Development of the pulse NMR method utilizing the short-lived β-emitter 12 B

Measurements of the spin-spin relaxation time T ₂ of the short-lived $\upbeta $ -emitter $^{12}B (I^{\uppi }$ = 1^?+?, T _1/2 = 20 ms) in Si have been performed. By applying the spin echo method to $\upbeta $ -NMR measurements, the intrinsic T ₂ for ¹²B in Si was successfully determined with the effect of the static magnetic field inhomogeneity removed. The temperature dependence of T ₂ for ¹²B in Si shows that T ₂ becomes longer with increasing temperature, which seems to reflect the effect of motional narrowing.     

Magnetic hyperfine field at Cr site in AgCrO2 given by Perturbed angular correlations

This work presents an electric field gradient and magnetic hyperfine field study, in the AgCrO₂ multiferroic with triangular spin lattice. The temperature dependence of the electric field gradient (efg) and magnetic hyperfine field (mhf) at Cr site was studied at isolde via perturbed angular correlation measurements with the ¹¹¹In probe, at room temperature and below the Néel temperature (T?≤?21 K) down to 12 K. The results show the presence of two distinct local environments. One axial symmetric efg with a very low mhf, and a non axially symmetric efg with a much higher one. The temperature dependences of mhf magnitude and of the angle between the mhf and the principle component of the efg are investigated.     

Relaxation Model and Mapping of Magnetic Field Gradients in MRI

The purpose of the work is development of algorithms for separate mapping of T ₂ relaxation time and gradients, using gradient recalled echo (GRE) sequence. Application of three-dimensional (3D) model of gradients and their volumetric averaging within a voxel lead to analytical model of relaxation function, which is consistent with experimental data for both regular macroscopic and randomized micro- and mesoscopic gradients. The model is verified by fitting into experimental data obtained on specially made phantoms. Verification of algorithms is completed by comparing gradient maps obtained on specially made cylindrical phantoms with theoretical maps of their exact 3D electro-dynamic solutions. Analytical model of relaxation function proved to be in good agreement with experimental relaxation curves. On the basis of this model, fast and unambiguous fittingless algorithms were developed. Gradient maps measured on special cylindrical phantoms are in good qualitative agreement with theory. 3D statistical model and fittingless algorithms provide the basis for separating the GRE signal into two meaningful parameters—T ₂ and gradients, thus doubling information from magnetic resonance imaging.     

A review of spin Hamiltonian forms for various point-group site symmetries

A review has been made of the spin Hamiltonian forms for all the 32 point groups, including linear magnetic field-dependent terms in spin operators $\hat O_1^m $ , $\hat O_3^m $ , $\hat O_5^m $ , $\hat O_1^m $ , $\hat O_3^m $ , and $\hat O_5^m $ . All spin operators, as well as their matrix elements, to be used in constructing spin Hamiltonian matrices, have been listed. The various point group aggregates for distinct spin-Hamiltonian forms have been classified. In addition, descent of symmetry point groups, useful for studying structural phase transitions, have been indicated.     

NMR in Magnetic Field of the Earth: Pre-Polarization of Nuclei with Alternating Magnetic Field

The polarization of nuclei in the low static magnetic field \(B_0\) with an alternating magnetic field \(B^{*} (B^{*} \gg B_0)\) at a very low frequency \(f_m\) (but \(f_m\gg 1\) / \({T_1}\) , where \(T_1\) is the spin-lattice relaxation time) has been investigated. The question of the optimization of the energy consumption during the pre-polarization is also considered. The possibilities of the method are illustrated by the observation of nuclear magnetic resonance signals from a few liquids.     

