Fast and accurate algorithm for the simulation of NMR spectra of large spin systems

The computational cost for the simulation of NMR spectra grows exponentially with the number of nuclei. Today, the memory available to store the Hamiltonian limits the size of the system that can be studied. Modern computers enable to tackle systems containing up to 13 spins [1], which obviously does not allow to study most molecules of interest in research. This issue can be addressed by identifying groups of spins or fragments that are not or only weakly interacting together, i.e., that only share weakly coupled spin pairs. Such a fragmentation is only permitted in the weak coupling regime, i.e., when the coupling interaction is weak compared to the difference in chemical shift of the coupled spins. Here, we propose a procedure that removes weak coupling interactions in order to split the spin system efficiently and to correct a posteriori for the effect of the neglected couplings. This approach yields accurate spectra when the adequate interactions are removed, i.e., between spins only involved in weak coupling interactions, but fails otherwise. As a result, the computational time for the simulation of 1D spectra grows linearly with the size of the spin system.     

Polynomially scaling spin dynamics simulation algorithm based on adaptive state-space restriction

We report progress with an old problem in magnetic resonance -- that of the exponential scaling of simulation complexity with the number of spins. It is demonstrated below that a polynomially scaling algorithm can be obtained (and accurate simulations performed for over 200 coupled spins) if the dimension of the Liouville state space is reduced by excluding unimportant and unpopulated spin states. We found the class of such states to be surprisingly wide. It actually appears that a majority of states in large spin systems are not essential in magnetic resonance simulations and can safely be dropped from the state space. In restricted state spaces the spin dynamics simulations scale polynomially. In cases of favourable interaction topologies (sparse graphs, e.g. in protein NMR) the asymptotic scaling is linear, opening the way to direct fitting of molecular structures to experimental spectra.     

Decay of correlations in spin systems

We investigate the decay of initial correlations in a spin system where each spin relaxes independently by an intramolecular mechanism. The equation of motion for the spin density matrix is assumed to be the Redfield equation, which is of the form of a quantum mechanical master equation. Our analysis of this problem is based on the techniques of Shuler, Oppenheim, and coworkers, who have studied the decay of correlations in systems which can be described by classical stochastic master equations. We find that the off-diagonal elements of the reduced spin density matrices approach their equilibrium values faster than the diagonal elements. The Ursell functions, which are a measure of the correlations in the system, decay to their zero equilibrium values faster than the spin density matrix except for the furthest off-diagonal elements. Far off-diagonal matrix elements of the spin density matrix approach equilibrium at the same rate as the Ursell functions, which is the important difference between the quantum mechanical model studied here and the classical models studied earlier.Supported in part by the National Science Foundation.     

Self-consistent treatment of spin and magnetization dynamic effect in spin transfer switching

The effect of itinerant spin moment (m) dynamic in spin transfer switching has been ignored in most previous theoretical studies of the magnetization (M) dynamics. Thus in this paper, we proposed a more refined micromagnetic model of spin transfer switching that takes into account in a self-consistent manner of the coupled m and M dynamics. The numerical results obtained from this model further shed insight on the switching profiles of m and M, both of which show particular sensitivity to parameters such as the anisotropy field, the spin torque field, and the initial deviation between m and M.     

Exact spin dynamics of inhomogeneous 1-d systems at high temperature

The evaluation of spin excitation dynamics in finite 1-d systems of spins with XY exchange interaction J acquired new interest because NMR experiments at high temperature (k_BTJ) confirmed the predicted spin wave behavior of mesoscopic echoes. In this work, we use the Jordan–Wigner transformation to obtain the exact dynamics of inhomogeneous chains and rings where the evolution is reduced to one-body dynamics. For higher dimensions, the spin excitations manifest many-body effects that can be interpreted as a simple dynamics of non-interacting fermions plus a decoherent process.     

Spontaneous emission of NMR signals in hyperpolarized proton spin systems

Hyperpolarization of nuclear spins is gaining increasing interest as a tool for improving the signal-to-noise ratio of NMR and MRI. While in principle, hyperpolarized samples are amenable to the same or similar experiments as are used in conventional NMR, the large spin polarization may give rise to unexpected effects. Here, spontaneous emission of signal was observed from proton spin systems, which were hyperpolarized to negative spin temperature by dynamic nuclear polarization (DNP). An unexpected feature of these emissions is that, without any radio-frequency excitation, multiple beats arise that cannot be explained by the Bloch equations with radiation damping. However, we show that a simple modification to these equations, which takes into account an additional supply of hyperpolarized magnetization from a reservoir outside of the active detection region, can phenomenologically describe the observed signal. The observed effect demonstrates that even well-known mechanisms of spin evolution can give rise to unexpected effects when working with hyperpolarized samples, which may need to be addressed through the development of new experimental techniques.     

Non-Markovian dynamics of spin squeezing

We evaluate the spin squeezing dynamics of N independent spin-1/2 particles with exchange symmetry. Each particle couples to an individual and identical reservoir. We study the time evolution of spin squeezing under the influence of different decoherence. The spin squeezing property vanishes with evolution time under Markovian decoherence, while it collapses quickly and revives under non-Markovian decoherence. As spin squeezing can be regarded as a witness of multipartite entanglement, our scheme shows the collapses and revivals of multipartite entanglement under the influence of non-Markovian decoherence.     

