Tensor Elements Research Articles

Crystallographic Spin Torque Conductivity Tensor of Epitaxial IrO2 Thin Films for Oxide Spintronics.

Unconventional spin-orbit torques arising from electric-field-generated spin currents in anisotropic materials have promising potential for spintronic applications, including for perpendicular magnetic switching in high-density memory applications. Here, all the independent elements of the spin torque conductivity tensor allowed by bulk crystal symmetries for the tetragonal conductor IrO2 are determined via measurements of conventional (in-plane) anti-damping torques for IrO2 thin films in the high-symmetry (001) and (100) orientations. It is then tested whether rotational transformations of this same tensor can predict both the conventional and unconventional anti-damping torques for IrO2 thin films in the lower-symmetry (101), (110), and (111) orientations, finding good agreement. The results confirm that spin-orbit torques from all these orientations are consistent with the bulk symmetries of IrO2, and show how simple measurements of conventional torques from high-symmetry orientations of anisotropic thin films can provide an accurate prediction of the unconventional torques from lower-symmetry orientations.

Second harmonic generation null angle polarization analysis for determining interfacial potential at charged interfaces.

Methods of quantifying the electrostatics of charged interfaces are important in a range of research areas. The surface-selective nonlinear optical technique second harmonic generation (SHG) is a sensitive probe of interfacial electrostatics. Recent work has shown that detection of the SHG phase in addition to its amplitude enables direct quantification of the interfacial potential. However, the experimental challenge of directly detecting the phase interferometrically with sufficient precision and stability has led to the proposal and development of alternative techniques to recover the same information, notably through wavelength scanning or angle scanning, each of which has their own associated experimental challenges. Here, we propose a new polarization-based approach to recover the required phase information, building upon the previously established nonlinear optical null ellipsometry (NONE) technique. Although NONE directly returns only relative phase information between different tensor elements of the second-order susceptibility, it is shown that a symmetry relation that connects the tensor elements of the potential-dependent third-order susceptibility can be used to generate the absolute phase reference required to calculate the interfacial potential. The sensitivity of the technique to potential at varying surface charge densities and ionic strengths is explored by means of simulated data of the silica:water interface. The error associated with the use of the linearized Poisson-Boltzmann approximation is discussed and compared to the error associated with the precision of the measured NONE null angles. Overall, the results suggest that NONE is a promising approach for performing phase-resolved SHG based quantification of interfacial potentials that experimentally requires only the addition of standard polarization optics to the basic single-wavelength, fixed-angle SHG apparatus.

Complete property tensors of some low-symmetry borate NLO crystals

Several low-symmetry borate crystals, such as α-BiB3O6 (BiBO), YCa4O(BO3)3 (YCOB) and La2CaB10O19 (LCB) show not only promising nonlinear optical (NLO) properties but also other favorable physical properties like large electro-optic (EO) coefficients and exceptionally large piezoelectric constants. Those materials may serve as high temperature sensors and electro- or acoustic- modulators beyond their traditional applications in high power laser generations. The knowledge of their full property tensors are indispensable for their efficient and practical usages. Due to the low-symmetry nature, more none-zero matrix elements are present and those elements most likely are combined when measuring them. Therefore, experimental determinations of the full tensor elements are not always easy especially for those high rank tensors. In fact, though being discovered over several decades, some of the property tensor matrices are still missing. Recently it is shown that by applying a modified post-DFT LD (density functional theory + London dispersion) correction based on linear combination of atomic orbitals (LCAO) and B3LYP functional, many important material property tensors of BiBO crystal are calculated in unprecedented precisions. Among them, theoretical calculation of the refractive indices in the terahertz (THz) range was firstly achieved. The calculation also confirms that BiBO has an exceptional large piezoelectric constant d22 = 40 pC/N and largest free EO coefficients on the order of 10 pm/V among borate crystals. The same calculation has been extended to the other low-symmetry borate NLO crystals, including YCOB and LCB. With those calculated material constants, practical devices may be designed with preferable figure of merits over existing materials.

