Anisotropic Coupling Constants Research Articles

Critical temperature in 2D square Ising model with anisotropic coupling constant using Kramers-Wannier duality

To solve the 2D square Ising model incorporating anisotropy, we discuss a graphical representation of Kramers-Wannier duality. The method yields an equation relating the critical temperature (Tc ) to the horizontal and vertical coupling constants. The result reproduces the known exact solution by Onsager. The equation derived was utilized to plot Tc as a function of anisotropy by introducing the ratio (α) of the coupling constants. A phase diagram is then obtained showing Tc as an increasing function of α In the limit as α approaches zero, the critical temperature asymptotically goes to zero. This agrees with the exact solution of the 1D model.

Monte Carlo studies of skyrmion stabilization under geometric confinement and uniaxial strain

Geometric confinement (GC) of skyrmions in nanodomains plays a crucial role in skyrmion stabilization. This confinement effect decreases the magnetic field necessary for skyrmion formation and is closely related to the applied mechanical stresses. However, the mechanism of GC is unclear and remains controversial. Here, we numerically study the effect of GC on skyrmion stabilization and find that zero Dzyaloshinskii–Moriya interaction (DMI) coupling constants imposed on the boundary surfaces of small thin plates cause confinement effects, stabilizing skyrmions in the low-field region. Moreover, the confined skyrmions are further stabilized by tensile strains parallel to the plate, and the skyrmion phase extends to the low-temperature region. This stabilization occurs due to the bulk anisotropic DMI coupling constant caused by lattice deformations. Our simulation data are qualitatively consistent with reported experimental data on skyrmion stabilization induced by tensile strains applied to a thin plate of the chiral magnet Cu2OSeO3.

Effect of the Dzyaloshinski Moria Interaction on Quantum Correlations for the XXZ Heisenberg Spin Chain

We have studied the effect of the Dzyaloshinskii Moria (DM) interaction on geometric quantum discord (GQD) and concurrence for two spin 1/2 particles in the XXZ Heisenberg model, we have also investigated the effects of the temperature, the strength of DM interaction (D) and the anisotropic coupling constant of the Heisenberg model Jz on them in the GQD and concurrence. Further, we have compared the behaviors of GQD and entanglement for our system under the above parameters.

Isotropic/Anisotropic NMR Editing by Resolution-Enhanced NMR Spectroscopy.

Modern resolution-enhanced NMR techniques can monitor the in situ discrimination of co-existing isotropic and anisotropic contributions of small molecules dissolved in weakly aligning PMMA/CDCl3 media. The simultaneous sign-sensitive determination of accurate Δδiso-aniso (1 H), Δδiso-aniso (13 C) and/or isotropic 1 JCH and anisotropic 1 TCH coupling constants (and consequently 1 H-13 C residual dipolar couplings and 1 H/13 C residual chemical shift anisotropies) can be performed from spectral-aliased heteronuclear single-quantum correlation spectra.

Study of Elastic and Acoustic Properties of TiN

This work is totally focused on three types of ultrasonic velocities (V1, V2, V3) in TiN single crystals. They are determined by using the SOEC (second order elastic constant) and TOEC (third order elastic constant) at room temperature. TiN possesses rock slats structure and the atoms in the unit cell is equally located in all the direction. Therefore ultrasonic waves are supposed to be propoagted alongany direction with the crystals axis. Finally ultrasonic attenuationdue to phonon-phonon interaction and thermoelastic relaxation phenomena in TiNis evaluated for longitudinal and shear waves along , and crystallographic directions at the different temperature (temperature varies from 150 to 400K) by utilizing the SOEC and TOEC of the materials. The SOEC and TOEC, ultrasonic velocities, thermalrelaxation, anisotropic and acoustical coupling constant have been computedfor the evaluation of ultrasonic attenuation in this temperature range. The crystallographic direction is responsible for propogating the longitudinal ultrasonic wave while , direction is the best direction for propogating the shear waves due to lowest values of ultrasonic attenuationdue to phonon-phonon vibration in these direction.

Effective spin-1/2exchange model for Tb2Ti2O7

Fits were performed to diffuse neutron scattering intensity patterns to determine anisotropic exchange coupling constants for Tb${}_{2}$Ti${}_{2}$O${}_{7}$. A symmetry-preserving map between non-Kramers Tb${}^{3+}$ states and spin-1/2 states is described. Using second-order perturbation theory, the Tb${}^{3+}$ nearest-neighbor exchange model is mapped to a spin-1/2 model, and the anisotropic exchange coupling constants for this model are calculated. Tb${}_{2}$Ti${}_{2}$O${}_{7}$ is found to be a spin-1/2 spin ice with corrections arising from transverse exchange terms.

