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The dynamics of magnetization coupled to an electron gas via s-d exchange interaction is investigated by using density matrix technique. Our theory shows that non-equilibrium spin accumulation induces a spin torque and the electron bath leads to a damping of the magnetization. For the two-dimensional magnetization thin film coupled to the electron gas with Rashba spin-orbit coupling, the result for the spin-orbit torques is consistent with the previous semi-classical theory. Our theory predicts a damping of the magnetization, which is absent in the semi-classical theory. The magnitude of the damping due to the electron bath is comparable to the intrinsic Gilbert damping and may be important in describing the magnetization dynamics of the system.

We have obtained new inelastic neutron scattering (INS) data for the molecular magnet Mn12-acetate which exhibit at least six magnetic peaks in the energy range 5-35 meV. These are compared with a microscopic Heisenberg model for the 12 quantum spins localised on the Mn ions, coupled by four inequivalent magnetic exchange constants. A fit to the magnetic susceptibility under the constraint that the spin of the ground state be S=10 yields two dominant exchange constants of very similar value, J1 ~ J2 ~ 65 K (~ 5.5 meV), and two smaller exchange constants J3 and J4. We compute the low-lying excitations by exact numerical diagonalisation and demonstrate that the parameters determined from the ground state and susceptibility fit provide qualitative agreement with the excitations observed by INS.

We introduce an inhomogeneous protocol to drive a weakly disordered quantum spin chain quasi-adiabatically across a quantum phase transition and minimize the residual energy of the final state. The number of spins that simultaneously reach the critical point is controlled by the length scale in which the magnetic field is modulated, introducing an effective size that favors adiabatic dynamics. The dependence of the residual energy on this length scale and the velocity at which the magnetic field sweeps out the chain is shown to be nonmonotonic. We determine the conditions for an optimal suppression of the residual energy of the final state and show that inhomogeneous driving can outperform conventional adiabatic schemes based on homogeneous control fields by several orders of magnitude.

We have performed depth dependent muon spin rotation/relaxation studies of the dynamics of single layer films of {\it Au}Fe and {\it Cu}Mn spin glasses as a function of thickness and of its behavior as a function of distance from the vacuum interface (5-70 nm). A significant reduction in the muon spin relaxation rate as a function of temperature with respect to the bulk material is observed when the muons are stopped near (5-10 nm) the surface of the sample. A similar reduction is observed for the whole sample if the thickness is reduced to e.g. 20 nm and less. This reflects an increased impurity spin dynamics (incomplete freezing) close to the surface although the freezing temperature is only modestly affected by the dimensional reduction.

$Ni Cl_2$-$4SC(NH_2)_2$ (known as DTN) is a spin-1 material with a strong single-ion anisotropy that is regarded as a new candidate for Bose-Einstein condensation (BEC) of spin degrees of freedom. We present a systematic study of the low-energy excitation spectrum of DTN in the field-induced magnetically ordered phase by means of high-field electron spin resonance measurements at temperatures down to 0.45 K. We argue that two gapped modes observed in the experiment can be consistently interpreted within a four-sublattice antiferromagnet model with a finite interaction between two tetragonal subsystems and unbroken axial symmetry. The latter is crucial for the interpretation of the field-induced ordering in DTN in terms of BEC.

We investigate weakly coupled spin-1/2 ladders in a magnetic field. The work is motivated by recent experiments on the compound $\mathrm{(C_5H_{12}N)_2CuBr_4}$ (BPCB). We use a combination of numerical and analytical methods, in particular the density matrix renormalization group (DMRG) technique, to explore the phase diagram and the excitation spectra of such a system. We give detailed results on the temperature dependence of the magnetization and the specific heat, and the magnetic field dependence of the nuclear magnetic resonance (NMR) relaxation rate of single ladders. For coupled ladders, treating the weak interladder coupling within a mean field approach, we compute the transition temperature of triplet condensation and its corresponding antiferromagnetic order parameter. Existing experimental measurements are discussed and compared to our theoretical results. Furthermore we compute, using time dependent DMRG, the dynamical correlations of a single spin ladder. Our results allow to directly describe the inelastic neutron scattering cross section up to high energies. We focus on the evolution of the spectra with the magnetic field and compare their behavior for different couplings. The characteristic features of the spectra are interpreted using different analytical approaches such as the mapping onto a spin chain, a Luttinger liquid (LL) or onto a t-J model. For values of parameters for which such measurements exist, we compare our results to inelastic neutron scattering experiments on the compound BPCB and find excellent agreement. We make additional predictions for the high energy part of the spectrum that are potentially testable in future experiments.

