rather different for electron spin S=1/2 paramagnetic species than for S⩾1 species due to the presence of zero-field splitting interactions in the electron spin Hamiltonians of the latter. When the zfs energy is larger than the electronic Zeeman energy, the electron spin precessional motion is spatially quantized with respect to the molecule-fixed principal axis system (PAS) of the zfs tensor rather than along the external laboratory magnetic field. An analytical theory of the orthorhombic zfs limit has been derived in which the motion of the electron spin variables is described in the zfs-PAS and that of the nuclear spin variables in the laboratory coordinate frame. The resulting theoretical expressions are simple in form and suggest a physically transparent interpretation of the experiment. The NMR relaxation enhancement R1p results from additive contributions, R1x, R1y, and R1z, arising from the molecular-frame Cartesian components of the time-dependent electron spin magnetic moment operator μr(t). Each Cartesian component R1r depends on the dipolar power density at the nuclear Larmor frequency that is produced by the corresponding Cartesian component of μr(t). The theory displays the dependence of the relaxation enhancement on the variables of molecular structure in a very simple and physically transparent form: R1r∝r−6[1+P2(cos θr)], where r is the interspin distance and cos θr is the direction cosine of the interspin vector with the rth principal axis of the zfs tensor. New experimental data are presented for the model S=1 complex [trans-Ni(II)(acac)2(H2O)2] (acac=acetylacetonato) in dioxane solvent. The magnetic field dependence of the proton T1 of the axial water ligands has been measured over the range 0.15–1.5 T, the lower end of which corresponds to the zfs limit. The experimental data have been analyzed using the new analytical theory for the zfs-limit regime in conjunction with spin dynamics simulations in the intermediate regime. Dipolar density power plots are presented as graphical devices which clearly exhibit the physical information in the experiment, and which permit a rapid differentiation of the sensitive and insensitive parameters of theory. The data analysis depends strongly on the zfs parameter |E| and on the electron spin relaxation time τS,z along the zfs-PAS z-axis, but only very weakly on the other parameters of theory. A fit of the data to theory provided the values |E|=1.8±0.1 cm−1 and τS,z=8.0±0.3 ps.

Sum Rules for the spin surface response of metal clusters within the time dependent local spin density approximation

We study surface spin collective modes of simple metallic clusters using a sum rule approach. We derive analytical expressions for the energy and cubic energy-weighted moments of the time-dependent local-spin-density approximation (TDLSDA) strength function. With these two moments we obtain a mean excitation energy of multipole spin modes and study its dispersion with cluster size up to very large sizes. The crucial roles played by the surface diffuseness and by correlation and kinetic energy effects on the resonance energies are stressed.

Rotating-frame nuclear magnetic relaxation of spins diffusing on a disordered lattice: a Monte Carlo model

The rotating-frame nuclear magnetic relaxation rate of spins diffusing on a disordered lattice has been calculated by Monte Carlo methods. The disorder includes not only variation in the distances between neighbouring spin sites but also variation in the hopping rate associated with each site. The presence of the disorder, particularly the hopping rate disorder, causes changes in the time-dependent spin correlation functions which translate into asymmetry in the characteristic peak in the temperature dependence of the dipolar relaxation rate. The results may be used to deduce the average hopping rate from the relaxation but the effect is not sufficiently marked to enable the distribution of the hopping rates to be evaluated. The distribution, which is a measure of the degree of disorder, is the more interesting feature and it has been possible to show from the calculation that measurements of the relaxation rate as a function of the strength of the radiofrequency spin-locking magnetic field can lead to an evaluation of its width. Some experimental data on an amorphous metal - hydrogen alloy are reported which demonstrate the feasibility of this novel approach to rotating-frame relaxation in disordered materials.