Study of the anisotropy of α-<sup>33</sup>S single crystal thermal expansion

A technique for arbitrary symmetry crystals unit cell parameters refining on modern single-crystal diffractometers is described. The technique is based on the 2D detector position calibration. The elementary orthorhombic unit cell parameters of the α-33S single crystal have been refined. The anisotropy of parameters changes in the range of 90–350 K has been studied. It is shown that the relative increase in parameter c is 6.4%. The obtained dependences are approximated by second–third degree polynomials. The absolute increase in cell volume is 138.4 A3, and the relative increase is 4.3%. The temperature dependencies of the thermal expansion tensor elements has been refined. The coefficients of α-33S thermal expansion tensor at the room temperature are: α11 = 15.35 × 10–5, α22 = 8.56 × 10–5, α33 = 9.12 × 10–5 К–1.

Variations in Diffusion Coefficients on Equinox Days at Specified Critical Heights of the Ionosphere at the Equator

This study investigates the local time diffusion coefficient for stable and unstable ( , ) states at the equator (00), "the geographical latitude where the first peak of the magnetic equatorial trough in the ionosphere occurs," during the spring and fall equinoxes (March 21 and September 23). The findings show that the diffusion tensor in a steady state is completely real and has a magnitude equal to the speed of light in a steady state. But in the unsteady state, the diffusion tensor consists of two parts, real and imaginary. The diagonal elements of the real part tensor are of the size of the conductivity in the ionosphere and the elements of the imaginary part are of the size of the speed of sound with about the same magnitude. Furthermore, for all assumed conditions, the diffusion elements form the first peak of the magnetic equatorial trough at 6.00 am local time.

Comprehensive measurement of three-dimensional thermal conductivity tensor using a beam-offset square-pulsed source (BO-SPS) approach

Accurately measuring the three-dimensional thermal conductivity tensor is essential for understanding and engineering the thermal behavior of anisotropic materials. Existing methods often struggle to isolate individual tensor elements, leading to large measurement uncertainties and time-consuming iterative fitting procedures. In this study, we introduce the Beam-Offset Square-Pulsed Source (BO-SPS) method for comprehensive measurements of three-dimensional anisotropic thermal conductivity tensors. This method uses square-pulsed heating and precise temperature rise measurements to achieve high signal-to-noise ratios, even with large beam offsets and low modulation frequencies, enabling the isolation of thermal conductivity tensor elements. We demonstrate and validate the BO-SPS method by measuring X-cut and AT-cut quartz samples. For X-cut quartz, with a known relationship between in-plane and cross-plane thermal conductivities, we can determine the full thermal conductivity tensor and heat capacity simultaneously. For AT-cut quartz, assuming a known heat capacity, we can determine the entire anisotropic thermal conductivity tensor, even with finite off-diagonal elements. Our results yield consistent principal thermal conductivity values for both quartz types, demonstrating the method's reliability and accuracy. This research highlights the BO-SPS method's potential to advance the understanding of thermal behavior in complex materials.

Bulk photovoltaic effect in ferroelectric nematic liquid crystals.

The bulk photovoltaic (BPV) effect in ferroelectric liquid crystals is of increasing scientific interest owing to its great potential for light-energy conversion. The ferroelectric nematic phase exhibits a huge spontaneous polarization that can be aligned to a preferred direction. In this Letter, we investigate the tensorial properties of the BPV effect in the planarly aligned ferroelectric nematic phase of the liquid crystalline material RM734. A steady-state short-circuit photocurrent of ~160 pA and an open-circuit photovoltage of ~50 mV were observed in a cell with a thickness of 5.5 µm under the illumination of ultraviolet light without any bias voltage. Based on the photocurrent measurements in different electrode configurations, the non-zero elements of the BPV tensor were obtained. The BPV effect is attributed to the combination of the spontaneous polarization and the asymmetric distribution of photoinduced charge carriers. This study not only provides an understanding of the bulk PV mechanism in soft ferroelectrics but also promises a wide range of unprecedented, to the best of our knowledge, benefits for light harvesting to engineer marketable photovoltaic devices.

Surface populations as a model for the distance-dependence of the interfacial refractive index.

Vibrational sum frequency spectra provide information about interfaces that is sensitive to the orientation of molecules, their electronic environment, and the local electric fields. Here, we use molecular dynamics simulations in order to study a surfactant, para-cyanophenol, at the air-water interface. The volume fractions of water and the organic surfactant are considered at various points over the nanometer-scale region in a Lorentz-Lorenz model. We find that the calculated ratios of nonlinear susceptibility tensor elements are in agreement with experimental data only when this depth profile was considered. We also use these data to evaluate the ratio of the C-N hyperpolarizability tensor elements in the interfacial region.