Influence of quadrupole–quadrupole-type interaction on the chaotic dynamics of $$\alpha $$-helical proteins

We calculate the electronic band dispersion of graphene monolayer on a two-dimensional transition metal dichalcogenide substrate (GrTMD) around K and \(\mathbf{K}^{\prime }\) points by taking into account the interplay of the ferromagnetic impurities and the substrate-induced interactions. The latter are (strongly enhanced) intrinsic spin–orbit interaction (SOI), the extrinsic Rashba spin–orbit interaction (RSOI) and the one related to the transfer of the electronic charge from graphene to substrate. We introduce exchange field (M) in the Hamiltonian to take into account the deposition of magnetic impurities on the graphene surface. The cavalcade of the perturbations yield particle–hole symmetric band dispersion with an effective Zeeman field due to the interplay of the substrate-induced interactions with RSOI as the prime player. Our graphical analysis with extremely low-lying states strongly suggests the following: The GrTMDs, such as graphene on \(\hbox {WY}_{2}\), exhibit (direct) band-gap narrowing / widening (Moss–Burstein (MB) gap shift) including the increase in spin polarisation (P) at low temperature due to the increase in the exchange field (M) at the Dirac points. The polarisation is found to be electric field tunable as well. Finally, there is anticrossing of non-parabolic bands with opposite spins, the gap closing with same spins, etc. around the Dirac points. A direct electric field control of magnetism at the nanoscale is needed here. The magnetic multiferroics, like \(\hbox {BiFeO}_{3}\) (BFO), are useful for this purpose due to the coupling between the magnetic and electric order parameters.     

Paramagnetische Resonanz von Zentren mit den Symmetrienn,\bar n undn/mundn/m

The consequences of applying the spin-Hamiltonians ofAbragam andPryce to paramagnetic centers with the low symmetriesn,\(\bar n\) andn/m(C _n ,C _nh ,S _n ) are examined. The asymmetry of theg- and the hfs-tensors, described in an earlier paper, is considered in this context. The point is that for the symmetries under consideration the coordinate systems are not determined by the symmetry elements. For this reason it is possible to introduce separate coordinate systems for the magnetic field, the electron spin and the spins of the nuclei and this allows the symmetrisation of the tensors under certain conditions. This procedure also leeds to an understanding of the independent parameters found in the Hamiltonians. Ambiguities between the spin-Hamiltonians and the esr-spectra indicate the limits of theAbragam andPryce formalism. The application of the theory to paramagnetic centers under the influence of external, electrical fields is discussed and reveals interesting aspects.     

Nuclear magnetic relaxation of spin<Emphasis Type="Italic">I</Emphasis>=1/2 scalar coupled to a quadrupolar nucleus in the presence of cross-correlation effects

The rigorous treatment of relaxation for the dipolar-multipolarAX spin system (I=1/2,S>1/2) in the presence of the dipolarI-S coupling, anisotropy chemical shift and quadrupolar interaction ofS spin is proposed. The calculations of the spin evolution under the relaxation Hamiltonian are based on the second-order time-dependent perturbation theory and are carried out in the operator representation. For this task the double commutator identities of the type [[I _±S _z ⁿ ,A _q ^μp ]A _?q ^μp ] and [[I _zS _z ⁿ ,A _q ^μp ]A _?q ^μp. ] are derived. The fist-order differential equations for the evolution of longitudinal two-spin orderI _zS _z ⁿ , z=magnetization ofS spinS _z ⁿ and coherences <I _±S _z ⁿ > in the spin systemIS with scalar coupling between spin 1/2 and quadrupolar spinS>1/2 were obtained. These equations are used to get equations for the evolutions of each component of the multiplet structure of spinI. The imaginary part of the cross-correlation spectral density function and indirect spin-spin coupling Hamiltonian are taken into account. Equations for the longitudinal components of theI spin spectrum in the presence of cross-correlation effects were obtained also. Longitudinal and transverse relaxation times and cross-relaxation times in the presence of cross-correlation D-CSA, Q-CSA, Q-D were analyzed.     

Unexpected Features of the Intramolecular Spin Exchange in Imidazoline Nitroxide Biradicals Dissolved in Ionic Liquids

