Hamiltonian Parameters Research Articles

Analytical expression of tensorial rotational operators for semi-classical interpretation of molecular spectra. Relations between molecular Hamiltonian parameters in different formalisms

We present a formal development of the tensorial rotational Hamiltonian using symbolic calculations. Algebraic manipulations thanks to the open-source Maxima software allow us to get formal expressions of use for various molecular spectroscopy problems. We first present some simple applications to the so-called semi-classical approach that allows the study of level structures in the molecular rotational energy spectrum. Then, we perform some comparisons between the tensorial approach and Watson’s Hamiltonian, giving exact effective molecular parameter correspondence formula between the two formalisms.

Theoretical examination of defect structures and spin Hamiltonian parameters of manganese (II)- and cobalt (II)-doped ZnO nanowires

This study theoretically investigates the defect structures of Mn2+ at 3 and 10 at. % as well as those of Co2+ at 5 at. % in ZnO nanowires by analyzing their experimental spin Hamiltonian parameters (g factors, hyperfine structure constants A, and zero-field splitting D) based on perturbation formulae in trigonally distorted tetrahedral 3 d5 and 3 d7 clusters, respectively. Unlike the trigonal distortion of the host Zn2+ site in ZnO nanowires, the impurities Mn2+ and Co2+ underwent displacements ΔZ (≈0.0223 and 0.0233 Å for Mn2+, and 0.040 and 0.043 Å for the two Co2+ centers) away from the ligand oxygen triangles along the C3 axis at 3 and 10 at. %, and at 5 at. %, respectively. In light of the significant covalent interactions of the two Co2+ centers, their contributions to the spin Hamiltonian parameters due to the charge transfer mechanism need to be included in the theoretical calculations. The defect structures and spectral properties are also discussed in view of the different crystalline morphologies of the doped samples, which indicate that the values of ΔZ of the Mn2+ centers decreased in low-dimensional materials, whereas those of the Co2+ centers remained nearly constant owing to strong covalence.

Study of the ground state and thermodynamic properties of Cu5-NIPA-like molecular nanomagnets

The thermodynamic properties of a spatially anisotropic spin-1/2 Heisenberg model for a Cu5 pentameric molecule is studied through exact diagonalization. The elementary geometry of the finite lattice is defined on nanomolecules consisting of an hourglass structure of two corner-sharing scalene triangles which are related by inversion symmetry. This microscopic magnetic model is quite suitable to describe the molecular nanomagnetic compound Cu5-NIPA. The ground-state phase diagram, as well as the corresponding total magnetization, are obtained as a function of the anisotropic exchange interactions and the external magnetic field. The thermodynamic behavior of the model at finite temperatures is also studied and the corresponding magnetocaloric effects are analyzed for various values of the Hamiltonian parameters.

Theoretical analysis on strontium-tellurium content dependencies of defect structures and spin Hamiltonian parameters for strontium-tellurium titanium borate glasses with V2O5 dopants

Based on the perturbation formulae of the spin Hamiltonian parameters (SHPs) for a tetragonally compressed octahedral 3d1 cluster, the defect structures and SHPs of V4+ in strontium-tellurium borate ((30-x)SrO-xTeO2-10TiO2-58B2O3-2V2O5 at distinct TeO2 contents x = 1, 2, 3, 4 and 5 mol %) glasses are systematically investigated. The involved model quantities (i.e. covalent factor N, tetragonal compression ratio τ, core polarization constant κ and reduction factor H) at various x reasonably reproduce the experimental SHPs, and these quantities are further fitted with uniform Fourier-type content functions (FTCF) with merely three adjusted parameters. The different content fluctuations of these quantities are ascribed to content declines of the strong network modifier SrO and hence the modulations in local tetragonal compression, system compactness and electron cloud distribution near vanadium in the glass network.