Polarized Raman Study of First-Order Phonons in Self-Flux Grown Single-Crystalline WTe2.

Bulk single crystals of WTe2 were grown by the self-flux method and characterized by X-ray diffraction, polarized micro-Raman spectroscopy, and optical microscopy. All methods revealed a high crystalline quality, thus demonstrating the advantages of the growth method used as a starting base for the synthesis of high-quality 2D materials. In each main scattering configuration, we recorded a series of Raman spectra in different sample orientations achieved by rotating the sample around the incident laser beam. In addition to the well-established case of excitation along the c crystal axis, we also applied laser excitation along the a and b axes. Thus, scattering configurations were also realized in the XZ and YZ polarization planes, for which no comparative literature data have yet been established. In these experiments, two new Raman-active phonons with B2 symmetry and frequencies of 89 cm-1 and 122 cm-1 were identified. The obtained experimental data enabled us to derive the magnitude ratios of all three tensor elements of the A1 modes and to find their phase differences.

State diagrams to determine tree tensor network operators

This work is concerned with tree tensor network operators (TTNOs) for representing quantum Hamiltonians. We first establish a mathematical framework connecting tree topologies with state diagrams. Based on these, we devise an algorithm for constructing a TTNO given a Hamiltonian. The algorithm exploits the tensor product structure of the Hamiltonian to add paths to a state diagram, while combining local operators if possible. We test the capabilities of our algorithm on random Hamiltonians for a given tree structure. Additionally, we construct explicit TTNOs for nearest neighbour interactions on a tree topology. Furthermore, we derive a bound on the bond dimension of tensor operators representing arbitrary interactions on trees. Finally, we consider an open quantum system in the form of a Heisenberg spin chain coupled to bosonic bath sites as a concrete example. We find that tree structures allow for lower bond dimensions of the Hamiltonian tensor network representation compared to a matrix product operator structure. This reduction is large enough to reduce the number of total tensor elements required as soon as the number of baths per spin reaches 3.

Gravitational form factors of charmonia

We investigate the gravitational form factors of charmonium. Our method is based on a Hamiltonian formalism on the light front known as basis light-front quantization. The charmonium mass spectrum and light-front wave functions were obtained from diagonalizing an effective Hamiltonian that incorporates confinement from holographic QCD and one-gluon exchange interaction from light-front QCD. We proposed a quantum many-body approach to construct the hadronic matrix elements of the energy momentum tensor T++ and T+−, which are used to extract the gravitational form factors A(Q2) and D(Q2). The obtained form factors satisfy the known constraints, e.g., the von Laue condition. From these quantities, we also extract the energy, pressure and light-front energy distributions of the system. We find that hadrons are multilayer systems. Published by the American Physical Society 2024

A generalizable framework for low-rank tensor completion with numerical priors

Low-Rank Tensor Completion, a method which exploits the inherent structure of tensors, has been studied extensively as an effective approach to tensor completion. Whilst such methods attained great success, none have systematically considered exploiting the numerical priors of tensor elements. Ignoring numerical priors causes loss of important information regarding the data, and therefore prevents the algorithms from reaching optimal accuracy. Despite the existence of some individual works which consider ad hoc numerical priors for specific tasks, no generalizable frameworks for incorporating numerical priors have appeared. We present the Generalized CP Decomposition Tensor Completion (GCDTC) framework, the first generalizable framework for low-rank tensor completion that takes numerical priors of the data into account. We test GCDTC by further proposing the Smooth Poisson Tensor Completion (SPTC) algorithm, an instantiation of the GCDTC framework, whose performance exceeds current state-of-the-arts by considerable margins in the task of non-negative tensor completion, exemplifying GCDTC’s effectiveness. Our code is open-source.