Vector-magneto-optical generalized ellipsometry

We present the setup of a variable-angle vector-magneto-optical generalized ellipsometer (VMOGE) in the spectral range from 300 to 1100 nm using an octupole magnet, and demonstrate VMOGE measurements of the upper 3 × 4 submatrix of the Mueller matrix in a magnetic field of arbitrary orientation and magnitude up to 0.4 T at room temperature. New "field orbit" measurements can be performed without physically moving the sample, which is useful to study magnetic multilayer or nanostructure samples. A 4 × 4 matrix formalism is employed to model the experimental VMOGE data. Searching the best match model between experimental and calculated VMOGE data, the magneto-optical dielectric tensor ɛ(MO) of each layer in a multilayer sample system can be determined. In this work, we assume that the nonsymmetric terms of ɛ(MO) are induced by an external magnetic field and depend linearly on the sample magnetization. Comparison with vector magnetometer measurements can provide the anisotropic magneto-optical coupling constants Q(x), Q(y), Q(z).

Static magnetic susceptibility, crystal field and exchange interactions in rare earth titanatepyrochlores

The experimental temperature dependence (T = 2–300 K) of single crystal bulk and site susceptibilities of rare earth titanate pyrochloresR2Ti2O7 (R = Sm, Eu, Gd, Tb, Dy, Ho, Er, Yb) is analyzed in the framework of crystal field theory and amean field approximation. Analytical expressions for the site and bulk susceptibilities ofthe pyrochlore lattice are derived taking into account long range dipole–dipole interactionsand anisotropic exchange interactions between the nearest neighbor rare earth ions. Thesets of crystal field parameters and anisotropic exchange coupling constants havebeen determined and their variations along the lanthanide series are discussed.

Single-crystal EPR study and DFT structure of the [Mo(CO) 5PPh 3] +· radical cation

A radical species characterized by a large g-anisotropy and a clearly resolved hyperfine structure with 95/97Mo and 31P nuclei is formed, at 77 K, by radiolysis of a single crystal of Mo(CO) 5PPh 3. The corresponding EPR signals disappear irreversibly with increasing temperature and the angular dependence of the various coupling constants imply a spin delocalization of ∼60% and ∼4% on the molybdenum and the phosphorus atoms, respectively and are, a priori, consistent with the trapping of a one-electron deficient centre. The ability of DFT to predict the EPR tensors for a 17-electron Mo (I) species is verified by calculating the g-tensor and the various 14N and 13C coupling tensors previously reported by Hayes for [Mo(CN) 5NO] 3−. Calculations at the B3LYP/ZORA/SOMF level of theory show that, in contrast to Mo(CO) 5PH 3, one-electron oxidation of Mo(CO) 5PPh 3 causes an appreciable change in the geometry of the complex. The g-tensor and the 95/97Mo and 31P isotropic and anisotropic coupling constants calculated for [Mo(CO) 5PPh 3] +· confirm the trapping of this species in the irradiated crystal of Mo(CO) 5PPh 3; they also show that the conformational modifications induced by the electron release are probably hindered by the nearby complexes.

Role of interference in quantum state transfer through spin chains

We examine the role that interference plays in quantum state transfer through several types of finite spin chains, including chains with isotropic Heisenberg interaction between nearest neighbors, chains with reduced coupling constants to the spins at the end of the chain, and chains with anisotropic coupling constants. We evaluate quantitatively both the interference corresponding to the propagation of the entire chain and the interference in the effective propagation of the first and last spins only, treating the rest of the chain as a black box. We show that perfect quantum state transfer is possible without quantum interference and provide evidence that the spin chains examined realize interference-free quantum state transfer to a good approximation.

The melting transition of a vortex lattice in the uniformly frustratedXY model with quasi-one-dimensional and quasi-two-dimensional coupling anisotropy

The uniformly frustrated XY model on the cubic lattice with an anisotropic coupling constant is studied numerically.Quasi-one-dimensional and quasi-two-dimensional systems are examined as models for acharge density wave in a ring crystal and a layer superconductor, respectively. Themelting transition of a vortex lattice is investigated by means of non-equilibriumrelaxation analysis. We find scaling behaviour of the relaxation with a power law,which indicates that the phase transition is of second order, in contrast to thefirst-order transition in the isotropic case. The critical exponents are estimated asβ = 0.28 and zν = 2.3 for the quasi-one-dimensional system andβ = 0.40 and zν = 2.9 for the quasi-two-dimensional system, andα≈0 for both cases. This implies that the universality classes of the two are different.