We explore the structure of the spin foam-like vertex expansion in loop quantum cosmology and discuss properties of the corresponding amplitudes, with the aim of elucidating some of the expansion's useful properties and features. We find that the expansion is best suited for consideration of conceptual questions and for investigating short-time, highly quantum behavior. In order to study dynamics at cosmological scales, the expansion must be carried to very high order, limiting its direct utility as a calculational tool for such questions. Conversely, it is unclear that the expansion can be truncated at finite order in a controlled manner.

We investigate the dynamics of spinning binaries of compact objects at the next-to-leading order in the quadratic-in-spin effects, which corresponds to the third post-Newtonian order (3PN). Using a Dixon-type multipolar formalism for spinning point particles endowed with spin-induced quadrupoles and computing iteratively in harmonic coordinates the relevant pieces of the PN metric within the near zone, we derive the post-Newtonian equations of motion as well as the equations of spin precession. We find full equivalence with available results. We then focus on the far-zone field produced by those systems and obtain the previously unknown 3PN spin contributions to the gravitational-wave energy flux by means of the multipolar post-Minkowskian (MPM) wave generation formalism. Our results are presented in the center-of-mass frame for generic orbits, before being further specialized to the case of spin-aligned, circular orbits. We derive the orbital phase of the binary based on the energy balance equation and briefly discuss the relevance of the new terms.

Using the approach of low-energy effective field theory, the phase diagram is studied for a mixture of two species of pseudospin-$\1/2$ Bose atoms with interspecies spin-exchange. There are four mean-field regimes on the parameter plane of $g_e$ and $g_z$, where $g_e$ is the interspecies spin-exchange interaction strength, while $g_z$ is the difference between the interaction strength of interspecies scattering without spin-exchange of equal spins and that of unequal spins. Two regimes, with $|g_z| > |g_e|$, correspond to ground states with the total spins of the two species parallel or antiparallel along $z$ direction, and the low energy excitations are equivalent to those of two-component spinless Bosons. The other two regimes, with $|g_e| > |g_z|$, correspond to ground states with the total spins of the two species parallel or antiparallel on $xy$ plane, and the low energy excitations are described by a sine-Gordon model coupled with a free scalar field, where the effective fields are combinations of the phases of the original four Boson fields. In (1+1)-dimension, they are described by Kosterlitz-Thouless renormalization group (RG) equations, and there are three sectors in the phase plane of a scaling dimension and a dimensionless parameter proportional to the strength of the cosine interaction, both depending on the densities. The gaps of these elementary excitations are experimental probes of the underlying many-body ground states.

Using the approach of low-energy effective field theory, the phase diagram is studied for a mixture of two species of pseudospin-$\1/2$ Bose atoms with interspecies spin-exchange. There are four mean-field regimes on the parameter plane of $g_e$ and $g_z$, where $g_e$ is the interspecies spin-exchange interaction strength, while $g_z$ is the difference between the interaction strength of interspecies scattering without spin-exchange of equal spins and that of unequal spins. Two regimes, with $|g_z| > |g_e|$, correspond to ground states with the total spins of the two species parallel or antiparallel along $z$ direction, and the low energy excitations are equivalent to those of two-component spinless Bosons. The other two regimes, with $|g_e| > |g_z|$, correspond to ground states with the total spins of the two species parallel or antiparallel on $xy$ plane, and the low energy excitations are described by a sine-Gordon model coupled with a free scalar field, where the effective fields are combinations of the phases of the original four Boson fields. In (1+1)-dimension, they are described by Kosterlitz-Thouless renormalization group (RG) equations, and there are three sectors in the phase plane of a scaling dimension and a dimensionless parameter proportional to the strength of the cosine interaction, both depending on the densities. The gaps of these elementary excitations are experimental probes of the underlying many-body ground states.

Quantum plasmas is a rapidly expanding field of research, with applications ranging from nanoelectronics, nanoscale devices and ultracold plasmas, to inertial confinement fusion and astrophysics. Here we give a short systematic overview of quantum plasmas. In particular, we analyze the collective effects due to spin using fluid models. The introduction of an intrinsic magnetization due to the plasma electron (or positron) spin properties in the magnetohydrodynamic limit is discussed. Finally, a discussion of the theory and examples of applications is given.

Spin chains can realise perfect quantum state transfer between the two ends via judicious choice of coupling strengths. In this paper, we study what other states can be created by engineering a spin chain. We conclude that, up to local phases, all single excitation quantum states with support on every site of the chain can be created. We pay particular attention to the generation of W-states that are superposed over every site of the chain.