Enhanced second-order nonlinear susceptibility in type-II asymmetric quantum well structures

Asymmetric quantum wells (AQWs) utilizing interband transitions enhance second-order susceptibility over a wide wavelength range compared to natural crystals. The nonlinear susceptibility is further enhanced in AQWs with type-II band alignment as compared to type-I band alignment, a result of the larger interband charge shift. This enhancement is demonstrated in this work by analyzing three type-I and type-II AQW designs based on the lattice-matched InP/AlGaInAs materials systems using the envelope wavefunction approximation. The calculated interband second-order susceptibility tensor elements in type-II structures range between 20 and 1.60 × 103 pm/V for nearly resonant optical rectification and difference frequency generation applications at near-infrared and terahertz wavelengths, an improvement of nearly 1 order of magnitude over the type-I structures and 1–2 orders of magnitude over natural crystals such as LiNbO3, KTiOPO4 (KTP), or GaAs. A factor of 2–3 further enhancement of the tensor elements is achieved by optimizing the well widths and band offsets of the type-II asymmetric quantum wells. The type-II structure can be implemented in other material systems spanning the longwave infrared to visible wavelengths, enhancing nonlinear susceptibility for various applications, including photonic integrated circuits.

Large transverse thermoelectric effect induced by the mixed-dimensionality of Fermi surfaces

Transverse thermoelectric effect, the conversion of longitudinal heat current into transverse electric current, or vice versa, offers a promising energy harvesting technology. Materials with axis-dependent conduction polarity, known as p × n-type conductors or goniopolar materials, are potential candidate, because the non-zero transverse elements of thermopower tensor appear under rotational operation, though the availability is highly limited. Here, we report that a ternary metal LaPt2B with unique crystal structure exhibits axis-dependent thermopower polarity, which is driven by mixed-dimensional Fermi surfaces consisting of quasi-one-dimensional hole sheet with out-of-plane velocity and quasi-two-dimensional electron sheets with in-plane velocity. The ideal mixed-dimensional conductor LaPt2B exhibits an extremely large transverse Peltier conductivity up to ∣αyx∣ = 130 A K−1 m−1, and its transverse thermoelectric performance surpasses those of topological magnets utilizing the anomalous Nernst effect. These results thus manifest the mixed-dimensionality as a key property for efficient transverse thermoelectric conversion.

Magneto-transport in the monolayer MoS2 material system for high-performance field-effect transistor applications

Electronic transport in monolayer MoS2 is significantly constrained by several extrinsic factors despite showing good prospects as a transistor channel material. Our paper aims to unveil the underlying mechanisms of the electrical and magneto-transport in monolayer MoS2. In order to quantitatively interpret the magneto-transport behavior of monolayer MoS2 on different substrate materials, identify the underlying bottlenecks, and provide guidelines for subsequent improvements, we present a deep analysis of the magneto-transport properties in the diffusive limit. Our calculations are performed on suspended monolayer MoS2 and MoS2 on different substrate materials taking into account remote impurity and the intrinsic and extrinsic phonon scattering mechanisms. We calculate the crucial transport parameters such as the Hall mobility, the conductivity tensor elements, the Hall factor, and the magnetoresistance over a wide range of temperatures, carrier concentrations, and magnetic fields. The Hall factor being a key quantity for calculating the carrier concentration and drift mobility, we show that for suspended monolayer MoS2 at room temperature, the Hall factor value is around 1.43 for magnetic fields ranging from 0.001 to 1 Tesla, which deviates significantly from the usual value of unity. In contrast, the Hall factor for various substrates approaches the ideal value of unity and remains stable in response to the magnetic field and temperature. We also show that the MoS2 over an Al2O3 substrate is a good choice for the Hall effect detector. Moreover, the magnetoresistance increases with an increase in magnetic field strength for smaller magnetic fields before reaching saturation at higher magnetic fields. The presented theoretical model quantitatively captures the scaling of mobility and various magnetoresistance coefficients with temperature, carrier densities, and magnetic fields.

Spectroscopic analysis of the sum-frequency response of the carbon-hydrogen stretching modes in collagen type I.