Three imidazoline-type nitroxide biradicals of the similar composition R ₅ ^NO –CH=N–N=CH–R ₅ ^N , B1, R ₅ ^NO –CH=N–N=C(CH₃)–R ₅ ^N , B2, and R ₅ ^N –C(CH₃)=N–N=C(CH₃)–R ₅ ^N , B3, with R ₅ ^N and R ₅ ^NO denoting, respectively, the nitroxide rings 1-oxyl-2,2,5,5-tetramethyl-3-imidazoline and 1-oxyl-2,2,5,5-tetramethyl-3-N–oxide imidazoline, have been studied by X-band electron paramagnetic resonance (EPR) spectroscopy. Variations of the intramolecular electron spin exchange in these biradicals dissolved in ethanol and the room temperature ionic liquid bmimBF₄ were characterized as a function of temperature by means of the analysis of the EPR lines shape. Thermodynamic parameters of the conformational rearrangements in ethanol were calculated. Analyzing the EPR spectra of these biradicals in bmimBF₄, it was revealed that the two-conformational model does not describe their conformational transitions. Moreover, the observed EPR spectra are not central symmetric especially at low temperatures that cannot be described and explained in the framework of the current theory of the intramolecular spin exchange. Probable reasons of this “strange” behavior are discussed.     

Nuclear magnetic relaxation induced by the relaxation of electron spins

A physical mechanism responsible for the relaxation of nuclear spins coupled by the hyperfine interaction to relaxed electron spins in materials with spin ordering is proposed. The rate of such induced nuclear spin relaxation is proportional to the dynamic shift of the nuclear magnetic resonance (NMR) frequency. Therefore, its maximum effect on the NMR signal should be expected in the case of nuclear spin waves existing in the system. Our estimates demonstrate that the induced relaxation can be much more efficient than that occurring due to the Bloch mechanism. Moreover, there is a qualitative difference between the induced and Bloch relaxations. The dynamics of nuclear spin sublattices under conditions of the induced relaxation is reduced to the rotation of m₁ and m₂ vectors without any changes in their lengths (m ₁ ² (t) = m ₂ ² (t) = m ₀ ² (t)= const). This means that the excitation of NMR signals by the resonant magnetic field does not change the temperature T _n of the nuclear spin system. This is a manifestation of the qualitative difference between the induced and Bloch relaxations. Indeed, for the latter, the increase in T _n accompanying the saturation of NMR signals is the dominant effect.     

Warm modified Chaplygin gas shaft inflation

In this paper, we examine the possible realization of a new inflation family called “shaft inflation” by assuming the modified Chaplygin gas model and a tachyon scalar field. We also consider the special form of the dissipative coefficient \(\Gamma ={a_0}\frac{T^{3}}{\phi ^{2 }}\) and calculate the various inflationary parameters in the scenario of strong and weak dissipative regimes. In order to examine the behavior of inflationary parameters, the \(n_s \)–\( \phi ,\, n_s \)–r, and \(n_s \)–\( \alpha _s\) planes (where \(n_s,\, \alpha _s,\, r\), and \(\phi \) represent the spectral index, its running, tensor-to-scalar ratio, and scalar field, respectively) are being developed, which lead to the constraints \(r< 0.11\), \(n_s=0.96 \pm 0.025\), and \(\alpha _s =-0.019 \pm 0.025\). It is quite interesting that these results of the inflationary parameters are compatible with BICEP2, WMAP \((7+9)\) and recent Planck data.     

Spectroscopy of the hyperfine structure of antiprotonic 4He and 3He

The spin magnetic moment $\mu^{\overline{p}}_{s}$ of the antiproton can be determined by comparing the measured transition frequencies in $\overline{p}^4$ He^?+? with three-body QED calculations. A comparison between the proton and antiproton can then be used as a test of CPT invariance. The highest measurement precision of the difference between the proton and the antiproton spin magnetic moments to date is 0.3%. A new experimental value of the spin magnetic moment of the antiproton was obtained as $\mu^{\overline{p}}_{s} = -2.7862(83)\mu_{N}$ , slightly better than the previously best measurement. This agrees with $\mu^{p}_{s}$ within 0.24%. In 2009, a new measurement with antiprotonic ³He has been started. A comparison between the theoretical calculations and experimental results would lead to a stronger test of the theory and address systematic errors therein. A measurement of this state will be the first HF measurement on $\overline{p}^3$ He^?+?. We report here on the new experimental setup and the first tests.     