Dynamic correlations of antiferromagnetic spin- XXZ chains at arbitrary temperature from complete diagonalization

All eigenstates and eigenvalues are determined for the spin- 1/2 $XXZ$ chain $H = 2J \sum_i ( S_{i}^{x} S_{i + 1}^{x} + S_{i}^{y} S_{i + 1}^{y} + \Delta S_i^z S_{i + 1}^{z})$ for rings with up to N=16 spins, for anisotropies $\Delta=0 , \cos(0.3\pi)$, and 1. The dynamic spin pair correlations $< S_{l+n}^{\mu}(t) S_l^{\mu} > , (\mu=x,z)$, the dynamic structure factors $S^{\mu}(q,\omega)$, and the intermediate structure factors $I^{\mu}(q,t)$ are calculated for arbitrary temperature T. It is found, that for all T, $S^{z}(q,\omega)$ is mainly concentrated on the region $|\omega| < \varepsilon_2(q)$, where $\varepsilon_2(q)$ is the upper boundary of the two-spinon continuum, although excited states corresponding to a much broader frequency spectrum contribute. This is also true for the Haldane-Shastry model and the frustrated Heisenberg model. The intermediate structure factors $I^{\mu}(q,t)$ for $\Delta \neq 0$ show exponential decay for high T and large q. Within the accessible time range, the time-dependent spin correlation functions do not display the long-time signatures of spin diffusion.

Dynamic Stability of Spinning Beams with an Unsymmetrical Cross-Section and Distinct Boundary Conditions Subjected to Time-Dependent Spin Speed*

ABSTRACT The equations of motion of a spinning beam with a rectangular cross-section are formulated using the Euler beam theory and the assumed mode method. The spin speed consists of steady-state and time-dependent portions. The resulting equations of motion are not in standard Mathieu-Hill's equation form, due to the time-dependent coefficient of the gyroscopic term. These equations of motion are then reduced to a set of first-order differential equations with time-dependent coefficients. The regions of instability due to parametric excitations are determined using the multiple scale method. Numerical results are presented for a spinning beam subjected to combinations of end conditions in the two orthogonal planes of transverse vibration. Widths of the unstable regions are found to decrease as the aspect ratio of the rectangular cross-section approaches unity for spinning beams with an identical set of end conditions in both transverse vibration planes.These regions vanish when the aspect ratio becomes one. However, this is not the case when the beam is subjected to distinct end conditions in the two planes. For a given aspect ratio, interesting changes in the unstable regions are observed as the spin speed varies within, as well as across, critical spin speed zones.

DYNAMIC STABILITY OF SPINNING TIMOSHENKO SHAFTS WITH A TIME-DEPENDENT SPIN RATE

The equation of motion of a spinning Timoshenko shaft with time-dependent spin rate are formulated using Hamilton's principle and the assumed mode method. The deformations of the shaft are expressed in terms of an inertial reference frame. The time-dependent spin rate is assumed to be a steady state average value superimposed by sinusoidal perturbations. The resulting governing equations of motion involve periodic coefficients, which are not in the form of standard Mathieu-Hill equations. The periodic functions are embedded in both the gyroscopic and stiffness coefficient matrices. By the use of the multiple scales method, the regions of instability due to parametric excitations are determined. Numerical results for a simply supported spinning shaft are presented.

Macroscopic and Microscopic Fields in High-Resolution Liquid NMR

The microscopic magnetic-induction field “seen by each nucleus” in a material medium and which is generated by a rapidly time-dependent spin magnetization gives rise to surprising new features in high-resolution nuclear magnetic resonance experiments. The purpose of the present paper is to show how the relations between the macroscopic average fields, the magnetization, and the microscopic fields (which were studied and clarified long ago at thermal equilibrium) can be extended to the present NMR context in which the magnetization can become rapidly time dependent and unrelated to thermal equilibrium properties.