We report a neutron scattering study of the dynamic spin correlations in Rb$_2$MnF$_4$, a two-dimensional spin-5/2 antiferromagnet. By tuning an external magnetic field to the value for the spin-flop line, we reduce the effective spin anisotropy to essentially zero, thereby obtaining a nearly ideal two-dimensional isotropic antiferromagnet. From the shape of the quasielastic peak as a function of temperature, we demonstrate dynamic scaling for this system and find a value for the dynamical exponent $z$. We compare these results to theoretical predictions for the dynamic behavior of the two-dimensional Heisenberg model, in which deviations from $z=1$ provide a measure of the corrections to scaling.

We construct and analyze a two-dimensional frustrated quantum spin model with plaquette order, in which the low-energy dynamics is controlled by spin singlets. At a critical value of frustration the singlet spectrum becomes gapless, indicating a quantum transition to a phase with dimer order. This T=0 transition belongs to the 3D Ising universality class, while at finite temperature a 2D Ising critical line separates the plaquette and dimerized phases. The magnetic susceptibility has an activated form throughout the phase diagram, whereas the specific heat exhibits a rich structure and a power law dependence on temperature at the quantum critical point. We argue that the novel quantum critical behavior associated with singlet criticality discussed in this work can be relevant to a wide class of quantum spin systems, such as antiferromagnets on Kagome and pyrochlore lattices, where the low-energy excitations are known to be spin singlets, as well as to the CAVO lattice and several recently discovered strongly frustrated square-lattice antiferromagnets.

The linear equations for transverse spin dynamics in weakly polarised degenerate Fermi liquid with arbitrary relationship between temperature and polarization are derived from Landau-Silin phenomenological kinetic equation with general form of two-particle collision integral. The temperature and polarization dependence of the spin current relaxation time is established. It is found in particular that at finite polarization transverse spin wave damping has a finite value at T=0. The analogy between temperature dependences of spin waves attenuation and ultrasound absorption in degenerate Fermi liquid at arbitrary temperature is presented. We also discuss spin-polarized Fermi liquid in the general context of the Fermi-liquid theory and compare it with "Fermi liquid" with spontaneous magnetization.

The spin coherence phenomena and the possibility of their observation in nanomagnetic insulators attract more and more attention in the last several years. Recently it has been shown that in these systems in large transverse magnetic field there can be a fairly narrow "coherence window" for phonon and nuclear spin-mediated decoherence. What kind of spin dynamics can then be expected in this window in a crystal of magnetic nanomolecules coupled to phonons, to nuclear spin bath and it to each other via dipole-dipole interactions? Studying multispin correlations, we determine the region of parameters where "coherent clusters" of collective spin excitations can appear. Although two particular systems, namely crystals of $Fe_8$-triazacyclonane and $Mn_{12}$-acetate molecules, are used in this work to illustrate the results, here we are not trying to predict an existence of collective coherent dynamics in some particular system. Instead, we discuss the way how any crystalline system of dipole-dipole coupled nanomolecules can be analyzed to decide whether this system is suitable for attempts to observe coherent dynamics. The presented analysis can be useful in the search for magnetic systems showing the spin coherence phenomena.

Multiferroic materials have attracted much interest due to the unusual coexistence of ferroelectric and (anti-)ferromagnetic ground states in a single compound. They offer an exciting platform for new physics and potentially novel devices. BiFeO$_3$ is one of the most celebrated of multiferroic materials with highly desirable properties. It is the only known room-temperature multiferroic with $T_\mathrm{C}\approx 1100~ \mathrm{K}$ and $T_\mathrm{N}\approx 650~\mathrm{K}$, and exhibits one of the largest spontaneous electric polarisation, $P\approx 80~\mu\mathrm{C/cm}^2$. At the same time, it has a magnetic cycloid structure with an extremely long period of 630~\AA, which arises from a competition between the usual symmetric exchange interaction and antisymmetric Dzyaloshinskii-Moriya (DM) interaction. There is also an intriguing interplay between the DM interaction and the single ion anisotropy. In this review, we have tried to paint a complete picture of bulk BiFeO$_3$ by summarising the structural and dynamical properties of both spin and lattice parts, and their magneto-electric coupling.

We present results of numerical simulations on a one-dimensional Ising spin glass with long-range interactions. Parameters of the model are chosen such that it is a proxy for a short-range spin glass above the upper critical dimension (i.e. in the mean-field regime). The system is quenched to a temperature well below the transition temperature $T_c$ and the growth of correlations is observed. The spatial decay of the correlations at distances less than the dynamic correlation length $\xi(t)$ agrees quantitatively with the predictions of a static theory, the "metastate", evaluated according to the replica symmetry breaking (RSB) theory. We also compute the dynamic exponent $z(T)$ defined by $\xi(t) \propto t^{1/z(T)}$ and find that it is compatible with the mean-field value of the critical dynamical exponent for short range spin glasses.

