Field-dependent nuclear relaxation of spins 1/2 induced by dipole-dipole couplings to quadrupole spins: LaF3 crystals as an example

A general theory of spin-lattice nuclear relaxation of spins I=1/2 caused by dipole-dipole couplings to quadrupole spins S1, characterized by a non-zero averaged (static) quadrupole coupling, is presented. In multispin systems containing quadrupolar and dipolar nuclei, transitions of spins 1/2 leading to their relaxation are associated through dipole-dipole couplings with certain transitions of quadrupole spins. The averaged quadrupole coupling attributes to the energy level structure of the quadrupole spin and influences in this manner relaxation processes of the spin 1/2. Typically, quadrupole spins exhibit also a complex multiexponential relaxation sensed by the dipolar spin as an additional modulation of the mutual dipole-dipole coupling. The proposed model includes both effects and is valid for an arbitrary magnetic field and an arbitrary quadrupole spin quantum number. The theory is applied to interpret fluorine relaxation profiles in LaF3 ionic crystals. The obtained results are compared with predictions of the 'classical' Solomon relaxation theory.     

Diffusion effects on longitudinal relaxation in poorly mixed compartments

Diffusion of spins between physical or virtual, communicating compartments having different states of longitudinal magnetization leads to diffusion-driven longitudinal relaxation. Herein, in two model systems, the effects of diffusion-driven longitudinal relaxation are explored experimentally and analyzed quantitatively. In the first case, longitudinal relaxation in a single slice of a water phantom is monitored spectroscopically as a function of slice thickness. In the second case, mimicking vascular flow/diffusion effects, longitudinal relaxation is monitored in a two-compartment, semi-permeable fiber phantom. In both cases, apparent longitudinal relaxation, though clearly multi-exponential, is well-modeled as bi-exponential.     

Nuclear spin-lattice relaxation mechanisms in kaolinite confirmed by magic-angle spinning

Spin-lattice relaxation mechanisms in kaolinite have been reinvestigated by magic-angle spinning (MAS) of the sample. MAS is useful to distinguish between relaxation mechanisms: the direct relaxation rate caused by the dipole-dipole interaction with electron spins is not affected by spinning while the spin diffusion-assisted relaxation rate is. Spin diffusion plays a dominant role in ¹H relaxation. MAS causes only a slight change in the relaxation behavior, because the dipolar coupling between ¹H spins is strong. ²⁹Si relaxes directly through the dipole-dipole interaction with electron spins under spinning conditions higher than 2 kHz. A spin diffusion effect has been clearly observed in the ²⁹Si relaxation of relatively pure samples under static and slow-spinning conditions. ²⁷Al relaxes through three mechanisms: phonon-coupled quadrupole interaction, spin diffusion and dipole-dipole interaction with electron spins. The first mechanism is dominant, while the last is negligibly small. Spin diffusion between ²⁷Al spins is suppressed completely at a spinning rate of 2.5 kHz. We have analyzed the relaxation behavior theoretically and discussed quantitatively. Concentrations of paramagnetic impurities, electron spin-lattice relaxation times and spin diffusion rates have been estimated.     

Suppression of spin relaxation in an InAs nanowire double quantum dot

We investigate the triplet-singlet relaxation in a double quantum dot defined by top gates in an InAs nanowire. In the Pauli spin blockade regime, the leakage current can be mainly attributed to spin relaxation. While at weak and strong interdot coupling relaxation is dominated by two individual mechanisms, the relaxation is strongly reduced at intermediate coupling and finite magnetic field. In addition we observe a characteristic bistability of the spin-nonconserving current as a function of magnetic field. We propose a model where these features are explained by the polarization of nuclear spins enabled by the interplay between hyperfine and spin-orbit mediated relaxation.     

Collective relaxation of nuclear spins and “superradiance” of magnons in ferromagnets

The Heisenberg model of ferromagnet, which contains nuclear spins interacting with electronic spins of own atoms by means of hyperfine interaction, is considered. A nonlinear evolution equation for collective nuclear spin z-component is obtained for the initial condition with the inverted nuclear spins (of the value 1/2). The exact solution of this equation is obtained. The collective relaxation of nuclear spins reveals the cooperative behaviour of superradiant type accompanied by magnons generation.     

Effects of magic-angle spinning on spin-lattice relaxations in talc

The spin-lattice relaxation times T₁ of ¹H and ²⁹Si spins in talc have been measured at room temperature with and without magic-angle spinning (MAS) of the sample. Paramagnetic impurities work as relaxation centers. ¹H T₁ depends on the spinning rate, whereas ²⁹Si T₁ is independent of the spinning rate. These facts demonstrate that spin diffusion plays an important role in ¹H relaxation but not in ²⁹Si relaxation. ²⁹Si spins relax through dipole-dipole interactions with electron spins directly, which mechanism is not affected by spinning. The relaxation rates have been analyzed theoretically.     

