Measurement of Dipolar Cross Correlation in Scalar-Coupled Systems

In systems with dipolar relaxation in isotropic phase, it is possible to measure the extent of cross correlation of the fluctuations of two selected dipole–dipole interactions A–M and A–X by selectively exciting and spin-locking the transverse magnetization of spin A. If the system comprises only three spins A, M, and X, the conversion of in-phase magnetization[formula]into doubly antiphase magnetization[formula]during the spin-locking period occurs spontaneously through relaxation. The rate of this conversion is proportional to the spectral density of the cross correlation of the random fluctuations of the dipolar A–M and A–X interactions. In this paper, larger systems, comprising at least a fourth spin K, are investigated. The complexity of the situation is increased, since other forms of three-spin order such as[formula]or[formula]become accessible. Furthermore, this paper addresses the role of scalar couplings, which are a prerequisite for making three-spin order observable, but which are also a source of perturbations, since scalar couplings can contribute significantly to the creation of various three-spin-order terms. If the spin-locking field is too weak compared to the width of the multiplet under investigation, residual scalar interactions lead to the generation of three-spin order. If the spin-locking field is too strong compared to the relative offsets of other “passive” spins, further complications occur. These can be avoided most effectively by using very high static magnetic fields. If coherent contributions to three-spin order can be suppressed or accounted for through simulations, the remaining buildup of three-spin-order terms arising from dipolar cross-correlation effects can be interpreted in terms of structural and motional parameters.     

Magnetic interactions in strongly correlated systems: Spin and orbital contributions

We present a technique to map an electronic model with local interactions (a generalized multi-orbital Hubbard model) onto an effective model of interacting classical spins, by requiring that the thermodynamic potentials associated to spin rotations in the two systems are equivalent up to second order in the rotation angles, when the electronic system is in a symmetry-broken phase. This allows to determine the parameters of relativistic and non-relativistic magnetic interactions in the effective spin model in terms of equilibrium Green’s functions of the electronic model. The Hamiltonian of the electronic system includes, in addition to the non-relativistic part, relativistic single-particle terms such as the Zeeman coupling to an external magnetic field, spin–orbit coupling, and arbitrary magnetic anisotropies; the orbital degrees of freedom of the electrons are explicitly taken into account. We determine the complete relativistic exchange tensors, accounting for anisotropic exchange, Dzyaloshinskii–Moriya interactions, as well as additional non-diagonal symmetric terms (which may include dipole–dipole interaction). The expressions of all these magnetic interactions are determined in a unified framework, including previously disregarded features such as the vertices of two-particle Green’s functions and non-local self-energies. We do not assume any smallness in spin–orbit coupling, so our treatment is in this sense exact. Finally, we show how to distinguish and address separately the spin, orbital and spin–orbital contributions to magnetism, providing expressions that can be computed within a tight-binding Dynamical Mean Field Theory.     

Low-temperature magnetization dynamics of magnetic molecular solids in a swept field

The swept-field experiments on magnetic molecular solids such as Fe₈ are studied using Monte Carlo simulations, and a kinetic equation developed to understand collective magnetization phenomena in such solids, where the collective aspects arise from dipole–dipole interactions between different molecules. Because of these interactions, the classic Landau–Zener–Stückelberg theory proves inadequate, as does another widely used model constructed by Kayanuma. It is found that the simulations provide a quantitatively accurate account of the experiments. The kinetic equation provides a similarly accurate account except at very low sweep velocities, where it fails modestly. This failure is attributed to the neglect of short-range correlations between the dipolar magnetic fields seen by the molecular spins. The simulations and the kinetic equation both provide a good understanding of the distribution of these dipolar fields, although analytic expressions for the final magnetization remain elusive.     

Identification of Spin Diffusion Pathways in Isotopically Labeled Biomolecules

One-dimensional NOE experiments applicable to labeled macromolecules are presented which allow the manipulation of specific spin diffusion pathways and thus unambiguously identify clandestine spins through which the direct NOE is mediated. A treatment of spin diffusion using average Liouvillian theory is shown to describe adequately these phenomena. Experiments are carried out on an 15N-labeled sample of human ubiquitin.     