Gauge theory approach for diffusive and precessional spin dynamics in a two-dimensional electron gas

We develop a gauge theory for diffusive and precessional spin dynamics in a two-dimensional electron gas. Our approach reveals a direct connection between the absence of the equilibrium spin current and a strong anisotropy in the spin relaxation: both effects arise if spin-orbit coupling is reduced to a pure gauge SU(2) field. In this case, the spin-orbit coupling can be removed by a gauge transformation in the form of a local SU(2) spin rotation. The resulting spin dynamics is exactly described in terms of two kinetic coefficients: the spin diffusion and electron mobility. After the inverse transformation, full diffusive and precessional spin density dynamics, including the anisotropic spin relaxation, formation of stable spin structures, and spin precession induced by a macroscopic current are restored. Explicit solutions of the spin evolution equations are found for the initially uniform spin density and for stable, nonuniform structures. Our analysis demonstrates a universal relation between the spin relaxation rate and spin-diffusion coefficient.     

Photo-induced magnetic-solitons and spin dynamics in diluted magnetic semiconductor quantum wells

The localization mechanism of transport property in the randomly distributed system of the hole-induced magnetic solitons with the alloy potential fluctuations in diluted magnetic semiconductors has been proposed, by using the effective Lagrangian of diffusion modes. The mechanism of the long relaxation of the spin dynamics below Curie temperature in diluted magnetic semiconductor wells and the bulk system has been discussed.     

Origin of large spin Hall magnetoresistance in Fe/CuOx bilayers

We have compared the spin Hall magnetoresistance (SMR) in Fe/Pt and Fe/CuO_x (with natural oxidation) bilayers with varying the thickness of Fe layer. A larger SMR in Fe/CuO_x bilayers has been found when the thickness of Fe layer is 3 nm. Moreover, the SMR of the two bilayers decrease with increasing the thickness of Fe from 3 nm to 10 nm, but that of Fe/CuO_x drops more sharply due to shunting current effect. Through harmonic measurements, the emergent spin current is proved to be generated in the Fe/CuO_x bilayers. The mixed phase of CuO_x has been confirmed including CuO, Cu₂O and Cu, which performs strong spin-orbit coupling and produce large spin current. On the other hand, the interface-generated spin current should be ruled out. All the results have been compared with those in Fe/Al₂O₃ bilayers with negligible spin current.     

Non-equilibrium dynamics in 3d spin glasses

The random spin structure of a quenched spin glass experiences a continuous re-structuring in the low-temperature spin glass phase; the spin glass ages. Some recent experimental studies of relaxation and temperature dependence of the low-frequency AC-susceptibility and DC-magnetisation have given essential new information on which are the governing physical parameters for the spontaneous re-construction of the spin configuration. These results are briefly reviewed and put into the context of a phenomenological real space picture of the spin glass phase. This picture includes: domains of spin glass ordered regions that use spontaneous droplet excitations as the only mechanism for their growth at constant temperature, chaos with temperature and overlap on short length scales between the equilibrium states at two different temperatures.     

A new formalism for the statistical dynamics of vector spin systems

The relaxational dynamics of a classical vector Heisenberg spin system is studied using the Fokker-Planck equation. To calculate the eigenvalues of the Fokker-Planck operator, a new approach is introduced. In this connection, a number space repesentation is introduced, which enables us to visualize the eigenvalue structure of the Fokker-Planck operator. The mean field approximation is derived and a systematic method to improve the mean field approximation is presented.     

A new formalism for the statistical dynamics of planar spin systems

The relaxational dynamics of a classical planar Heisenberg spin system is studied using the Fokker-Planck equation. A new approach is introduced in which we attempt to directly calculate the eigenvalues of the Fokker-Planck operator. In this connection a number space representation is introduced, which enables us to visualize the eigenvalue structure of the Fokker-Planck operator. The mean field approximation is derived and a systematic method to improve the mean field approximation is presented.     

The simulation of XYZ-spin chain in coupled cavities

We simulated anisotropic XYZ-spin chain with an array of coupled cavities, each of which contains one 4-level atom. The anisotropic parameters of the effective Hamilton can be tuned by controlling the external lasers. The validity of our approximations is confirmed via a numerical simulation.     

Fluctuation-dissipation ratio in three-dimensional spin glasses

We present an analysis of the data on aging in the three-dimensional Edwards-Anderson spin-glass model with nearest-neighbor interactions, which is well suited for the comparison with a recently developed dynamical mean-field theory. We measure the parameterx(q) describing the violation of the relation among correlation and response functions implied by the fluctuation-dissipation theorem.     

Thermo field dynamics of quantum spin systems

Thermo field dynamics of quantum spin systems is formulated, which gives a new variational principle at finite temperatures. The KMS relation is reformulated as identities among thermal vacuum states. Path integral formulations of the thermal vacuum state are given, which yield a new thermo field Monte Carlo method. Thermo field dynamics of finite-spin systems are studied in detail as simple examples of the present method. Pertubational expansion methods of the thermal state and time-dependent state are also given.     

Polarization transfer from para-hydrogen to heteronuclei: effect of H/D substitution. The case of AA'X and A2A2'X spin systems

Upon hydrogenation from para-hydrogen (p-H(2)), hyperpolarization transfer toward a heteronucleus may be possible even if the two protons are chemically equivalent in the final product (but not magnetically equivalent), provided that J couplings with the heteronucleus exist. It is however shown (theoretically and experimentally) that this transfer effectively occurs if the spin system in the hydrogenated molecule is of the type AA'X (A and A' denoting the two protons originating from p-H(2) and X the heteronucleus) but does not occur for a spin system of the A(2)A(2)(')X type. A theory has been worked out for assessing the details of the X spectrum (multiplet patterns) in the case of ALTADENA and PASADENA experiments. Experimental verifications are provided.