Consequence of reputation in the Sznajd consensus model

In this work we study a modified version of the Sznajd sociophysics model. In particular we introduce reputation, a mechanism that limits the capacity of persuasion of the agents. The reputation is introduced as a score which is time-dependent, and its introduction avoid dictatorship (all spins parallel) for a wide range of parameters. The relaxation time follows a log-normal-like distribution. In addition, we show that the usual phase transition also occurs, as in the standard model, and it depends on the initial concentration of individuals following an opinion, occurring at a initial density of up spins greater than 1/2. The transition point is determined by means of a finite-size scaling analysis.     

Anisotropic spin relaxation in graphene

Spin relaxation in graphene is investigated in electrical graphene spin valve devices in the nonlocal geometry. Ferromagnetic electrodes with in-plane magnetizations inject spins parallel to the graphene layer. They are subject to Hanle spin precession under a magnetic field B applied perpendicular to the graphene layer. Fields above 1.5 T force the magnetization direction of the ferromagnetic contacts to align to the field, allowing injection of spins perpendicular to the graphene plane. A comparison of the spin signals at B=0 and B=2 T shows a 20% decrease in spin relaxation time for spins perpendicular to the graphene layer compared to spins parallel to the layer. We analyze the results in terms of the different strengths of the spin-orbit effective fields in the in-plane and out-of-plane directions and discuss the role of the Elliott-Yafet and Dyakonov-Perel mechanisms for spin relaxation.     

Probing pores using elementary quantum mechanics.

The relaxation of polarized spins in a porous medium has been utilized as a probe of its structure. We note that the governing diffusion problem has a close parallel to that of a particle in a box, an elementary Quantum mechanics toy model. Following the spirits of "free electron" model, we use generic properties of the eigen spectrum to understand features common to a wide variety of pore geometry, consistent with large scale numerical simulations and experimental data.     

Long-lived states in solution NMR: theoretical examples in three- and four-spin systems

Long-lived spin states have been observed in a variety of systems. Although the dynamics underlying the long lifetimes of these states are well understood in the case of two-spin systems, the corresponding dynamics in systems containing more spins appear to be more complex. Recently it has been shown that a selection rule for transitions mediated by intramolecular dipolar relaxation may play a role in determining the lifetimes of long-lived states in systems containing arbitrary numbers of spins. Here we present a theory of long-lived states in systems containing three and four spins and demonstrate how it can be used to identify states that have little or no intramolecular dipolar relaxation.     

Evolution of solid state systems containing mutually coupled dipolar and quadrupole spins: perturbation treatment

Perturbation approach to time evolution of multi-spin systems containing quadrupole and dipolar spins has been presented and discussed. The treatment comprises polarization transfer effects, field-dependent relaxation processes of dipolar as well as quadrupole spins and combined results of both of them. Complete theories dealing with various aspects of the spin dynamic processes have been proposed. Because of an educational character of this paper, relevant assumptions, limitations and even particular steps of the proposed treatments have been discussed in detail. Special emphasis is put on understanding of validity regimes of the perturbation treatment, depending on relative strengths of spin interactions and timescales of relevant motional processes affecting them. Motional regimes required for spins to be involved in essentially different evolution pathways like polarization transfers or relaxation have been illustrated by experimental examples.     

Theoretical Study of Dipolar Relaxation of Coupled Nuclear Spins at Variable Magnetic Field

A theoretical study was made of magnetic field-dependent dipolar relaxation in two- and three-spin systems. The results for the nuclear magnetic relaxation dispersion (NMRD) curves were compared with those for the simpler model of fluctuating local fields. For both models it was found that at low fields spins tend to relax with a common T ₁-relaxation time. Sharp features in the NMRD curves coming from nuclear spin level anti-crossings are also predicted by both models. However, the simple model fails to describe the behavior of so-called long-lived spin states (LLS). We have studied the LLS as function of magnetic field and molecular geometry and simulated experimental results for the LLS in histidine amino acid obtained at the laboratory of Prof. H.-M. Vieth (Free University Berlin, Germany). In addition, we described polarization transfer in a three-spin system where two spins are protons, which are initially hyperpolarized by para-hydrogen induced polarization (PHIP), while the third spin is a spin ½ hetero-nucleus, which acquires polarization in the course of cross-relaxation.     

The time-dependence of exchange-induced relaxation during modulated radio frequency pulses

The problem of the relaxation of identical spins 1/2 induced by chemical exchange between spins with different chemical shifts in the presence of time-dependent RF irradiation (in the first rotating frame) is considered for the fast exchange regime. The solution for the time evolution under the chemical exchange Hamiltonian in the tilted doubly rotating frame (TDRF) is presented. Detailed derivation is specified to the case of a two-site chemical exchange system with complete randomization between jumps of the exchanging spins. The derived theory can be applied to describe the modulation of the chemical exchange relaxation rate constants when using a train of adiabatic pulses, such as the hyperbolic secant pulse. Theory presented is valid for quantification of the exchange-induced time-dependent rotating frame longitudinal T1rho,ex and transverse T2rho,ex relaxations in the fast chemical exchange regime.     