Ground states of the Triangular Ising model with two-and three-spin interactions

The possible ground state spin configurations of an Ising model on a plane triangular lattice are investigated. The model incorporates competing interactions between spins at nearest and next-nearest neighbour sites as well as a coupling between three spins at the vertices of a nearest-neighbour triangle, and an external magnetic field. Models of this type are frequently used to describe the structures of adsorbate layers on hexagonal substrates. The analysis is based on linear inequalities involving the magnetization, two- and three-spin correlations, and on simple convexity arguments. Part of the inequalities needed are proved with the aid of a computer. For vanishing three-spin coupling the results of earlier studies are confirmed; in addition, the resulting seven topologically distinct structures are shown to be unique. Two of these structures are energetically degenerate; the degeneracy cannot be lifted by any further two-spin interaction. For nonzero three-spin coupling only an almost complete solution is given, involving four additional spin configurations. The ground state phase diagrams are discussed.     

The transient EPR spectra and spin dynamics of coupled three-spin systems in photosynthetic reaction centres

The concept of introducing an additional, stable paramagnetic species into photosynthetic reaction centres to increase the information content of their spin polarized transient EPR spectra is investigated theoretically. The light-induced electron transfer in such systems generates a series of coupled three-spin states consisting of sequential photoinduced radical pairs coupled to the stable spin which acts as an “observer”. The spin polarized transient EPR spectra are investigated using the coupled three-spin system P⁺I⁻Q⁻ _A in pre-reduced bacterial reaction centres as a specific example which has been studied experimentally. The evolution of the spin system and the spin polarized EPR spectra of P⁺I⁻Q⁻ _A and Q⁻ _A following recombination of the radical pair (P = primary donor, I = primary acceptor, Q_A = quinone acceptor) are calculated numerically by solving the equations of motion for the density matrix. The net polarization of the observer spin is also calculated analytically by perturbation theory for the case of a single, short-lived, charge-separated state. The result bears a close resemblance to the chemically induced nuclear polarization (CIDNP) generated in photolysis reactions in which a nuclear spin plays the role of the observer interacting with the radical pair intermediates. However, because the Zeeman frequencies of the three electron spins involved are usually quite similar, the polarization of the electron observer spin in strong magnetic fields can reflect features of the CIDNP effect in both, high and low magnetic fields. The dependence of the quinone spin polarization on the exchange couplings in the three-spin system is investigated by numerical simulations, and it is shown that the observed emissive polarization pattern is compatible with either sign, positive or negative, for a range of exchange couplings, J_PI, in the primary pair. The microwave frequency and orientation dependence of the spectra are discussed as two of several possible criteria for determining the sign of J_PI.     

Theoretical progress in many-body physics with ultracold dipolar gases

Recent experimental progress in trapping and cooling of molecular gases boosts interest in the interdisciplinary field of quantum gases with dominant dipole–dipole interactions. An unprecedented level of experimental control together with specific physical properties of dipole–dipole interaction provide a unique possibility to find new physical phenomena and practical applications.     

Steady state and transient Overhauser effect in systems of three spins

The rate equations describing spin polarization in a system of three spins are derived and solved for the case of a free radical dissolved in a solvent containing two nuclear spins. Triple irradiation experiments indicate that a nuclear spin A can be effectively coupled to an electron spin C via a second nuclear spin B and measurements of both the steady state and transient Overhauser effects are in accord with the theoretical predictions for a three-spin system. The ‘three spin effect’ is found to operate only in dilute solutions of free radicals in which case the probabilities for transitions between different nuclear or electronic energy levels can be determined. It was found to be effective for fluorine nuclei—in the presence of both protons and a free radical and for carbon [13] nuclei in the presence of either protons or fluorine nuclei and a free radical. Detailed measurements have been performed for CHFCl₂, para-difluorobenzene, and meta-fluorotoluene containing the tritertiary butyl phenoxyl radical.     

Generation of non-equilibrium thermal quantum discord and entanglement in a three-spin XX chain by multi-spin interaction and an external magnetic field

The generation of non-equilibrium thermal quantum discord and entanglement is investigated in a three-spin chain whose two end spins are respectively coupled to two thermal reservoirs at different temperatures. We show that the spin chain can be decoupled from the thermal reservoirs by homogeneously applying a magnetic field and including a strong three-spin interaction, and then the maximal steady-state quantum discord and entanglement in the two end spins can always be created. In addition, the present investigation may provide a useful approach to control coupling between a quantum system and its environment.     

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.     