We study vortex dynamics in trapped two-component Bose-Einstein condensates with a laser- induced spin-orbit coupling using the numerical analysis of the Gross-Pitaevskii equation. The spin-orbit coupling leads to three distinct ground state phases, which depend on some experimentally controllable parameters. When a vortex is put in one or both of the two-component condensates, the vortex dynamics exhibits very different behaviors in each phase, which can be observed in experiments. These dynamical behaviors can be understood by clarifying the stable vortex structure realized in each phase.

Metastable states in Ising spin-glass models are studied by finding iterative solutions of mean-field equations for the local magnetizations. Two different equations are studied: the TAP equations which are exact for the SK model, and the simpler `naive-mean-field' (NMF) equations. The free-energy landscapes that emerge are very different. For the TAP equations, the numerical studies confirm the analytical results of Aspelmeier et al., which predict that TAP states consist of close pairs of minima and index-one (one unstable direction) saddle points, while for the NMF equations saddle points with large indices are found. For TAP the barrier height between a minimum and its nearby saddle point scales as (f-f_0)^{-1/3} where f is the free energy per spin of the solution and f_0 is the equilibrium free energy per spin. This means that for `pure states', for which f-f_0 is of order 1/N, the barriers scale as N^{1/3}, but between states for which f-f_0 is of order one the barriers are finite and also small so such metastable states will be of limited physical significance. For the NMF equations there are saddles of index K and we can demonstrate that their complexity Sigma_K scales as a function of K/N. We have also employed an iterative scheme with a free parameter that can be adjusted to bring the system of equations close to the `edge of chaos'. Both for the TAP and NME equations it is possible with this approach to find metastable states whose free energy per spin is close to f_0. As N increases, it becomes harder and harder to find solutions near the edge of chaos, but nevertheless the results which can be obtained are competitive with those achieved by more time-consuming computing methods and suggest that this method may be of general utility.

Metastable states in Ising spin-glass models are studied by finding iterative solutions of mean-field equations for the local magnetizations. Two different equations are studied: the TAP equations which are exact for the SK model, and the simpler `naive-mean-field' (NMF) equations. The free-energy landscapes that emerge are very different. For the TAP equations, the numerical studies confirm the analytical results of Aspelmeier et al., which predict that TAP states consist of close pairs of minima and index-one (one unstable direction) saddle points, while for the NMF equations saddle points with large indices are found. For TAP the barrier height between a minimum and its nearby saddle point scales as (f-f_0)^{-1/3} where f is the free energy per spin of the solution and f_0 is the equilibrium free energy per spin. This means that for `pure states', for which f-f_0 is of order 1/N, the barriers scale as N^{1/3}, but between states for which f-f_0 is of order one the barriers are finite and also small so such metastable states will be of limited physical significance. For the NMF equations there are saddles of index K and we can demonstrate that their complexity Sigma_K scales as a function of K/N. We have also employed an iterative scheme with a free parameter that can be adjusted to bring the system of equations close to the `edge of chaos'. Both for the TAP and NME equations it is possible with this approach to find metastable states whose free energy per spin is close to f_0. As N increases, it becomes harder and harder to find solutions near the edge of chaos, but nevertheless the results which can be obtained are competitive with those achieved by more time-consuming computing methods and suggest that this method may be of general utility.

This chapter describes spin-wave excitations in nanosized dots and rings in the presence of the vortex state. The special attention is paid to the manifestation of the competition between exchange and dipolar interactions in the spin-wave spectrum as well as the correlation between the spectrum and the stability of the vortex. The calculation method uses the dynamic matrix for an all-discrete system, the numerical diagonalization of which yields the spectrum of frequencies and spin-wave profiles of normal modes of the dot. We study in-plane vortices of two types: a circular magnetization in circular dots and rings and the Landau state in square rings. We examine the influence of the dipolar-exchange competition and the geometry of the dot on the stability of the vortex and on the spectrum of spin waves. We show that the lowest-frequency mode profile proves to be indicative of the dipolar-to-exchange interaction ratio and the vortex stability is closely related to the spin-wave profile of the soft mode. The negative dispersion relation is also shown. Our results obtained for in-plane vortices are in qualitative agreement with results for core-vortices obtained from experiments, micromagnetic simulations, and analytical calculations.

Using fast electron spin resonance spectroscopy of a single nitrogen-vacancy defect in diamond, we demonstrate real-time readout of the Overhauser field produced by its nuclear spin environment under ambient conditions. These measurements enable narrowing the Overhauser field distribution by post-selection, corresponding to a conditional preparation of the nuclear spin bath. Correlations of the Overhauser field fluctuations are quantitatively inferred by analysing the Allan deviation over consecutive measurements. This method allows to extract the dynamics of weakly coupled nuclear spins of the reservoir.