Lifetimes of the singlet-states under coherent off-resonance irradiation in NMR spectroscopy

Singlet-states |S=(|alphabeta> - |betaalpha>)/sq.rt.2 can be excited in pairs of coupled spins I and S, first by preparing either a non-vanishing zero-quantum coherence I(+)S(-) or a state of longitudinal two-spin order I(z)S(z) and then by applying a coherent radio-frequency (RF) irradiation with a carrier frequency omega(rf) = (Omega(I) + Omega(S))/2 that lies half-way between the chemical shifts of the two spins involved. The life-times T(S) can be much longer than the spin-lattice relaxation time T(1) of longitudinal magnetization, but singlet-states are ultimately relaxed, not only by dipolar interactions between the active spins or with the external spins, but also as a result of a non-vanishing offset Deltaomega = omega(rf) - (Omega(I) + Omega(S))/2 or an insufficient amplitude of the RF irradiation that fails to fulfill the condition omega(1) > DeltaOmega = (Omega(I) - Omega(S)). In this work, the effect of off-resonance irradiation is explored and an approximate formula for the effective relaxation rate of the singlet population is provided on the basis of perturbation theory. The qualitative features of the dependence of the relaxation rate of the singlet population on the offset Deltaomega and on the difference DeltaOmega of the chemical shifts of the two spins are illustrated by comparison with numerical simulations.     

Indirect detection of selective nuclear spin-spin interactions in a hostile environment

We present a number of techniques which may be used to obtain precise values of selective spin-spin interactions between two nuclear spins in a hostile environment. Such an environment may be characterized by very fast relaxation and decoherence, e.g. due to the strong coupling of the two spins of interest to electron spins in their vicinity as well as other nuclei. Here, we used dilute paramagnetic Ce(3+) centers hosted in a single crystal of CaF(2). Selected (19)F internuclear interactions were measured indirectly by applying different electron nuclear double resonance (ENDOR) pulse sequences.     

Theoretical predictions about ENDOR of biradicals in liquid solution

Starting from the equation of motion for the density matrix, ENDOR spectra are computed for a biradical for the first time. The model biradical carries two electronic spins S = 1/2 and two nuclear spins I = 1/2. The relaxation operator is calculated ab initio for three distinct relaxation mechanisms. These mechanisms are the modulation of the isotropic exchange interaction, the hyperfine tensor and the zero-field splitting tensor. The dependence of the ENDOR effect on the amplitudes of the radiofrequency and microwave fields, on the strength of the zero-field splitting tensor, and on the correlation times of the correlation functions is investigated.     

Electron spin relaxation in very diluted CdMnTe quantum wells

Electron spin dephasing is studied by time-resolved Kerr rotation in n-type modulation-doped CdMnTe quantum wells with very dilute Mn content. We find good agreement between measured and calculated electron spin relaxation times, considering relaxation induced by fluctuating exchange field created by the Mn spins, and taking into account inhomogeneous heating of the Mn spins by laser pulses.     

Giant isotope effect in the incoherent tunneling specific heat of the molecular nanomagnet Fe8

Time-dependent specific heat experiments on the molecular nanomagnet Fe8 and the isotopic enriched analogue 57Fe8 are presented. The inclusion of the 57Fe nuclear spins leads to a huge enhancement of the specific heat below 1 K, ascribed to a strong increase in the spin-lattice relaxation rate gamma arising from incoherent, nuclear-spin-mediated magnetic quantum tunneling (MQT) in the ground doublet. Since gamma is found comparable to the expected tunneling rate, the MQT process has to be inelastic. A model for the coupling of the tunneling spins to the lattice is presented. Under transverse field, a crossover from nuclear-spin-mediated to phonon-induced tunneling is observed.     

Intrinsic spin fluctuations reveal the dynamical response function of holes coupled to nuclear spin baths in (In,Ga)As quantum dots

The problem of how single central spins interact with a nuclear spin bath is essential for understanding decoherence and relaxation in many quantum systems, yet is highly nontrivial owing to the many-body couplings involved. Different models yield widely varying time scales and dynamical responses (exponential, power-law, gaussian, etc.). Here we detect the small random fluctuations of central spins in thermal equilibrium [holes in singly charged (In,Ga)As quantum dots] to reveal the time scales and functional form of bath-induced spin relaxation. This spin noise indicates long (400 ns) spin correlation times at a zero magnetic field that increase to ～5 μs as dominant hole-nuclear relaxation channels are suppressed with small (100 G) applied fields. Concomitantly, the noise line shape evolves from Lorentzian to power law, indicating a crossover from exponential to slow [～1/log(t)] dynamics.     

Stabilization of homogeneously precessing domains by large magnetic fields in superfluid 3He-B

We have studied the catastrophic relaxation in superfluid 3He-B as a function of magnetic field for a sample pressure of 31 bars. "Catastrophic relaxation" refers to a novel magnetic relaxation process which rapidly disrupts the homogeneous precession of nuclear spins in NMR experiments on the B phase. The catastrophe was observed through its effect on the evolution of a long-lived coherent dynamic state, the homogeneously precessing domain. Our measurements reveal that the onset of catastrophic relaxation is suppressed to lower temperatures by a strong magnetic field.