DFT‐EPR study of radiation‐induced radicals in α‐D‐glucose

AbstractThe structures of two radiation‐induced radicals in solid‐state α‐D‐glucose have been identified by means of single‐molecule density function theory (DFT) calculations. Using the original crystalline structure as input, several radical models were created and their geometries optimized. Subsequently, electron paramagnetic resonance (EPR) parameters were calculated. During these calculations, the global orientation of the radical structure was kept fixed with respect to the crystal axes reference frame. This was essential to allow for an easy analysis of the hyperfine tensor principal directions, besides the isotropic and anisotropic coupling constants. By comparing these calculated EPR parameters with their experimentally determined counterparts, a plausible identification of two carbon‐centered glucose radicals was possible. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004

Phosphaalkenes with Inverse Electron Density: Electrochemistry, Electron Paramagnetic Resonance Spectra, and Density Functional Theory Calculations of Aminophosphaalkene Derivatives

Cyclic voltammetry of Mes*PC(NMe2)2 (1) and Mes*PC(CH3)NMe2 (2) shows that, in solution in DME, these compounds are reversibly oxidized at 395 and 553 mV, respectively. Electrochemical oxidation or reaction of 1 (or 2) with [Cp2Fe]PF6 leads to the formation of the corresponding radical cation, which was characterized by its electron paramagnetic resonance (EPR) spectra. Experimental 31P and 13C isotropic and anisotropic coupling constants agree with density functional theory (DFT) calculations showing that the unpaired electron is strongly localized on the phosphorus atom, in accord with the description Mes*P•−(C(NMe2)2)+. Electrochemical reduction of 1 is essentially irreversible and leads to a radical species largely delocalized on the C(NMe2)2 moiety; this neutral radical results from the protonation of the phosphorus atom and corresponds to Mes*(H)P−•C(NMe2)2. No paramagnetic species is obtained by reduction of 2. The presence of the amino groups, responsible for the inverted electron distribution at ...

13C–77Se and77Se–77Se spin–spin coupling tensors in carbon diselenide: NMR experiments and ZORA DFT calculations

The isotropic average and anisotropy of the 13C–77Se and 77Se–77Se spin–spin coupling tensors in carbon diselenide (CSe2) were calculated by applying relativistic density functional theory. Computed nuclear shielding anisotropies are also reported. The coupling tensor anisotropies were derived experimentally with the liquid crystal (LC) NMR method. Due to the fact that the number of adjustable parameters in the experimental analysis is greater than the number of anisotropic coupling constants, DexpMN, the ratio of the coupling tensor anisotropies, ΔJCSe/ΔJSeSe, had to be fixed to the value obtained from the calculations. It appears that both tensor anisotropies are large, and in particular ½JanisoSeSe is a clearly dominating contribution in DexpSeSe. The remarkable ½JanisoCSe contribution in the DexpCSe leads to a correction of the earlier reported shielding tensor anisotropies, ΔσC and ΔσSe, determined by LCNMR.

The origin of ferromagnetic ordering in PrNi 3.9Cu 1.1

Although both PrNi 5 and PrCu 5 are non-magnetic, PrNi 5− x Cu x alloys for 0.9⩽ x⩽2.6 were recently discovered to order with Curie temperature T C ⩽3.6 K . In order to understand the mechanism of these ferromagnetic orderings, we have carried out mean-field model calculations and obtained crystal-field parameters and anisotropic Heisenberg coupling constants for x=1.1. The effects of quadrupolar coupling and magneto-elastic interactions were also taken into account in order to better fit the magnetization along the hard [0 0 1] direction. Based on our theoretical studies, we conclude that Cu substitution for Ni strongly changes the crystal field acting on the 4f electrons, and considerably enhances the Pr–Pr exchange interaction. The onset of ferromagnetism below T C is therefore attributed to an interplay between the exchange interactions and crystalline electric field effects.

Periodic trends in indirect nuclear spin-spin coupling tensors: relativistic density functional calculations for interhalogen diatomics.

There have been significant advances in the calculation and interpretation of indirect nuclear spin-spin coupling (J) tensors during the past few years; however, much work remains to be done, especially for molecules containing heavy atoms where relativistic effects may play an important role. Many J tensors cannot be explained based solely on a nonrelativistic Fermi-contact mechanism. In the present work, the relativistic zeroth-order regular approximation density-functional (ZORA-DFT) implementation for the calculation of J has been applied to the complete series of homonuclear and heteronuclear diatomic halogen molecules: F(2), Cl(2), Br(2), I(2), At(2), ClF, BrF, IF, ClBr, ClI, and BrI. For all of these compounds, the reduced isotropic coupling constant (K(iso)) is positive and the reduced anisotropic coupling constant (DeltaK) is negative. With the exception of molecular fluorine, the magnitudes of K(iso) and DeltaK are shown to increase linearly with the product of the atomic numbers of the coupled nuclei. ZORA-DFT calculations of J for F(2) and ClF are in excellent agreement with the results obtained from multiconfigurational self-consistent-field calculations. The relative importance of the various coupling mechanisms is approximately constant for all of the compounds, with the paramagnetic spin-orbit term being the dominant contributor to K(iso), at approximately 70-80%. Available experimental stimulated resonant Raman spectroscopy data are exploited to extract the complete J((127)I,(127)I) tensor for iodine in two rotational states. The dependence of K(iso) and DeltaK on bond length and rovibrational state is investigated by using calculated results in combination with available experimental data. In addition to providing new insights into periodic trends for J coupling tensors, this work further demonstrates the utility of the ZORA-DFT method and emphasizes the necessity of spin-orbit relativistic corrections for J calculations involving heavy nuclei.