Allowed Values of Ratios of the Rotational Diffusion Constants for a Radical with Four Equivalent I = 1/2 Nuclei

The ESR line widths of a radical (S = 1/2) with four equivalent I = 1/2 nuclei divided into two completely equivalent pairs can be used to obtain ratios of the elements of the rotational diffusion tensor when it is not possible to determine the individual tensor elements, Di. Two nuclei are equivalent if the zero-order spin Hamiltionian, H0, is invariant with respect to their interchange; the nuclei are completely equivalent if the time-dependent spin Hamiltonian responsible for the relaxation, H1(t), is also invariant with respect to their interchange. The anion radicals of para-disubstituted benzenes are examples of this type of spin equivalence; the ratio of the reorientational line width parameters C/B can be used to obtain a second degree equation that gives two values of ρx = Dx/Dz for a given ρy = Dy/Dz ≥ 0. The analysis of C/B for p-benzosemiquinone (PBSQ) in ethyl alcohol (EtOH) shows that one of the values of ρx is always positive while the other is always negative (and physically unacceptable)....

NMR of diffusing atoms in a periodic porous medium in the presence of a nonuniform magnetic field.

A detailed theory is developed for calculating the average time-dependent precessing nuclear spin of an atom diffusing through a porous medium in the presence of a nonuniform aligning field. An expansion in cumulant averages of the phase shift of the precessing spin is set up in terms of the diffusion propagator. For a periodic porous medium, a practical scheme of computation is exhibited which is based upon the diffusion eigenstates. This scheme is used to calculate the second and fourth order cumulants, both numerically and by asymptotic expansions for short and long precession times, when the field inhomogeneity is caused either by susceptibility differences between pore fluid and solid matrix or by an externally imposed field gradient. The results are used to calculate the diffusion effect on the transverse relaxation rate of spin polarization, and to discuss the validity of the Gaussian approximation for the distribution of phase shifts of the precessing spins. (c) 1995 The American Physical Society

Time-dependent critical spin fluctuations in magnetic salts

A short perspective of dynamic critical scattering is given, together with an orientation to modern theories of static and dynamic critical phenomena. The materials discussed are magnetic salts that are believed to spontaneously order through correlations induced by a Heisenberg exchange interaction between atomic spin moments.

Time-dependent optimized effective potential.

Given an expression for the quantum mechanical action of an N -electron system as a functional of N time-dependent spin orbitals, we present a method of constructing the variationally best local time-dependent single-particle potentials which, when inserted in time-dependent singleparticle Schrodinger equations for the spin-up and spin-down electrons yield orbitals that make stationary. We also propose a simplification of this scheme leading to a time-dependent generalization of the static optimized effective potentials recently introduced by Krieger, Li, and Iafrate [Phys. Lett. A 146, 256 (1990)]. Owing to rapid experimental progress in the field of laser physics, ultrashort laser pulses of very high intensity have become available in recent years. The electric field produced in such pulses can reach the strength of the electric field caused by atomic nuclei. If an atomic system is placed in the focus of such a laser pulse, one observes a wealth of new phenomena [1] which cannot be explained by perturbation theory. The nonperturbative quantum mechanical description of interacting particles moving in a very strong time-dependent external field therefore has become a prominent problem of theoretical physics. Since its rigorous foundation by Runge and Gross [2], time-dependent density functional theory (TDDFT) [3 ‐ 5] is available as a method to deal with time-dependent many-particle problems of this kind. The central statement of TDDFT is that the time-dependent density of a system of interacting particles moving in an external potential can be calculated, in principle exactly, from a set of time-dependent single-particle equations which can be viewed as the time-dependent counterpart of the Kohn-Sham scheme. These singleparticle equations involve an exchange-correlation potential, , which is a functional of and has to be approximated in practice. An extension of TDDFT to spin-polarized systems has been proposed by Liu and Vosko [6]. Neglecting magnetic effects associated with the orbital motion of the electrons, they consider external time-dependent potentials acting on electrons with spin only. In this case, two different corresponding to the two spin orientations are needed which are functionals of the spin densities . Again, the key problem is to obtain good approximations of . To date, only a rather crude adiabatic approximation is available which adopts the functional form of the static exchangecorrelation potential. The purpose of this paper is to introduce a different approach to the construction of