A theoretical and numerical consideration of the longitudinal and transverse relaxations in the rotating frame

We previously derived a simple equation for solving time-dependent Bloch equations by a matrix operation. The purpose of this study was to present a theoretical and numerical consideration of the longitudinal (R_1ρ = 1/T_1ρ) and transverse relaxation rates in the rotating frame (R_2ρ = 1/T_2ρ), based on this method. First, we derived an equation describing the time evolution of the magnetization vector (M(t)) by expanding the matrix exponential into the eigenvalues and the corresponding eigenvectors using diagonalization. Second, we obtained the longitudinal magnetization vector in the rotating frame (M_1ρ(t)) by taking the inner product of M(t) and the eigenvector with the smallest eigenvalue in modulus, and then we obtained the transverse magnetization vector in the rotating frame (M_2ρ(t)) by subtracting M_1ρ(t) from M(t). For comparison, we also computed the spin-locked magnetization vector. We derived the exact solutions for R_1ρ and R_2ρ from the eigenvalues, and compared them with those obtained numerically from M_1ρ(t) and M_2ρ(t), respectively. There was excellent agreement between them. From the exact solutions for R_1ρ and R_2ρ, R_2ρ was found to be given by R_2ρ = (2R₂ + R₁)/2 − R_1ρ/2, where R₁ and R₂ denote the conventional longitudinal and transverse relaxation rates, respectively. We also derived M_1ρ(t) and M_2ρ(t) for bulk water protons, in which the effect of chemical exchange was taken into account using a 2-pool chemical exchange model, and we compared the R_1ρ and R_2ρ values obtained from the eigenvalues and those obtained numerically from M_1ρ(t) and M_2ρ(t). There was also excellent agreement between them. In conclusion, this study will be useful for better understanding of the longitudinal and transverse relaxations in the rotating frame and for analyzing the contrast mechanisms in T_1ρ- and T_2ρ-weighted MRI.     

The influence of spin-flip scattering on the preparation and detection of a single spin state in a quantum dot attached to a spin battery

Recently, the possibility of an all electrical scheme of preparation and readout for a single spin state in a single quantum dot attached to spin biased leads has been shown [F. Chi et al. Phys. Rev. B 81, 075310 (2010)]. However, spin scattering mechanisms have been omitted. To remedy this lack we consider the influence of the spin-flip scattering process on the proposed preparation and readout scheme.     

TOWARDS DEEP AND SIMPLE UNDERSTANDING OF THE TRANSCENDENTAL EIGENPROBLEM OF STRUCTURAL VIBRATIONS

When using exact methods for undamped free vibration problems the generalized linear eigenvalue problem (K−ω²M) D=0 of approximate methods, e.g., finite elements, is replaced by the transcendental eigenvalue problem K (ω) D=0. Here ω is the circular frequency; D is the displacement amplitude vector; M and K are the mass and static stiffness matrices; and K (ω) is the dynamic stiffness matrix, with coefficients which include trigonometric and hyperbolic functions involving ω and mass because elements (for example, bars or beams) are analyzed exactly by solving their governing differential equations. The natural frequencies of this transcendental eigenvalue problem are generally found by the Wittrick-Williams algorithm which gives the number of natural frequencies below ω_t, a trial value of ω, as ∑J_m+s{K (ω_t)} wheres {} denotes the readily computed sign count property of K (ω) and the summation is over the clamped-clamped natural frequencies of all elements of the structure. Understanding the alternative solution forms of the transcendental eigenvalue problem is important both to accelerate convergence to natural frequencies, e.g., by plotting ∣K (ω)∣, and to improve the mode calculations, which lack the complete reliability of natural frequencies obtained by using the Wittrick-Williams algorithm. The three solution forms are: ∣K (ω)∣=0; D=0 with ∣K (ω)∣→∞; and ∣K (ω)∣≠0 with D≠0. The literature covers the first two forms thoroughly but the third form has been almost totally ignored. Therefore, it is now examined thoroughly, principally by analytical studies of simple bar structures and also by confirmatory numerical results for a rigidly jointed plane frame. Although structures are unlikely to have exactly the properties giving this form, it needs to be understood, particularly because ill-conditioning can occur for structures approximating those for which it occurs.     