Cosmology from a gauge induced gravity

The main goal of the present work is to analyze the cosmological scenario of the induced gravity theory developed in previous works. Such a theory consists on a Yang–Mills theory in a four-dimensional Euclidian spacetime with \({ SO}(m,n)\) such that \(m+n=5\) and \(m\in \{0,1,2\}\) as its gauge group. This theory undergoes a dynamical gauge symmetry breaking via an Inönü–Wigner contraction in its infrared sector. As a consequence, the \({ SO}(m,n)\) algebra is deformed into a Lorentz algebra with the emergency of the local Lorentz symmetries and the gauge fields being identified with a vierbein and a spin connection. As a result, gravity is described as an effective Einstein–Cartan-like theory with ultraviolet correction terms and a propagating torsion field. We show that the cosmological model associated with this effective theory has three different regimes. In particular, the high curvature regime presents a de Sitter phase which tends towards a \(\Lambda \)CDM model. We argue that \({ SO}(m,n)\) induced gravities are promising effective theories to describe the early phase of the universe.     

Theoretical study of diaquamalonatozinc(II) single crystal for applications in non-linear optical devices

The aim of the present paper is to employ theoretical methods to investigate the zero field splitting (ZFS) parameter and to investigate the position of the dopant in the host. These theoretical calculations have been compared with the empirical results. The superposition model (SPM) with the microscopic spin-Hamiltonian (MSH) theory and the coefficient of fractional parentage have been employed to investigate the dopant manganese(II) ion substitution in the diaquamalonatozinc(II) (DAMZ) single crystal. The magnetic parameters, viz. g-tensor and D-tensor, has been determined by using the ORCA program package developed by F Neese et al. The unrestricted Kohn–Sham orbitals-based Pederson–Khanna (PK) as the unperturbed wave function is observed to be the most suitable for the computational calculation of spin–orbit tensor (\(D^{\mathrm{SO}})\) of the axial ZFS parameter D. The effects of spin–spin dipolar couplings are taken into account. The unrestricted natural orbital (UNO) is used for the calculation of spin–spin dipolar contributions to the ZFS tensor. A comparative study of the quantum mechanical treatment of Pederson–Khanna (PK) with coupled perturbation (CP) is reported in the present study. The unrestricted Kohn–Sham-based natural orbital with Pederson–Khanna-type of perturbation approach validates the experimental results in the evaluation of ZFS parameters. The theoretical results are appropriate with the experimental ones and indicate the interstitial occupancy of \(\hbox {Mn}^{2+}\) ion in the host matrix.     

Surface-NMR relaxation and echo of aquifers in geomagnetic field

Macroscopic samples of near-surface water in pores or fractures of rocks down to 100 m and deeper are studied by the measurement of proton relaxation and echo in the Earth’s magnetic field. The excitation and reception of the surface nuclear magnetic resonance (SNMR) signal is accomplished with the help of an antenna, circle or 8-shaped (for the minimization of the outer electromagnetic jamming influence), placed at the surface. The frequency of magnetic resonance in the case considered amounts to several kilohertz, the dead time of the instrumentation to several milliseconds. Water in extremely small pores of water-resisting rocks (e.g., in argillaceous grounds), is chemically bound, crystallization or frozen water has smaller times of spin relaxation and is not registered. The distribution of water concentration with depth is determined by inversion of an integral equation, including the model and measured dependences of the SNMR signal against the intensity of excitation. The current state of the art of the SNMR sounding and perspectives of this method on the basis of free induction decay and spin echo detection and relaxation times measurement are presented. Free induction decayT ₂ ^* equal to 60 ms, spin-echoT ₂ equal to 220 ms, and inversion-recoveryT ₁ equal to 700 ms relaxation times have been measured for medium-to coarse-grained sand aquifer. Microscopic characteristics of the aquifer — longitudinal relaxivity (7·10^?3 cm/s), transverse relaxivity (3.5·10^?2 cm/s), and local magnetic field gradient (2·10^?2 G/cm) — have been estimated from experimental data. The importance of spin relaxation and echo measurements for obtaining the information about the microstructure of pores and fractures, as well as filtration, properties of aquifers and diamagnetic, paramagnetic and hydrocarbon contamination, is emphasized.     