13C spin-lattice relaxation in natural diamond: Zeeman relaxation at 4.7 T and 300 K due to fixed paramagnetic nitrogen defects

13C spin-lattice relaxation times in the laboratory frame, ranging from 1.4 to 36 h, have been measured on a suite of five natural type Ia and Ib diamonds at 4.7 T and 300 K. Each of the diamonds contains two types of fixed paramagnetic centers with overlapping inhomogeneous electron paramagnetic resonance (EPR) lines. EPR techniques have been employed to identify these defects and to determine their concentrations and relaxation times at X-band. Spin-lattice relaxation behavior of 13C in diamonds containing paramagnetic P1, P2, N2. and N3 centers are discussed. Depending on the paramagnetic impurity types and concentrations present in each diamond, three different nuclear spin-lattice relaxation (SLR) paths exist, namely that due to electron SLR mechanisms and two types of three-spin processes (TSPs). The one three-spin process (TSP1) involves a simultaneous transition of two electron spins belonging to the same hyperfine EPR line and a flip of a 13C spin, while the other process (TSP2) involves two electron spins belonging to different hyperfine EPR lines and a 13C spin. It is shown that the thermal contact between the 13C nuclear Zeeman and electron dipole-dipole interaction reservoirs is field dependent, thus forming a bottleneck in the 13C relaxation path due to TSP1 at high magnetic fields.     

Electron Spin–Nuclear Spin Cross-Correlation Effects on Multiplet Splittings in Paramagnetic Proteins

The effects of cross-correlation between Curie spin–nuclear dipole and nuclear dipole–nuclear dipole interactions on the linewidths and resonance frequencies of the individual lines of anAXmultiplet in paramagnetic systems have been calculated. The implication of the relaxation-induced frequency shift of the lines (dynamic frequency shift) for the accurate measurement of residual dipolar couplings in field-oriented systems has been discussed. Our simulations indicate that these effects may play a role in the precise measurement of residual dipolar couplings in systems which belong to the small and intermediate tumbling regime, i.e., correlation times less than 5 ns.     

Dipolar Order in Molecular Fluids: II. Molecular Influence

The influence on the short-range packing in dipolar fluids by molecular shape and by additional higher order electrostatic moments has been investigated by molecular dynamic simulations. The dipole polarization was found to decrease as the particles were elongated parallel to the dipole and to increase for elongation perpendicular to the dipole, eventually forming a nematic order. The addition of a quadrupole lead to a reduction of the polarization, and the influence of an axial octupole was weaker and more complex. Both a decrease and an increase of the polarization is possible depending on the relative dipole–dipole and octupole–octupole interaction strengths and the relative direction of the symmetry axes of the moments. These observations were attributed to the different parity of a dipole and a quadrupole and the same parity of a dipole and an axial octupole under reflection. In addition, further insights into the formation of dipole polarization were obtained. Short polar and long equatorial radii and strong dipole–dipole interaction are particle properties that promote a fluid with a high dipole polarization.     

13C spin-lattice relaxation in natural diamond: Zeeman relaxation in fields of 500 to 5000 G at 300 K due to fixed paramagnetic nitrogen defects

¹³C Spin–lattice relaxation (SLR) times in the laboratory frame have been measured at room temperature as a function of field in the range of 500 to 5000 G on two natural type Ib and Ia diamonds after dynamic nuclear polarization. Each of the diamonds contains two types of fixed paramagnetic centers with overlapping inhomogeneous electron paramagnetic resonance (EPR) lines. EPR techniques have been employed to identify these defects and to determine their concentrations and relaxation times at X-band. Three different nuclear SLR paths, namely that due to electron SLR and two types of three spin processes, are discussed. The one three-spin process (TSP) (type 1) involves a simultaneous transition of two electron spins belonging to the same hyperfine EPR line and a ¹³C spin while the other process (type 2) involves two electron spins belonging to different hyperfine EPR lines and a ¹³C spin. It is shown that the thermal contact between the ¹³C nuclear Zeeman and electron dipole–dipole interaction reservoirs decreases with an increase in field intensity, thus forming a bottleneck in the ¹³C relaxation path due to the type 1 TSP. The contribution of TSP of type 1 dominates that due to electron SLR and the type 2 TSP in relaxing the ¹³C nuclei in type Ib diamond from about 1200 to 5000 G, while for type Ia diamond it dominates from 500 up to about 2200 G. In type Ia diamond over the range 2200 to 5000 G it seems that the type 2 TSP, which involves electrons of neighboring P2 hyperfine lines, dominates that of electron spin–lattice and the type 1 TSP. Over the range 500 to about 1200 G, a field-dependent electron SLR mechanism associated with N3 centers appears to dominate the ¹³C SLR.     