Spin gauge fields: From Berry phase to topological spin transport and Hall effects

The paper examines the emergence of gauge fields during the evolution of a particle with a spin that is described by a matrix Hamiltonian with n different eigenvalues. It is shown that by introducing a spin gauge field a particle with a spin can be described as a spin multiplet of scalar particles situated in a non-Abelian pure gauge (forceless) field U (n). As the result, one can create a theory of particle evolution that is gauge-invariant with regards to the group Uⁿ (1). Due to this, in the adiabatic (Abelian) approximation the spin gauge field is an analogue of n electromagnetic fields U (1) on the extended phase space of the particle. These fields are force ones, and the forces of their action enter the particle motion equations that are derived in the paper in the general form. The motion equations describe the topological spin transport, pumping, and splitting. The Berry phase is represented in this theory analogously to the Dirac phase of a particle in an electromagnetic field. Due to the analogy with the electromagnetic field, the theory becomes natural in the four-dimensional form. Besides the general theory, the article considers a number of important particular examples, both known and new.     

Energy, momentum, and force in classical electrodynamics: Application to negative-index media

The classical theory of electromagnetism is based on Maxwell's macroscopic equations, an energy postulate, a momentum postulate, and a generalized form of the Lorentz law of force. These seven postulates constitute the foundation of a complete and consistent theory, thus eliminating the need for physical models of polarization P and magnetization M — these being the distinguishing features of Maxwell's macroscopic equations. In the proposed formulation, P(r, t) and M(r, t) are arbitrary functions of space and time, their physical properties being embedded in the seven postulates of the theory. The postulates are self-consistent, comply with special relativity, and satisfy the laws of conservation of energy, linear momentum, and angular momentum. The Abraham momentum density p_EM(r,t) = E(r,t) × H(r,t) / c² emerges as the universal electromagnetic momentum that does not depend on whether the field is propagating or evanescent, and whether or not the host media are homogeneous, transparent, isotropic, linear, dispersive, magnetic, hysteretic, negative-index, etc. Any variation with time of the total electromagnetic momentum of a closed system results in a force exerted on the material media within the system in accordance with the generalized Lorentz law.     

Organic radical molecular solids based on [(TCNQ)n] (n=1 or 2): Syntheses, crystal structures, magnetic properties and DFT analyses

Four molecular solids consisting of the 7,7,8,8-tetracyanoquinodimethane (TCNQ) radical and benzylpyridinium or benzylquinolinium derivatives with molar ratios of 1:1 (1-3) and 2:1 (4) have been prepared and characterized. In the crystals of 1 and 3, TCNQ⁻ monoanions and the corresponding cations form segregated stacks, which are regular in 1 but irregular in 3. Instead of segregated stacks, TCNQ⁻ monoanions in 2 form isolated π-dimers. In the crystals of 4, two crystallographic independent TCNQ species possess almost equal fractional negative charge (ca. −0.5). Two types of TCNQ species form a tetrad, these tetrads make a TCNQ stack with the pattern …BAAB…BAAB… along the crystallographic a-b direction. The magnetisms for 1-4 can be simply explained by the formation of singlet spin state. A broken symmetry approach in a density functional theory framework at the ub3lyp/6-31 g level was used to calculate the magnetic exchange constants in 1-4. The results qualitatively demonstrate the observed magnetic properties.     