Internal rotation analysis of the microwave and millimeter wave spectra of fluoral (CF3CHO)

The rotational spectrum (4–40 GHz and 50–330 GHz) has been measured and analyzed for trifluoroacetaldehyde, also known as fluoral (CF3CHO), which is one of the degradation products of the fluorinated contaminants emitted into the atmosphere. The complexity of the spectroscopic analysis of this molecule arises from the strong coupling between the internal rotation motion of CF3 group and the overall rotation of the molecule. The value obtained for its coupling constant (ρ = 0.91723481(49)) is comparable to the corresponding value of methanol (CH3OH, ρ = 0.81), which is known for its complex spectrum. A total of 12,322 transitions of the ground, the first and second excited torsional states (ΔE1υt = 62.0183(13)cm−1; ΔE2υt = 120.3315(13)cm−1) with J ≤ 50 were included in the analysis that was performed employing the rho-axis-method (RAM), and the RAM36 code. A fit within experimental error (root mean square deviation equals to 35 kHz) has been achieved for this dataset using 47 parameters of the RAM torsion-rotation Hamiltonian. In the course of the analysis, it became evident that for such high ρ value, as it is determined for fluoral, a larger than usual torsional basis set at the first diagonalization step of the two-step diagonalization procedure is required for achieving a fit within experimental error.

Neutrino magnetic and electric dipole moments: From measurements to parameter space

Searches for neutrino magnetic moments/transitions in low energy neutrino scattering experiments are sensitive to effective couplings, which are an intricate function of the Hamiltonian parameters. We study the parameter space dependence of these couplings in the Majorana (transitions) and Dirac (moments) cases, as well as the impact of the current most stringent experimental upper limits on the fundamental parameters. In the Majorana case we find that for reactor, short-baseline, and solar neutrinos, $CP$ violation can be understood as a measurement of parameter space vectors misalignments. The presence of nonvanishing $CP$ phases opens a blind spot region where---regardless of how large the parameters are---no signal can be observed in either reactor or short-baseline experiments. Identification of these regions requires a combination of different datasets and allows for the determination of those $CP$ phases. We point out that stringent bounds not necessarily imply suppressed Hamiltonian couplings, thus allowing for regions where disparate upper limits can be simultaneously satisfied. In contrast, in the Dirac case stringent experimental upper limits necessarily translate into tight bounds on the fundamental couplings. In terms of parameter space vectors, we provide a straightforward mapping of experimental information into parameter space.

Laser control of a dark vibrational state of acetylene in the gas phase-Fourier transform pulse shaping constraints and effects of decoherence.

We propose a methodology to tackle the laser control of a non-stationary dark ro-vibrational state of acetylene (C2H2), given realistic experimental limitations in the 7.7 μm (1300cm-1) region. Simulations are performed using the Lindblad master equation, where the so-called Lindblad parameters are used to describe the effect of the environment in the dilute gas phase. A phenomenological representation of the parameters is used, and they are extracted from high-resolution spectroscopy line broadening data. An effective Hamiltonian is used for the description of the system down to the rotational level close to experimental accuracy. The quality of both the Hamiltonian and Lindblad parameters is assessed by a comparison of a calculated infrared spectrum with the available experimental data. A single shaped laser pulse is used to perform the control, where elements of optics and pulse shaping using masks are introduced with emphasis on experimental limitations. The optimization procedure, based on gradients, explicitly takes into account the experimental constraints. Control performances are reported for shaping masks of increasing complexity. Although modest performances are obtained, mainly due to the strong pulse shaping constraints, we gain insights into the control mechanism. This work is the first step toward the conception of a realistic experiment that will allow for population characterization and manipulation of a non-stationary vibrational "dark" state. Effects of the collisions on the laser control in the dilute gas phase, leading to decoherence in the molecular system, are clearly shown.

Super-Heisenberg scaling in Hamiltonian parameter estimation in the long-range Kitaev chain

In quantum metrology, nonlinear many-body interactions can enhance the precision of Hamiltonian parameter estimation to surpass the Heisenberg scaling. Here, we consider the the estimation of the interaction strength in linear systems with long-range interactions and using the Kitaev chains as a case study, we establish a transition from the Heisenberg to super-Heisenberg scaling in the quantum Fisher information by varying the interaction range. We further show that quantum control can improve the prefactor of the quantum Fisher information. Our results explore the advantage of optimal quantum control and long-range interactions in many-body quantum metrology.