Multispin coherences and asymptotic similarity of time correlation functions in solids

The time evolution of multispin (n-particle) correlations in solids (the growth in the number of correlated states) observed by means of multiquantum NMR spectroscopy has been investigated. The contributions from the spins of the immediate environment of each of the spins in the lattice to the time correlation functions that describe this evolution are shown to be mutually asymptotically similar. In this case, the infinite system of coupled ordinary differential equations for the time correlation functions turns out to be equivalent to a diffusion-type partial differential equation with a purely imaginary diffusion coefficient. Its analytical solution has been obtained. It is concluded that the evolution of multispin correlations is probably attributable to multiparticle processes among the spins of a “distant” (with respect to some spin) environment similar to the processes that shape the NMR absorption line wings.     

Three-spin correlation of the Ising model on the generalized checkerboard lattice

The Ising model on the generalized checkerboard lattice is studied and the three-spin correlation function is obtained for the three nodal spins surrounding a unit cell of the checkerboard lattice. As an application of this result, the spontaneous magnetization of the internal spin within a unit cell is calculated.     

Ferromagnetic resonance investigation of collective phenomena in two-dimensional periodic arrays of Co particles

The ferromagnetic resonance (FMR) method is used to study the collective phenomena in two-dimensional periodic arrays of disk-shaped Co particles. A study of geometrically similar structures with different periods reveals a broadening of the FMR resonance lines due to the excitation of additional size-dependent non-uniform spin waves. It is shown that these collective spin-wave modes are based on dipole–dipole interactions between the ferromagnetic particles in the array. Qualitative and quantitative data on magnetic interparticle interactions can thus be obtained from FMR spectra for two-dimensional periodic arrays of ferromagnetic particles. PACS 73.21.-b, 75.75.+a, 76.50.+g     

Correction of spin diffusion during iterative automated NOE assignment

Indirect magnetization transfer increases the observed nuclear Overhauser enhancement (NOE) between two protons in many cases, leading to an underestimation of target distances. Wider distance bounds are necessary to account for this error. However, this leads to a loss of information and may reduce the quality of the structures generated from the inter-proton distances. Although several methods for spin diffusion correction have been published, they are often not employed to derive distance restraints. This prompted us to write a user-friendly and CPU-efficient method to correct for spin diffusion that is fully integrated in our program ambiguous restraints for iterative assignment (ARIA). ARIA thus allows automated iterative NOE assignment and structure calculation with spin diffusion corrected distances. The method relies on numerical integration of the coupled differential equations which govern relaxation by matrix squaring and sparse matrix techniques. We derive a correction factor for the distance restraints from calculated NOE volumes and inter-proton distances. To evaluate the impact of our spin diffusion correction, we tested the new calibration process extensively with data from the Pleckstrin homology (PH) domain of Mus musculus beta-spectrin. By comparing structures refined with and without spin diffusion correction, we show that spin diffusion corrected distance restraints give rise to structures of higher quality (notably fewer NOE violations and a more regular Ramachandran map). Furthermore, spin diffusion correction permits the use of tighter error bounds which improves the distinction between signal and noise in an automated NOE assignment scheme.     

Spin–Spin Interactions and Nuclear Magnetic Relaxation in Magnetic Solids

The influence of the orientational fluctuations of the electronic magnetization, which modulate nuclear spin–spin interactions (Suhl–Nakamura and dipole–dipole), on the spin-lattice relaxation of magnetic nuclei with spin I = 1/2 in the magnetically ordered solids has been investigated. It has been shown that this mechanism of the spin-lattice relaxation is less effective in comparison with the process of spin-lattice relaxation caused by the direct fluctuations of hyperfine fields, which appear when there are the fluctuations of electronic magnetization direction.     

Switching mechanism due to the spontaneous emission cancellation in photonic band gap materials doped with nano-particles

We have investigated the switching mechanism due to the spontaneous emission cancellation in a photonic band gap (PBG) material doped with an ensemble of four-level nano-particles. The effect of the dipole–dipole interaction has also been studied. The linear susceptibility has been calculated in the mean field theory. Numerical simulations for the imaginary susceptibility are performed for a PBG material which is made from periodic dielectric spheres. It is predicted that the system can be switched between the absorbing state and the non-absorbing state by changing the resonance energy within the energy bands of the photonic band gap material.