Eu(III) and Tb(III) luminescent lanthanide systems derived from DTPA-bisamide and DTTA-based ligands incorporating bipyridine antenna

Four new polycarboxylate ligands H₃Lⁿ have been synthesized by the attachment of two or one 2,2′-bipyridine subunits onto a diethylenetriamine pentacarboxylic acid (DTPA-bisamide derivatives: H₃L¹, H₃L²) or a diethylenetriamine tricarboxylic acid (DTTA derivatives: H₃L³, H₃L⁴) core. The neutral Eu^III and Tb^III complexes of these chelates have been prepared and studied from their UV-vis and luminescence data. The main photophysical characteristics of these complexes, i.e. the absorption and luminescence spectra, the metal-centred lifetimes and the overall luminescence yields (Φ) were measured in buffered aqueous solutions. In addition the role played by non-radiative paths (vibrational energy transfer involving coordinated water molecules, involvement of ligand-to-metal charge-transfer excited states, or metal→ligand back-transfer) was investigated. In all complexes, we found that the bidentate bipyridine chromophore is not coordinated to the lanthanide ion, allowing one (LnL¹, LnL²) or two (LnL³, LnL⁴) water molecules to penetrate the first coordination sphere of the metal. Although the bipyridine chromophore behaves as remote (from the binding site) light-harvesting unit for the lanthanide ion in these systems, a sizeable sensitization of the Eu- and Tb-centred luminescence can be effective (LnL², LnL³, Φ=16-19% in aerated D₂O solutions). Our photophysical investigations show that overall non-radiative deactivation is not dependant of thermally activated non-radiative channels but the efficiency of the ligand→Ln intramolecular energy transfer has to be taken into account to explain the obtained results.     

Suppression of spin beats in magneto-oscillation phenomena in two-dimensional electron gas

Theory of magneto-oscillation phenomena has been developed for two-dimensional electron systems with linear-in-k spin splitting. Both Dresselhaus and Rashba contributions are taken into account. It has been shown that the pattern of the magneto-oscillations depends drastically on the ratio between the above terms. The presence of only one type of the k-linear terms gives rise to the beats, i.e. two close harmonics corresponding to the spin-split subbands. However, if the strengths of both contributions are comparable, the third (central) harmonic appears in the spectrum of the magneto-oscillations. For equal strengths of the contributions, only the central harmonic survives, and the oscillations occur at a single frequency, although the k-linear terms remain in the Hamiltonian. Such suppression of the spin beats is studied in detail by the example of the Shubnikov-de Haas effect.     

Surface-modification of TiO2 with new metalloporphyrins and their photocatalytic activity in the degradation of 4-notrophenol

A new mono-functionalized porphyrin derivative, 5-mono-[4-(2-(4-hydroxy)-phenoxy)ethoxy]-10,15,20-triphenylporphyrin (3) and its Cu(II) (3a), Zn(II) (3b) and Ni(II) (3c) metalloporphyrins were synthesized and characterized by using various spectroscopic techniques. The corresponding 3a, 3b, 3c-TiO₂ photocatalysts were then prepared and characterized by means of FT-IR and diffused reflectance spectra, X-ray diffraction (XRD) and scanning electron microscopy (SEM). The photocatalytic activities of 3a, 3b, 3c-TiO₂ were investigated by testing the photodegradation of 4-nitrophenol (4-NP) in aqueous solution under the halogen lamp irradiation. The results indicated that all the 3a, 3b, 3c enhanced the photocatalytic efficiency of bare TiO₂ in photodegrading the 4-NP, and 3a-TiO₂ exhibited the highest photocatalytic activity. The result is considered a combined action of potential match of 3a with TiO₂ CB and effective impregnated of 3a onto the surface of TiO₂.     