Two-dimensional (2D) pulsed electron paramagnetic resonance study of VO(2+)-triphosphate interactions: evidence for tridentate triphosphate coordination, and relevance to bone uptake and insulin enhancement by vanadium pharmaceuticals.

Two- and four-pulse electron spin echo envelope modulation (ESEEM) and four-pulse two-dimensional hyperfine sublevel correlation (HYSCORE) spectroscopies have been used to determine the solution structure of a 3:1 triphosphate:vanadyl solution at pH 5.0. Limited quantitative data were extracted from the two pulse spectra; however, HYSCORE proved to be more useful in the detection and interpretation of the (31)P and (1)H couplings. Three sets of cross-peaks were observed for each nucleus. For the (31)P couplings, three sets of cross-peaks were observed in the HYSCORE spectrum, and contour line shape analysis yielded coupling constants of approximately 15, 9, and 1 MHz. HYSCORE cross-peaks in the proton region were partially overlapping; however, interpretation of the proton coupling was simplified through the use of one-dimensional four-pulse ESEEM and subsequent analysis of the sum combination peaks. Comparison of the derived isotropic and anisotropic coupling constants with results from earlier ESEEM and electron nuclear double resonance (ENDOR) studies was consistent with the presence of at least one, and most likely two, water molecules coordinated in the equatorial plane of the vanadyl cation. The vanadyl-triphosphate system was shown to be an accurate model of the in vivo vanadyl-phosphate coupling constants determined in an earlier study (Dikanov, S. A.; Liboiron, B. D.; Thompson, K. H.; Vera, E.; Yuen, V. G.; McNeill, J. H.; Orvig, C. J. Am. Chem. Soc. 1999, 121, 11004.) Comparison of these values to those found in previous spectroscopic studies of vanadyl-triphosphate interactions, along with a detailed structural interpretation, are presented. This work represents the first detection of tridentate polyphosphate coordination to the vanadyl ion, and the first observation of an axial phosphate interaction not previously reported in earlier ENDOR and pulsed electron paramagnetic resonance studies.

Characterization of transient radicals in the reduction product of the –PCCP– system: EPR and theoretical studies

The EPR spectrum obtained at room temperature after electrochemical or chemical reduction of a solution of Ar–PCCP–Ar in THF exhibits hyperfine interaction (165 MHz) with two equivalent 31P nuclei. Additional couplings with two equivalent 13C are observed with Ar–P13C13CP–Ar. The 31P anisotropic coupling constants could be obtained from spectra recorded at low temperature. They indicate that the unpaired electron is mainly localized (78%) on the two phosphorus atoms. Quantum chemical calculations (DFT and ab initio SCI) were performed on the various isomers of the two radical anions: [H–PCCP–H]˙− and [H–PCH–CHP–H]˙−. Although the optimized geometries of these two species are clearly different, neither of them leads to 13C/31P hyperfine tensors in conflict with the experimental results. The absence of any 1H splitting on the EPR spectrum together with the quasi-reversibility of the reduction wave make the identification of [Ar–PCCP–Ar]˙− more probable.

Interplay of polaronic and disorder effects on electronic charge transport

We study the effect of spatial disorder and anisotropy on the mobility of charge carriers using a dynamical Monte Carlo simulation. Our transfer rate is based on a polaronic model of phonon-assisted hopping in an effective diabatic potential. Even without the consideration of anisotropic charge localisations and different coupling constants in different space co-ordinates, as expected for semiconducting polymers, we find distinct effects of disorder and anisotropy on the mobility depending on the external electrical field. This makes generalisations of simulational data and the interpretation of fitting parameters for disorder and anisotropy to experiments rather complicated. A detailed topological knowledge of measured samples is of paramount importance for a comparison of simulational and experimental results.

Optical Spectroscopy of Mn2+ Ions in CaF2

Excitation and emission spectra of Mn2+ ions in calcium fluoride have been studied using the photoluminescence technique. An analysis of the positions of the Mn2+ crystal-field transitions with aid of the model developed by Curie et al. was performed to determine the relevant crystal-field parameters and the covalency parameters f_s and fp of the Mn2+ ions entering substitutionally for Ca2+ ions in an Oh symmetry cubic environment. The As isotropic and Ap anisotropic superhyperfine coupling constants of Mn2+ in CaF2 are also calculated and compared with those previously measured through the use of EPR technique.