We studied the origin of the vibrational signatures in the sum-frequency generation (SFG) spectrum of fibrillar collagen type I in the carbon-hydrogen stretching regime. For this purpose, we developed an all-reflective, laser-scanning SFG microscope with minimum chromatic aberrations and excellent retention of the polarization state of the incident beams. We performed detailed SFG measurements of aligned collagen fibers obtained from rat tail tendon, enabling the characterization of the magnitude and polarization-orientation dependence of individual tensor elements Xijk2 of collagen's nonlinear susceptibility. Using the three-dimensional atomic positions derived from published crystallographic data of collagen type I, we simulated its Xijk2 elements for the methylene stretching vibration and compared the predicted response with the experimental results. Our analysis revealed that the carbon-hydrogen stretching range of the SFG spectrum is dominated by symmetric stretching modes of methylene bridge groups on the pyrrolidine rings of the proline and hydroxyproline residues, giving rise to a dominant peak near 2942cm-1 and a shoulder at 2917cm-1. Weak asymmetric stretches of the methylene bridge group of glycine are observed in the region near 2870cm-1, whereas asymmetric CH2-stretching modes on the pyrrolidine rings are found in the 2980 to 3030cm-1 range. These findings help predict the protein's nonlinear optical properties from its crystal structure, thus establishing a connection between the protein structure and SFG spectroscopic measurements.

Tunable Chemochromism and Elastic Properties in Intercalated MoO3: Au-, Cr-, Fe-, Ge-, Mn-, and Ni-MoO3.

Chemical tunability of the elastic constants of α-MoO3, a two-dimensional layered oxide, is demonstrated with mutability on the order of tens of GPa, simply by choice of a metal intercalant including Au, Cr, Fe, Ge, Mn, and Ni. Using Brillouin laser light scattering from confined acoustic phonons in nanometer-thick materials, the in-plane angular dispersion of the quantized acoustic phonon branches of 2D layered, intercalated MoO3 is measured and used to determine the bulk modulus (K), Young's moduli (E11, E22, and E33), each of the nine independent elastic tensor elements (cij), and the thickness. Intercalation of metals generally reduces the anisotropy in MoO3 except in Ge-MoO3, for which the in-plane longitudinal elastic anisotropy is unaffected. Chemochromism from transparent white (MoO3 and Fe-MoO3) to near black (Ni-MoO3) to brilliant dark blue (Ge-MoO3) is demonstrated and is associated with a reduction in electronic band gap with intercalation and an increase in absorption >600 nm for some intercalants (Cr-, Ge-, and Mn-MoO3).

Friction tensor for an ellipsoid enclosed in a rarefied gas

This research renders calculations of rotranslational friction and diffusion tensors in a rarefied gas, considering both specular and diffuse reflection off ellipsoidal particles. Calculations were conducted in a spherical polar coordinate system, revealing the dynamic nature of these off-diagonal tensors. The tensor elements were determined analytically, intending to compute the surface integrals. All diagrams, and pictures of two-dimensional surfaces were obtained by the numerical integration process in MATLAB. Additionally, we performed calculations without using the time parameter and time derivatives in the relevant relations. Deviations from the state of spherical symmetry were observed in the results for an ellipsoid and show that the tensors are dynamic quantities. Therefore, it is necessary to provide average values. We established that the non-zero elements of the friction tensor for an ellipsoid represent the directions of linear momentum transfer. Also, the non-zero components of the diffusion tensor signify the extent of fluctuations in relevant momentum transfers in corresponding directions.

Hydraulic conductivity tensor of anisotropic soils: the impact on seepage flow

Natural or artificial changes in soil stratigraphic-plane (i.e., the deposition of soil and sediments into distinct layers) orientation can cause variations in hydraulic conductivity in different direction. Hydraulic conductivity must, therefore, be considered – in this case – as a nondiagonal, full tensor to appropriately represent the effect of the orientation of soil stratigraphic planes on the seepage flow pattern. This paper introduces the derivation of the formula for the three-dimensional nondiagonal hydraulic conductivity full tensor calculation in terms of azimuth and vertical angles. Furthermore, two-dimensional numerical simulations of the seepage flow beneath a concrete dam are presented to demonstrate the need to account for the nondiagonal elements of the hydraulic conductivity tensor in anisotropic soils of varying degrees of stratigraphic tilt with respect to the coordinate system.

Accessing the gravitational form factors of the nucleon and nuclei through a massive graviton

In contrast to the electromagnetic form factors of the nucleon and nuclei that have been extensively studied in electron scattering, there is no known way to directly measure the gravitational form factors (GFFs), the off-forward hadronic matrix element of the QCD energy-momentum tensor. I suggest exploring the possibility to access the GFFs of the proton and nuclei in conjunction with massive graviton searches at future TeV-scale lepton-ion colliders. Published by the American Physical Society 2024