Y0.5Ca0.5BaCo4O7 was recently introduced as a possible candidate for capturing some of the predicted classical spin kagome ground state features. Stimulated by this conjecture we have taken up a more complete study of the spin correlations in this compound with neutron scattering methods on a powder sample characterized with high-resolution neutron diffraction and the temperature dependence of magnetic susceptibility and specific heat. We have found that the frustrated near neighbor magnetic correlations involve not only the kagome planes but concern the full Co sub-lattice as evidenced by the analysis of the wavevector-dependence of the short range order. We conclude from our results that the magnetic moments are located on the Co sub-lattice as a whole and that correlations extend beyond the two-dimensional kagome planes. We identify intriguing dynamical properties, observing high-frequency fluctuations with a lorentzian line-width {\Gamma}

We report the study of high quality samples of the frustrated S = 1/2 kagome antiferromagnet vesignieite, Cu3Ba(VO5H)2. Neutron powder diffraction measurements evidence the high quality of the kagome lattice and show no sign of a transition to long-range order. A kink in the susceptibility below T = 9 K is matched to a reduction in paramagnetic-like correlations in the diffraction data and a slowing of the spin dynamics observed by MuSR. Our results point to an exotic quantum state below 9 K with coexistance of both dynamical and small frozen moments \sim 0.1 \muB. We propose that Dzyaloshinsky-Moriya interaction is large enough in this system to stabilize this novel quantum ground state.

We investigate the spin-dependent transport properties of a two-dimensional electron gas formed at oxides' interface in the presence of a magnetic field. We consider several scenarios for the oxides' properties, including oxides with co-linear or spiral magnetic and ferroelectric order. For spiral multiferroic oxides, the magnetoelectric coupling and the topology of the localized magnetic moments introduce additional, electric field controlled spin-orbit coupling that affects the magneto-oscillation of the current. An interplay of this spin-orbit coupling, the exchange field, and of the applied magnetic field results in a quantum, gate-controlled spin and charge Hall conductance.

The extension of Boltzmann-Gibbs thermostatistics, proposed by Tsallis, introduces an additional parameter $q$ to the inverse temperature $\beta$. Here, we show that a previously introduced generalized Metropolis dynamics to evolve spin models is not local and does not obey the detailed energy balance. In this dynamics, locality is only retrieved for $q=1$, which corresponds to the standard Metropolis algorithm. Non-locality implies in very time consuming computer calculations, since the energy of the whole system must be reevaluated, when a single spin is flipped. To circumvent this costly calculation, we propose a generalized master equation, which gives rise to a local generalized Metropolis dynamics that obeys the detailed energy balance. To compare the different critical values obtained with other generalized dynamics, we perform Monte Carlo simulations in equilibrium for Ising model. By using the short time non-equilibrium numerical simulations, we also calculate for this model: the critical temperature, the static and dynamical critical exponents as function of $q$. Even for $q\neq 1$, we show that suitable time evolving power laws can be found for each initial condition. Our numerical experiments corroborate the literature results, when we use non-local dynamics, showing that short time parameter determination works also in this case. However, the dynamics governed by the new master equation leads to different results for critical temperatures and also the critical exponents affecting universality classes. We further propose a simple algorithm to optimize modeling the time evolution with a power law considering in a log-log plot two successive refinements.

The extension of Boltzmann-Gibbs thermostatistics, proposed by Tsallis, introduces an additional parameter $q$ to the inverse temperature $\beta$. Here, we show that a previously introduced generalized Metropolis dynamics to evolve spin models is not local and does not obey the detailed energy balance. In this dynamics, locality is only retrieved for $q=1$, which corresponds to the standard Metropolis algorithm. Non-locality implies in very time consuming computer calculations, since the energy of the whole system must be reevaluated, when a single spin is flipped. To circumvent this costly calculation, we propose a generalized master equation, which gives rise to a local generalized Metropolis dynamics that obeys the detailed energy balance. To compare the different critical values obtained with other generalized dynamics, we perform Monte Carlo simulations in equilibrium for Ising model. By using the short time non-equilibrium numerical simulations, we also calculate for this model: the critical temperature, the static and dynamical critical exponents as function of $q$. Even for $q\neq 1$, we show that suitable time evolving power laws can be found for each initial condition. Our numerical experiments corroborate the literature results, when we use non-local dynamics, showing that short time parameter determination works also in this case. However, the dynamics governed by the new master equation leads to different results for critical temperatures and also the critical exponents affecting universality classes. We further propose a simple algorithm to optimize modeling the time evolution with a power law considering in a log-log plot two successive refinements.