Angle-resolved optically detected magnetic resonance as a tool for strain determination in nanostructures

In this paper, we apply the angle-resolved optically detected magnetic resonance (ODMR) technique to study a series of strained (Cd, Mn)Te/(Cd, Mg)Te quantum wells (QWs) produced by molecular beam epitaxy. By analyzing characteristic features of ODMR angular scans, we determine the strain-induced axial-symmetry spin Hamiltonian parameter $D$ with neV precision. Furthermore, we use low-temperature optical reflectivity measurements and x-ray diffraction scans to evaluate the local strain present in the QW material. In our analysis, we take into account different thermal expansion coefficients of the GaAs substrate and CdTe buffer. The additional deformation due to the thermal expansion effects has the same magnitude as the deformation that originates from the different compositions of the samples. Based on the evaluated deformations and values of the strain-induced axial-symmetry spin Hamiltonian parameter $D$, we find the strain spin-lattice coefficient ${G}_{11}=(72.2\ifmmode\pm\else\textpm\fi{}1.9)$ neV for ${\mathrm{Mn}}^{2+}$ in CdTe and shear deformation potential $b=(\ensuremath{-}0.94\ifmmode\pm\else\textpm\fi{}0.11)$ eV for CdTe.

Spin-orbit interactions may relax the rigid conditions leading to flat bands

Flat bands are of extreme interest in a broad spectrum of fields since, given their high degeneracy, a small perturbation introduced in the system is able to push the ground state in the direction of an ordered phase of interest. Hence, the flat-band engineering in real materials attracts huge attention. However, manufacturing a flat band represents a difficult task because its appearance in a real system is connected to rigid mathematical conditions relating a part of Hamiltonian parameters. Consequently, whenever a flat band is to be manufactured, these Hamiltonian parameters must be tuned exactly to the values fixed by these rigid mathematical conditions. Here we demonstrate that taking the many-body spin-orbit interaction into account, which can be continuously tuned, e.g., by external electric fields, these rigid mathematical conditions can be substantially relaxed. Consequently, we show that a $\ensuremath{\sim}20%--30%$ variation in the Hamiltonian parameters rigidly fixed by the flat-band conditions can also lead to flat bands in the same, or in a bit displaced, position on the energy axis. This percentage can even increase to $\ensuremath{\sim}80%$ in the presence of an external magnetic field. This study is made for the case of conducting polymers. These systems are relevant not only because they have broad application possibilities, but also because they can be used to present the mathematical background of the flat-band conditions in full generality, in a concise, clear, and understandable manner applicable everywhere in itinerant systems.

Nonreciprocal photocurrent in the nonlinear response of two-dimensional models

Monolayer two-dimensional crystalline systems with broken inversion symmetry have shown unique optical response properties. We calculate the nonreciprocal photocurrent in the nonlinear response of two-dimensional models involving the Berry connection in the presence of impurity scattering processes. Our results are based on quantum kinetic theory, where we calculate the nonequilibrium distribution function of the valence and conduction bands. We find that the significant current peak emerges at the interband absorption threshold in the electron-doped system and that the peak is remarkably sensitive to the electron density as well as the effective band masses. The current originates from trigonal warping and increases when the warping hopping parameter increases as well the band masses. A nonlinear Hall response is equally obtained for certain model Hamiltonian parameters. Our findings provide an alternative platform for nonlinear light-matter interaction engineering.

EPR characteristics of radiation-induced defects in Ge-rich α-quartz

Electron paramagnetic resonance (EPR) in a synthetic Si0.975Ge0.025O2 single crystal of α–quartz structure has been studied. After fast electron irradiation previously studied and new Ge-related paramagnetic centers (PCs) have been recognized using computer simulation of the observed EPR spectra. Increasing radiation doses allow to distinguish four paramagnetic [GeO4/M+]0 centers AGeLi, CGeLi, DGeLi, and AGeNa as well as four oxygen-vacancy electron centers Ge Eˊ1, Ge Eˊ2, Ge(IV) and a new Ge(V) center. The selective UV bleaching and distinct thermal stability of different centers allow us to determine the spin Hamiltonian parameters for the Ge(V) center.