Spectroscopic and thermodynamic features of conical bubble luminescence

The influence on luminescence from conical bubble collapse (CBL) with varying Ar gas content while perturbing the liquid 1,2-Propanediol (PD) has been investigated. The temporal, spatial, and spectral features were analysed with regards to the dynamics of collapse and liquid degradation. Sulphuric acid and sodium chloride were added to disturb the liquid. The following three cases were studied: PD/Ar, (I), (PD + H₂SO₄)/Ar, (II), and (PD + H₂SO₄ + NaCl)/Ar, (III). The intensities of those cases decrease as III > II > I. Temporally, single and multiple light emissions were found to occur. The pulse shape exhibited a large variety of profiles with a main maximum and up to two local maxima around the main maximum. These local maxima resembled those generated by laser cavitation. Spatially, no radial symmetry was detected in the light emissions. Spectrally, the Swan, CH and CN lines were observed at low volumes of gas and driving pressure. The OH radical and OH-Ar bands, as well as the Na and K lines, consistently appeared superimposed on an underlying continuum that almost disappeared in (III). The Na line was observed with two satellite diffuse bands representing Na-Ar complexes in (I) and (II), whereas in (III), only the line of sodium could be seen. Weak and diffuse emission lines from the Ar atom in the near-IR region were observed in (I) and (II).The proposed mechanism of bright CBL was based on the energy transfer from electron-excited homolytic cleavage products to the chromophore molecules generated during the collapse-rebound time line (∼8200 K and ∼1 ms of collapse time from model), which had accumulated inside the liquid and remained on the walls of cavity during the repetition of the collapse. A general mechanism for the bright CBL is broached.     

The synthesis and photophysical properties of novel cationic tetra pyridiloxy substituted aluminium, silicon and titanium phthalocyanines in water

This work reports on the synthesis, characterisation and photophysical properties of new unquaternized β-2,(3)-tetra-(2 pyridiloxy) aluminium(III) (3a), silicon(IV) (3b), titanium(IV) (3c) phthalocyanines and their water-soluble quaternized counterparts, 4a, 4b and 4c, respectively. The water-soluble silicon(IV) (4b) and titanium(IV) (4c) phthalocyanine derivatives were found to be aggregated in aqueous media but were partially or fully disaggregated in the presence of a surfactant Cremophor^® EL (CEL). The photophysical properties of aggregated complexes were investigated both in the presence of CEL and in pH 11 alone. Low triplet and fluorescence yield were obtained in pH 11 but an improvement was achieved upon addition of CEL for the aggregated complexes. The unquaternized silicon(IV) phthalocyanine complex (3b) gave the highest triplet quantum yield of 0.77 in DMF followed by its quaternized derivative (4b) with triplet yield of 0.73 in pH 11 plus CEL. The highest triplet lifetime of 220 μs was obtained for 4b in the presence of CEL. Higher fluorescence yields of 0.23 were obtained for quaternized water-soluble aluminium(III) phthalocyanine derivative (4a) in the presence of CEL.     

Supramolecular selectivity of [60]-fullerene among equivalently photoactive porphyrins

The photophysical investigation of different para-substituted tetraphenylporphyrins (TP), viz., meso-tetra(4′-hydroxyphenyl)-21H-23H-porphyrin(1),meso-tetrakis(4′-hex-5-enyloxyphenyl)-21H-23H-porphyrin(2), meso-tetrakis(4′-oct-7-enyloxyphenyl)-21H-23H-porphyrin(3) and meso-tetrakis(4′-undecyloxyphenyl)-21H-23H-porphyrin (4) revealed that except for quantum yield (φ) the para-substitution has little effect on any other photophysical properties like lifetime, excitation, emission wavelength, etc. The host-guest type interactions of these tetraarylporphyrins (TP 1-4), with [60]-fullerene (F) have been studied with ¹H NMR and fluorescence spectrometric techniques in carbon tetrachloride medium. Fluorescence studies revealed that the Q band of the TPs was sufficiently quenched upon addition of F. All the fullerene/porphyrin systems were found to produce stable complexes with 1:1 stoichiometry. Binding constants (K) of all the fullerene/porphyrin complexes have been determined by fluorescence quenching method. The association constant values for 1/F have been determined from plots of the Stern-Volmer equation (103.713×10⁴) and the Benesi-Hildebrand equation (110.440×10⁴). It has been observed that the insertion of long chain oxo-alkenyl/alkyl group in the para position of TPs in 2, 3 and 4 diminished the K values for F by two, four and even ten times with respect to that of 1. The observed trend in variation of the binding constants was supported by a gradual variation in the shift of ¹H NMR signal when measurements were carried out in CDCl₃.     