Our inelastic neutron scattering experiments of the spin excitations in the slightly overdoped La{1.83}Sr{0.17}CuO{4} compound show that, under the application of a magnetic field of 5 Tesla, the low-temperature susceptibility undergoes a weight redistribution centered at the spin-gap energy. Furthermore, by comparing the temperature dependence of the neutron data with ac-susceptibility and magnetization measurements, we conclude that the filling in of the spin gap tracks the irreversibility/melting temperature rather than Tc2, which indicates an unusual interplay between the magnetic vortices and the spin excitations even in the slightly overdoped regime of high-temperature superconductors.

We performed path integral simulations of spin evolution controlled by the Rashba spin-orbit interaction in the semiclassical regime for chaotic and regular quantum dots. The spin polarization dynamics have been found to be strikingly different from the D'yakonov-Perel' (DP) spin relaxation in bulk systems. Also an important distinction have been found between long time spin evolutions in classically chaotic and regular systems. In the former case the spin polarization relaxes to zero within relaxation time much larger than the DP relaxation, while in the latter case it evolves to a time independent residual value. The quantum mechanical analysis of the spin evolution based on the exact solution of the Schroedinger equation with Rashba SOI has confirmed the results of the classical simulations for the circular dot, which is expected to be valid in general regular systems. In contrast, the spin relaxation down to zero in chaotic dots contradicts to what have to be expected from quantum mechanics. This signals on importance at long time of the mesoscopic echo effect missed in the semiclassical simulations.

We use exact diagonalization and the modified Lanczos method to study the finite energy and finite momentum spectral weight of the longitudinal and transverse spin excitations of the anisotropic zig-zag ladder. We find that the spin excitations form continua of gapless or gapped spinons in the different regions of the phase diagram. The results obtained are consistent with a picture previously proposed that in the anisotropic case there is a transition from a gapped regime to a gapless regime, for small interchain coupling. In this regime we find a sharp low-energy peak in the structure function for the transverse spin excitations, consistent with a finite stiffness.

Optically pumped nuclear magnetic resonance (OPNMR) measurements were performed in two different electron-doped multiple quantum well samples near the fractional quantum Hall effect ground state nu=1/3. Below 0.5K, the spectra provide evidence that spin-reversed charged excitations of the nu=1/3 ground state are localized over the NMR time scale of ~40 microseconds. Furthermore, by varying NMR pulse parameters, the electron spin temperature (as measured by the Knight shift) could be driven above the lattice temperature, which shows that the value of the electron spin-lattice relaxation time lies between 100 microseconds and 500 milliseconds at nu=1/3.

Recently, inelastic neutron scattering (INS) experiments on the insulating parent compounds of high-T_c materials were analyzed to extract the value of the superexchange constant $J$. Starting point of the analysis was the nearest-neighbor Heisenberg model. Motivated by recent ARPES experiments, we consider the effects of a next-nearest neighbor hopping, $t'$ in the strong coupling limit of the spin-density wave formalism, where it leads to an antiferromagnetic exchange $J'>0$ between next-nearest neighbor spins. We show that a finite $J'$ (a) changes the spin-wave velocity and thus the value of $J$ extracted from the INS data, yielding almost identical values for $J$ in La_2CuO_4 and YBa_2Cu_3O_{6.15}, and (b) leads to a considerable change in the high-frequency spin-dynamics. Finally, we calculate the 1/S quantum corrections in the presence of $J'$ and discuss their relevance for the INS data.

We present formulas for the nuclear and electronic spin relaxation times due to the hyperfine interaction for nanostructed systems and show that the times depend on the square of the local density of electronic states at the nuclear position. A drastic sensitivity (orders of magnitude) of the electronic and nuclear spin coherence times to small electric fields is predicted for both uniformly distributed nuclear spins and for $\d$-doped layers of specific nuclei. This sensitivity is robust to nuclear spin diffusion.

We study manipulation of entanglement between two identical networks of quantum mechanical particles. Firstly, we reduce the problem of entanglement transfer to the problem of quantum state transfer. Then, we consider entanglement concentration and purification based on free dynamics on the networks and local measurements on the vertices. By introducing an appropriate measure of efficiency, we characterize the performance of the protocol. We give evidence that such a measure does not depend on the network topology, and we estimate the contribution given by the number of entangled pairs initially shared by the two networks.