Global modeling of the 12C32S2 line positions within the framework of the non-polyad model of effective Hamiltonian

The global modeling of 12C32S2 line positions in the 240 – 12 000 cm−1 region has been performed using the non-polyad model of effective Hamiltonian. The effective Hamiltonian parameters were fitted to the measured line positions collected from the literature. The fitted set of 99 effective Hamiltonian parameters allowed reproduction of more than 13 000 measured line positions with the dimensionless weighted standard deviation of 1.65. The root-mean-square of errors of the fitted high-resolution rotation-vibration line positions in the 240 - 466 cm−1 range is 0.0013 cm−1. A comparison of the calculated line positions based on the fitted model with HITRAN2020 is presented and discussed.

The vibrational-rotational high-resolution spectrum in the region of 3ν-=SUB=-4-=/SUB=-, ν-=SUB=-2-=/SUB=-+2ν-=SUB=-4-=/SUB=- and 2ν-=SUB=-2-=/SUB=-+ν-=SUB=-4-=/SUB=- bands of the -=SUP=-72-=/SUP=-GeH-=SUB=-4-=/SUB=- molecule

The high-resolution spectrum of the 72GeH4 molecule was recorded on a Bruker IFS 125HR Fourier spectrometer with an optical resolution of 0.003 cm-1. The line positions were analyzed for ten interacting vibrational-rotational bands 3ν4 (1F2, F1, 2F2), ν2+ 2ν4 (1E, F1, F2, 2E) and 2ν2+ν4 (1F2, F1, 2F2) in the range 2350-2750 cm-1. As a result of the analysis, 1726 experimental lines were identified with the maximum value of the quantum number Jmax = 17; then used in the fitting procedure with parameters of the effective Hamiltonian. The resulting set of 35 spectroscopic parameters describes the vibrational-rotational structure of the spectrum with drms = 7.5· 10-4 cm-1. Keywords: GeH4, spectroscopic parameters, vibrational spectrum analysis, high-resolution Fourier spectra.

Колебательно-вращательный спектр высокого разрешения в районе полос 3ν-=SUB=-4-=/SUB=-, ν-=SUB=-2-=/SUB=-+2ν-=SUB=-4-=/SUB=- и 2ν-=SUB=-2-=/SUB=-+ν-=SUB=-4-=/SUB=- молекулы -=SUP=-72-=/SUP=-GeH-=SUB=-4-=/SUB=-

The high-resolution spectrum of the 72GeH4 molecule was recorded on a Bruker IFS 125HR Fourier spectrometer with an optical resolution of 0.003 cm-1. The line positions were analyzed for ten interacting vibrational-rotational bands 3ν4 (1F2, F1, 2F2), v2+ 2ν4 (1E, F1, F2, 2E) and 2ν2+v4 (1F2, F1, 2F2) in the range 2350-2750 cm-1. As a result of the analysis, 1726 experimental lines were identified with the maximum value of the quantum number Jmax = 17; then used in the fitting procedure with parameters of the effective Hamiltonian. The resulting set of 35 spectroscopic parameters describes the vibrational-rotational structure of the spectrum with drms = 7.5 · 10-4 cm-1.

A Monte Carlo study on the temperature dependence of hysteresis loops in Ising Spin-1 Square Bilayers

A Metropolis Monte Carlo simulation is used in this paper to investigate the temperature dependency of the hysteresis loops of a spin-1 bilayer with square monolayers. In this system, the atoms interact ferromagnetically in-plane, with either ferromagnetic or antiferromagnetic interplane interactions. The effects of four distinct combinations of the Hamiltonian parameters on the hysteresis behaviours are discussed in detail. The geometry of the hysteresis loops changes depending on how the exchange couplings are combined. With ferromagnetic interlayer coupling, only the central hysteresis loop opens while for the antiferromagnetic case, the hysteresis loop becomes a double loop for the specific combination of coupling strengths. Additionally, in all these cases, the area of the hysteresis loops grows with the gradual lowering of the temperature.