Topological Spin Excitations Induced by an External Magnetic Field Coupled to a Surface with Rotational Symmetry

We study the Heisenberg model in an external magnetic field on curved surfaces with rotational symmetry. The Euler–Lagrange static equations, derived from the Hamiltonian, lead to the inhomogeneous double sine-Gordon equation. Nonetheless, if the magnetic field is coupled to the metric elements of the surface, and consequently to its curvature, the homogeneous double sine-Gordon equation emerges and a $2\pi $ -soliton solution is obtained. In order to satisfy the self-dual equations, surface deformations are predicted to appear at the sector where the spin direction is opposite to the magnetic field. On the basis of the model, we find the characteristic length of the $2\pi $ -soliton for three specific rotationally symmetric surfaces: the cylinder, the catenoid, and the hyperboloid. On finite surfaces, such as the sphere, torus, and barrels, fractional $2\pi $ -solitons are predicted to appear.     

Approximation Algorithms for Two-State Anti-Ferromagnetic Spin Systems on Bounded Degree Graphs

We show that for the anti-ferromagnetic Ising model on the Bethe lattice, weak spatial mixing implies strong spatial mixing. As a by-product of our analysis, we obtain what is to the best of our knowledge the first rigorous proof of the uniqueness threshold for the anti-ferromagnetic Ising model (with non-zero external field) on the Bethe lattice. Following a method due to Weitz [15], we then use the equivalence between weak and strong spatial mixing to give a deterministic fully polynomial time approximation scheme for the partition function of the anti-ferromagnetic Ising model with arbitrary field on graphs of degree at most  $d$ , throughout the uniqueness region of the Gibbs measure on the infinite $d$ -regular tree. By a standard correspondence, our results translate to arbitrary two-state anti-ferromagnetic spin systems with soft constraints. Subsequent to a preliminary version of this paper, Sly and Sun [13] have shown that our results are optimal in the sense that, under standard complexity theoretic assumptions, there does not exist a fully polynomial time approximation scheme for the partition function of such spin systems on graphs of maximum degree  $d$ for parameters outside the uniqueness region. Taken together, the results of [13] and of this paper therefore indicate a tight relationship between complexity theory and phase transition phenomena in two-state anti-ferromagnetic spin systems.     

On Cluster Properties of Classical Ferromagnets in an External Magnetic Field

Correlation functions of ferromagnetic spin systems satisfying a Lee-Yang property are studied. It is shown that, for classical systems in a non-vanishing uniform external magnetic field h, the connected correlation functions decay exponentially in the distances between the spins, i.e., the inverse correlation length (“mass gap”), m(h), is strictly positive. Our proof is very short and transparent and is valid for complex values of the external magnetic field h, provided that \(\mathrm {Re}\, h \not = 0\). It implies a mean-field lower bound on m(h), as \(h \searrow 0\), first established by Lebowitz and Penrose for the Ising model. Our arguments also apply to some quantum spin systems.     

Optical,Dielectric, and Conduction Properties of New Phosphorus-Modified Polysulfones

New phosphorus-modified polysulfones with different substitution degrees, obtained from chloromethylated polysulfones, were analyzed in terms of their optical, dielectric, and conduction properties. In order to obtain the optical parameters, the approach proposed by Tauc for amorphous semiconductors was used.^{[ 23} Tauc, J., Menth, A. and Wood, D. L. 1970. Optical and magnetic investigations of the localized states in semiconducting glasses. Phys. Rev. Lett., 25: 749–752. [Crossref] , [Google Scholar] ^{, 24} Tauc, J. and Menth, A. 1972. States in the gap. J. Non-Cryst. Solids, 8–10: 569–585. [Crossref] , [Google Scholar] ^] The determined parameters were found to be related to the influence of the polymer chain structure and the history of films’ preparations. The temperature and frequency dependence of dielectric constant and dielectric relaxation were investigated by AC-dielectric measurements. The nature of the relaxation mechanisms was established on the basis of the dielectric measurement results. The samples displayed two sub-glass relaxations, i.e. γ relaxation – where the activation energy changes insignificantly with the substitution degree, and β relaxation – with higher apparent activation energy for lower substitution degrees. The results obtained from Tauc's law and AC-conduction studies indicated that the conduction mechanism in the phosphorus-modified polysulfone was due to electronic hopping, and that a model based on the energy bandgap representation could be suitable for explaining the temperature dependence of electrical conductivity.