We report neutron scattering studies on single crystals of the electron-doped (n-type) superconducting cuprate Nd2-xCexCuO4 (x=0.15) with Tc = 18 K and 25 K. Unlike the hole-doped (p-type) superconducting cuprates where incommensurate magnetic fluctuations commonly exist, the n-type cuprate shows commensurate magnetic fluctuations at the tetragonal (1/2 1/2 0) reciprocal points both in the superconducting and in the normal state. A spin gap opens up when the n-type cuprate becomes superconducting, as in the optimally doped p-type La2-xSrxCuO4. The gap energy, however, increases gradually up to about 4 meV as T decreases from Tc to 2 K, which contrasts with the spin pseudogap behavior with a T-independent gap energy in the superconducting state of p-type cuprates.

In this article we discuss several aspects of the stochastic dynamics of spin models. The paper has two independent parts. Firstly, we explore a few properties of the multi-point correlations and responses of generic systems evolving in equilibrium with a thermal bath. We propose a fluctuation principle that allows us to derive fluctuation-dissipation relations for many-time correlations and linear responses. We also speculate on how these features will be modified in systems evolving slowly out of equilibrium, as finite-dimensional or dilute spin-glasses. Secondly, we present a formalism that allows one to derive a series of approximated equations that determine the dynamics of disordered spin models on random (hyper) graphs.

A "spin-flip transistor" is a lateral spin valve consisting of ferromagnetic source drain contacts to a thin-film normal-metal island with an electrically floating ferromagnetic base contact on top. We analyze the \emph{dc}-current-driven magnetization dynamics of spin-flip transistors in which the source-drain contacts are magnetized perpendicularly to the device plane by magnetoelectronic circuit theory and the macrospin Landau-Lifshitz-Gilbert equation. Spin flip scattering and spin pumping effects are taken into account. We find a steady-state rotation of the base magnetization at GHz frequencies that is tuneable by the source-drain bias. We discuss the advantages of the lateral structure for high-frequency generation and actuation of nanomechanical systems over recently proposed nanopillar structures.

Using spin-dynamics techniques we have performed large-scale computer simulations of the dynamic behavior of the classical three component XY-model (i.e. the anisotropic limit of an easy-plane Heisenberg ferromagnet), on square lattices of size up to 192^2, for several temperatures below, at, and above T_KT. The temporal evolution of spin configurations was determined numerically from coupled equations of motion for individual spins by a fourth order predictor-corrector method, with initial spin configurations generated by a hybrid Monte Carlo algorithm. The neutron scattering function S(q,omega) was calculated from the resultant space-time displaced spin-spin correlation function. Pronounced spin-wave peaks were found both in the in-plane and the out-of-plane scattering function over a wide range of temperatures. The in-plane scattering function S^xx also has a large number of clear but weak additional peaks, which we interpret to come from two-spin-wave scattering. In addition, we observed a small central peak in S^xx, even at temperatures well below the phase transition. We used dynamic finite size scaling theory to extract the dynamic critical exponent z. We find z=1.00(4) for all T

In this work, we study the spin dynamics of Mn12-acetate molecules in the regime of thermally assisted tunneling. In particular, we describe the system in the presence of a strong transverse magnetic field. Similar to recent experiments, the relaxation time/rate is found to display a series of resonances; their Lorentzian shape is found to stem from the tunneling. The dynamic susceptibility $\chi(w)$ is calculated starting from the microscopic Hamiltonian and the resonant structure manifests itself also in $\chi(w)$. Similar to recent results reported on another molecular magnet, Fe8, we find oscillations of the relaxation rate as a function of the transverse magnetic field when the field is directed along a hard axis of the molecules. This phenomenon is attributed to the interference of the geometrical or Berry phase. We propose susceptibility experiments to be carried out for strong transverse magnetic fields to study of these oscillations and for a better resolution of the sharp satellite peaks in the relaxation rates.

A new symplectic time-reversible algorithm for numerical integration of the equations of motion in magnetic liquids is proposed. It is tested and applied to molecular dynamics simulations of a Heisenberg spin fluid. We show that the algorithm exactly conserves spin lengths and can be used with much larger time steps than those inherent in standard predictor-corrector schemes. The results obtained for time correlation functions demonstrate the evident dynamic interplay between the liquid and magnetic subsystems.

We introduce a lattice spin model where frustration is due to multibody interactions rather than quenched disorder in the Hamiltonian. The system has a crystalline ground state and below the melting temperature displays a dynamic behaviour typical of fragile glasses. However, the supercooled phase loses stability at an effective spinodal temperature, and thanks to this the Kauzmann paradox is resolved. Below the spinodal the system enters an off-equilibrium regime corresponding to fast crystal nucleation followed by slow activated crystal growth. In this phase and in a time region which is longer the lower the temperature we observe a violation of the fluctuation-dissipation theorem analogous to structural glasses. Moreover, we show that in this system there is no qualitative difference between a locally stable glassy configuration and a highly disordered polycrystal.