Спектроскопия высокого разрешения сильно резонирующих полос ν-=SUB=-4-=/SUB=-, ν-=SUB=-6-=/SUB=-, ν-=SUB=-7-=/SUB=-, ν-=SUB=-8-=/SUB=- и ν-=SUB=-10-=/SUB=- дейтерированного этилена C-=SUB=-2-=/SUB=-H-=SUB=-3-=/SUB=-D

Rotational structure of strongly interacting bands v4,v6,v7,v8, and v10 of the C2H3D molecule is spectroscopically studied. Spectra were recorded by Fourier spectrometer Brucker IFD 125HR in the laboratory of physical and theoretical chemistry of Technical University of Braunschweig. 27950 transitions with maximum values of J=40 and Ka=20 were assigned to the studied bands. The effective Hamiltonian parameters were determined in the model including the v3 resonating state. The 4028 upper energy levels were used as incoming data. They are reproduced with root mean square deviation of drms = 1.7.10-4 cm-1. Corresponding value for more than 24000 line positions is drms = 2.1.10-4 cm-1.

EPR Study of the Mn-Doped Magnesium Titanate Ceramics

Manganese-doped magnesium titanate ceramic samples obtained by a solid-state reaction via sintering in the air from a mixture of MgO and TiO2 powders of different molar ratios were analyzed by electron paramagnetic resonance (EPR) technique. The EPR signals of Mn2+ ions (S = 5/2, І = 5/2) in crystal phases of MgO, Mg2TiO4, and MgTiO3 were detected. We have obtained the following spin Hamiltonian parameters for Mn2+ ions: g = 2.0015, A ∼81.0 × 10−4 cm−1 (in MgO phase); g = 2.0029, A ∼73.8 × 10−4 cm−1 , b 2 0 = 35 × 10−4 cm−1 (in Mg2TiO4 phase); g = 2.0040, A ∼79.0 × 10−4 cm−1 , b 2 0 = 165 × 10−4 cm−1 (in MgTiO3 phase). Despite the presence of Mn4+ centers in both Mg2TiO4:Mn and MgTiO3:Mn ceramics confirmed by previous optical studies, no EPR signals related to Mn4+ ions (S = 3/2, І = 5/2) were found. The Mn2+ EPR signals are proposed as structural probes in manganese-doped magnesium titanate ceramics.

High resolution spectroscopy of strongly interacting bands ν-=SUB=-4-=/SUB=-, ν-=SUB=-6-=/SUB=-, ν-=SUB=-7-=/SUB=-, ν-=SUB=-8-=/SUB=-, and ν-=SUB=-10-=/SUB=- of deuterated ethylene, C-=SUB=-2-=/SUB=-H-=SUB=-3-=/SUB=-D

Rotational structure of strongly interacting bands ν4, ν6, ν7, ν8, and ν10 of the C2H3D molecule is spectroscopically studied. Spectra were recorded by Fourier spectrometer Brucker 125HR in the laboratory of physical and theoretical chemistry of Technical University of Braunschweig. 27950 transitions with maximum values of Jmax = 40 and Kmaxa= 20 were assigned to the studied bands. The effective Hamiltonian parameters were determined in the model including the ν3 resonating state. The 4028 upper energy levels were used as incoming data. They are reproduced with root mean square deviation of drms =1.7· 10-4 cm-1. Corresponding value for more than 24000 line positions is drms = 2.1 · 10-4 cm-1. Keywords: ethylene, high resolution spectroscopy, strongly interacting bands, Fourier-spectroscopy.

Skyrmion-driven topological Hall effect in a Shastry-Sutherland magnet

The Shastry-Sutherland model and its generalizations have been shown to capture emergent complex magnetic properties from geometric frustration in several quasi-two-dimensional quantum magnets. Using an $sd$ exchange model, we show here that metallic Shastry-Sutherland magnets can exhibit a topological Hall effect driven by magnetic skyrmions under realistic conditions. The magnetic properties are modeled with competing symmetric Heisenberg and asymmetric Dzyaloshinskii-Moriya exchange interactions, while a coupling between the spins of the itinerant electrons and the localized moments describes the magnetotransport behavior. Our results, employing complementary Monte Carlo simulations and a novel machine learning analysis to investigate the magnetic phases, provide evidence for field-driven skyrmion crystal formation for an extended range of Hamiltonian parameters. By constructing an effective tight-binding model of conduction electrons coupled to the skyrmion lattice, we clearly demonstrate the appearance of the topological Hall effect. We further elaborate on the effects of finite temperatures on both magnetic and magnetotransport properties.