Photophysical properties of a series of high luminescent europium complexes with fluorinated ligands

A series of high luminescent europium complexes have been synthesized, such as Eu(TFNB)₃phen (1), Eu(PFNP)₃phen (2), Eu(HFNH)₃phen (3) and Eu(PFND)₃phen (4), which have β-diketone ligands containing fluorinated alkyl chains with different lengths and conjugated naphthyl groups, i.e., 4,4,4-trifluoro-1-(2-naphthyl)butane-1,3-dione (TFNB); 4,4,5,5,5-pentafluoro-1-(2-naphthyl)pentane-1,3-dione (PFNP); 4,4,5,5,6,6,6-heptafluoro-1-(2-naphthyl)hexane-1,3-dione (HFNH) and 4,4,5,5,6,6,7,7,8,8,9,9,10,10,10-pentadecafluoro-1-(2-naphthyl)decane-1,3-dione (PFND). And 10-phenanthroline (phen) is coordinated as the neutral second ligand in 1-4. The crystal structures of 1 and 2 have been studied, which are typical and similar to that of 3. The results of TGA-DTA suggest that these Eu complexes have good thermal stabilities. By means of absorption and (time resolved) emission spectroscopy including determination of luminescence quantum yields, energy transfer dynamics and so on, the following results have been obtained: first, these Eu complexes show characteristic pure red color photoluminescence emission with high quantum efficiencies from the central Eu³⁺ ions through the excitation of the ligands; secondly, photophysical properties of 1, 2, 3 and 4, especially the lifetimes of excited states ⁵D₀ of Eu³⁺ ions and quantum efficiencies are influenced by the different lengths of fluorinated alkyl chains, though the singlets (S₁) and triplets (T₁) of the fluorinated ligands are almost the same.     

An explicit derivation of a relation between magnetization M and saturation magnetization Ms

An explicit relationship between a magnetization vector M and its saturation magnetization M_s is derived using the definition of M along with assumptions of the continuum exchange theory. The obtained expression is found to be an extension of the commonly used fixed-length constraint and represents the continuous analog of it for the elementary moment per unit volume. The derivation of this relation is carried out in detail and important potential implications relating to equations for M are also highlighted.     

Probing spatial correlations in the inhomogeneous glassy state of the cuprates by Cu NMR

We discuss the crossover of the form of the Cu Nuclear magnetic resonance (NMR) spin echo decay at the onset of Cu wipeout in lanthanum cuprates. Experimentally, the echo decay undergoes a crossover from Gaussian to exponential form below the temperature where the Cu NMR intensity drops. The wipeout and the change in behavior both arise because the nuclei experience spatially inhomogeneous spin fluctuations at low temperatures. We argue that regions where the spin fluctuations remain fast are localized on length scales of order 1-2 lattice spacings. The inhomogeneity is characterized by the local activation energy E_a(r); we estimate the functional form of E_a(r) for points where E_a>(r)∼0.     

Easy axis reorientation and magneto-crystalline anisotropic resistance of tensile strained (Ga,Mn)As films

We present a study of magnetic anisotropy by using magneto-transport and direct magnetization measurements on tensile strained (Ga,Mn)As films. The magnetic easy axis of the films is in-plane at low temperatures, while the easy axis flips to out-of-plane when temperature is raised or hole concentration is increased. This easy axis reorientation is explained qualitatively in a simple physical picture by Zener’s p-d model. In addition, the magneto-crystalline anisotropic resistance was also investigated experimentally and theoretically based on the single magnetic domain model. The dependence of sheet resistance on the angle between the magnetic field and [1 0 0] direction was measured. It is found that the magnetization vector M in the single-domain state deviates from the external magnetic field H direction at low magnetic field, while for high magnetic field, M continuously moves following the field direction, which leads to different resistivity function behaviors.     