We study the spin dynamics of two dimensional electron gases (2DEGs) with Rashba spin-orbit coupling by taking account of electron-electron interactions. The diffusion equations for charge and spin densities are derived by making use of the path-integral approach and the quasiclassical Green's function. Analyzing the effect of the interactions, we show that the spin-relaxation time can be enhanced by the electron-electron interaction in the ballistic regime.

We investigate analytically and numerically the Multiple Quantum (MQ) NMR dynamics in systems of nuclear spins 1/2 coupled by the dipole-dipole interactions in the case of the dipolar ordered initial state. We suggest two different methods of MQ NMR. One of them is based on the measurement of the dipolar temperature in the quasi-equilibrium state which establishes after the time of order T2 after the MQ NMR experiment. The other method uses an additional resonance 45^0 -pulse after the preparation period of the standard MQ NMR experiment in solids. Many-spin clusters and correlations are created faster in such experiments than in the usual MQ NMR experiments and can be used for the investigation of many-spin dynamics of nuclear spins in solids.

In these lectures I will review some theoretical results that have been obtained for spin glasses. I will concentrate my attention on the formulation of the mean field approach and on its numerical and experimental verifications. I will present the various hypothesis at the basis of the theory and I will discuss their mathematical and physical status.

We study the collisionless spin dynamics of a harmonically trapped Fermi gas in a magnetic field gradient. In the absence of interactions, the system evolution is periodic: the magnetization develops twists, which evolve into a longitudinal polarization. Recurrences follow. For weak interaction, the exchange interactions lead to beats in these oscillations. We present an array of analytic and numerical techniques for studying this physics.

Various spin effects are expected to become observable in light-matter interaction at relativistic intensities. Relativistic quantum mechanics equipped with a suitable relativistic spin operator forms the theoretical foundation for describing these effects. Various proposals for relativistic spin operators have been offered by different authors, which are presented in a unified way. As a result of the operators' mathematical properties only the Foldy-Wouthuysen operator and the Pryce operator qualify as possible proper relativistic spin operators. The ground states of highly charged hydrogen-like ions can be utilized to identify a legitimate relativistic spin operator experimentally. Subsequently, the Foldy-Wothuysen spin operator is employed to study electron-spin precession in high-intensity standing light waves with elliptical polarization. For a correct theoretical description of the predicted electron-spin precession relativistic effects due to the spin angular momentum of the electromagnetic wave has to be taken into account even in the limit of low intensities.

We demonstrate that the transient non-autonomous dynamics of a spin torque nano-oscillator (STNO) under a radio-frequency (rf) driving signal is qualitatively different from the dynamics described by the Adler model. If the external rf current $I_{rf}$ is larger than a certain critical value $I_{cr}$ (determined by the STNO bias current and damping) strong oscillations of the STNO power and phase develop in the transient regime. The frequency of these oscillations increases with $I_{rf}$ as $\propto\sqrt{I_{rf} - I_{cr}}$ and can reach several GHz, whereas the damping rate of the oscillations is almost independent of $I_{rf}$. This oscillatory transient dynamics is caused by the strong STNO nonlinearity and should be taken into account in most STNO rf applications.

This paper treats 6j symbols or their orthonormal forms as a function of two variables spanning a square manifold which we call the "screen". We show that this approach gives important and interesting insight. This two dimensional perspective provides the most natural extension to exhibit the role of these discrete functions as matrix elements that appear at the very foundation of the modern theory of classical discrete orthogonal polynomials. Here we present 2D and 1D recursion relations that are useful for the direct computation of the orthonormal 6j, which we name U. We present a convention for the order of the arguments of the 6j that is based on their classical and Regge symmetries, and a detailed investigation of new geometrical aspects of the 6j symbols. Specifically we compare the geometric recursion analysis of Schulten and Gordon with the methods of this paper. The 1D recursion relation, written as a matrix diagonalization problem, permits an interpretation as a discrete Schr\"odinger-like equations and an asymptotic analysis illustrates semiclassical and classical limits in terms of Hamiltonian evolution.

We perform a theoretical study of the dynamics of the electric field excitations in a microtubule by taking into consideration the realistic cylindrical geometry, dipole-dipole interactions of the tubulin-based protein heterodimers, the radial electric field produced by the solvent, and a possible degeneracy of energy states of individual heterodimers. The consideration is done in the frames of the classical pseudo-spin model. We derive the system of nonlinear dynamical ordinary differential equations of motion for interacting dipoles, and the continuum version of these equations. We obtain the solutions of these equations in the form of snoidal waves, solitons, kinks, and localized spikes. Our results will help to a better understanding of the functional properties of microtubules including the motor protein dynamics and the information transfer processes. Our considerations are based on classical dynamics. Some speculations on the role of possible quantum effects are also made.