Sensitized luminescence properties of dinuclear lanthanide macrocyclic complexes bearing a benzophenone antenna

Dinuclear lanthanide (Ln=Tb³⁺ or Eu³⁺) complexes (Ln₂L2) of two octadentate macrocyclic polyaminopolycarboxylic ligands connected through a benzophenone (BP) moiety (L2) have been synthesized. Sensitized luminescence properties of Ln₂L2 in water have been studied in comparison to those of BP-conjugated mononuclear Ln complexes (LnL1). The luminescence intensity of Tb₂L2 is lower than that of TbL1 because of lower triplet quantum yield of the BP moiety. In contrast, Eu₂L2 shows higher intensity than EuL1. For both Eu complexes, energy level of triplet excited-state BP (³BP*) is only 3 kJ mol⁻¹ higher than that of ⁵D₂ excited-state of Eu³⁺. The ⁵D₂ state formed by a triplet-energy transfer (TET) from ³BP* is therefore deactivated by a back energy transfer (BET) to the ground-state BP, resulting in low luminescence intensity of EuL1. In contrast, within Eu₂L2, TET from ³BP* to ⁵D₀ state of two Eu³⁺ ions is accelerated, thus leading to higher luminescence intensity. Another notable feature of Eu₂L2 is the luminescence quantum yield independent of its concentration. In contrast, for EuL1 system, an intermolecular BET occurs from ⁵D₂ state of Eu³⁺ to the ground-state BP conjugated to another EuL1 complex, resulting in a yield decrease with the concentration increase.     

Spin susceptibility of cuprates in the model of a 2D frustrated antiferromagnet: Role of renormalization of spin fluctuations in describing neutron experiments

Experimental data on the spin susceptibility of HTSC cuprates are reproduced on the basis of a spherically symmetric approach in the frustrated Heisenberg model. The inclusion of real and imaginary renormalizations in spin Green’s functions makes it possible to explain the evolution of spin excitation spectrum ω(q) and susceptibility spectrum χ(q, ω) in the range from insulator to optimal doping. In the low-frustration limit corresponding to the weakly doped mode, the saddle singularity of ω(q) and scaling of χ_2D(ω) =∫d q Im χ(q, ω) are reproduced and an analytic expression is derived for the scaling function. In the strong frustration (optimal doping) mode, the stripe scenario is demonstrated; this leads to a peak of χ_2D (ω) in the region of ω～60 meV.     

Dynamic phenomena connected with magnetic and antiferroelectric interactions in trirutiles

Dynamic effects caused by the magnetoelectric and antiferroelectric interactions in tetragonal antiferromagnets are studied. The analysis is based on the example of trirutiles that are a series of antiferromagnets with different exchange structures and orientation states. We are mainly dealing with the excitation by an alternating electric field E(t) of spin waves typical of these magnets (antiferroelectric resonance) and the nuclear magnetoelectric resonance connected with these interactions. In the first case, special emphasis is placed on specific magnons (antimagnons), where only the antiferromagnetism vectors L take part in oscillations, whereas the total ferromagnetism vector M remains unchanged. The nuclear magnetoelectric resonance can be generated by oscillations of both L and M caused by field E(t). In this way, the field contributes to the hyperfine field, which acts on the nuclear spins. It is shown that the magnetic and antiferroelectric interactions in the dynamics can manifest themselves both at high (usually, exchange) frequencies ωw_E (antiferroelectric resonance) and at rather low nuclear frequencies of ω_n?ω_E. Particular cases of magnetic structures (phases) are considered where field E(t) can excite not only antimagnons, but also quasiantiferromagnons that have lower eigenfrequencies than those of quasimagnons (relativistic and semirelativistic).