Exact Spin Research Articles

Exact Theory Applied to the Lithium Atom.

The free complement (FC) theory for solving the scaled Schrödinger equation (SSE) was applied to the Li atom for calculating the exact wave functions, the energies, and the various properties of the ground doublet S and excited P states. The SSE is equivalent to the Schrödinger equation (SE) but does not have the divergence difficulty of the variational equation of the SE. Because the Li atom is a three-electron system, the variational exact FC calculations for solving the SSE are possible using the function g = 1 - exp(-γr) as the "correct" scaling function of the SSE. The "reasonable" scaling function g = r was also used as comparative calculations. We performed variational calculations to the order eight of the FC theory and could obtain essentially exact solutions of the SSE or SE with the "correct" g function of the FC theory. We report here the values of the exact energy, spin density, electron density, and electron-nuclear and electron-electron cusp values of the doublet S and P states. They agreed very well with the experimental values and the best theoretical values presented by Drake and collaborators. This is a simple example that the exact theory gives the exact solutions.

Investigation of the exact spin channels in laser-induced spin dynamics in two mononuclear Cu(II) complexes.

In the quest to harness the potential of nanospintronic applications, we analyze and investigate the spin channels for the ultrafast spin dynamics in mononuclear Cu2+(tdp)Cl2 (Cutdp) and Cu2+(tdp)Cl2·MeCN (Cutdp·MeCN) using a high-level ab initio many-body theory. In that spirit, we select two slightly different polymerizations arising from one parent complex. We establish the difference in magnetic behavior between the two complexes which arises solely from the geometrical differences. We calculate the static magnetic properties, such as the magnetic anisotropy of the complexes, which is analyzed by means of the magnetic moment of the ground state. The asymmetry of the core Cu-Cl-Cu-Cl axial plane unit is also reflected in the ground state absorption spectra of the two complexes. Comparisons with the experimental data are in good agreement with the exception of one peak in the theoretical calculations for each of the complexes, confirming the reliability of theoretical methods employed. A major finding in this work is the distinction between classical and coherent superpositions of Λ processes. We employ the selective blocking and retention (SBR) technique to find the unique path or paths for spin dynamic scenarios like spin flip and spin transfer. Additionally, we also present two different scenarios in which intermediate states are involved in spin dynamic processes, (i) classical superposition of Λ processes (i.e., there are many unique paths for transition, even with just one intermediate state the transition completes successfully), and (ii) collective coherent superposition of Λ processes (i.e., there is only one path for the transition, which requires more than one intermediate state to be in a specific coherent superposition). As a consequence, we gain insight into the type of correlations (static or dynamic) involved in a particular spin dynamic scenario.

On the circularly polarized luminescence of individual triplet sublevels.

We discuss the possibility of using circularly polarized luminescence (CPL) as a tool to probe individual triplet spin sublevels that are populated nonadiabatically following photoexcitation. This study is motivated by a mechanism proposed for chirality-induced spin selectivity in which coupled electronic-nuclear dynamics may lead to a non-statistical population of the three triplet sublevels in chiral systems. We find that low-temperature CPL should aid in quantifying the exact spin state/s populated through coupled electronic-nuclear motion in chiral molecules.

Exact spin polarization of massive and massless particles in relativistic fluids at global equilibrium

We present the exact form of the spin polarization vector and the spin density matrix of massive and massless free particles of any spin and helicity at general global equilibrium in a relativistic fluid with non-vanishing thermal vorticity, thus extending the known expression at the linear order. The exact form is obtained by means of the analytic continuation of the relativistic density operator to imaginary thermal vorticity and the resummation of the obtained series. The phenomenological implications for the polarization of the Lambda hyperon in relativistic heavy-ion collisions are addressed.

Terahertz Spin Current Dynamics in Antiferromagnetic Hematite.

An important vision of modern magnetic research is to use antiferromagnets (AFMs) as controllable and active ultrafast components in spintronic devices. Hematite (α-Fe2 O3 ) is a promising model material in this respect because its pronounced Dzyaloshinskii-Moriya interaction leads to the coexistence of antiferromagnetism and weak ferromagnetism. Here, femtosecond laser pulses are used to drive terahertz (THz) spin currents from α-Fe2 O3 into an adjacent Pt layer. Two contributions to the generation of the spin current with distinctly different dynamics are found: the impulsive stimulated Raman scatting that relies on the AFM order and the ultrafast spin Seebeck effect that relies on the net magnetization. The total THz spin current dynamics can be manipulated by a medium-strength magnetic field below 1 T. The control of the THz spin current achieved in α-Fe2 O3 opens the pathway toward tailoring the exact spin current dynamics from ultrafast AFM spin sources.

Relativistic energies and information entropy of the inversely quadratic Hellmann potential

The solutions to the Dirac equation are obtained in the spin and pseudospin symmetry limits are presented using the parametric Nikiforov-Uvarov (pNU) method with the inversely quadratic Hellman (IQH) potential. In the exact non-relativistic spin symmetry limit, the energy and wave function of the IQH potential are obtained and used to investigate the Shannon information entropy of the system. Numerical results of the relativistic energies of the spin and pseudospin symmetry limits of the Dirac equation with the IQH potential are presented and observed to exhibit degeneracy. Also, the results of the Shannon entropy for six states (n = 0, 1, 2, 3, 4, 5) show that the momentum space wave function and probability density are better localized than the position space wave function. Also, the Bialynicki-Birula and Mycielski (BBM) inequality is verified for the system. Our results are found to be consistent with those previously reported in the literature.

The Predictive Power of Exact Constraints and Appropriate Norms in Density Functional Theory.

Ground-state Kohn-Sham density functional theory provides, in principle, the exact ground-state energy and electronic spin densities of real interacting electrons in a static external potential. In practice, the exact density functional for the exchange-correlation (xc) energy must be approximated in a computationally efficient way. About 20 mathematical properties of the exact xc functional are known. In this work, we review and discuss these known constraints on the xc energy and hole. By analyzing a sequence of increasingly sophisticated density functional approximations (DFAs), we argue that (a) the satisfaction of more exact constraints and appropriate norms makes a functional more predictive over the immense space of many-electron systems and (b) fitting to bonded systems yields an interpolative DFA that may not extrapolate well to systems unlike those in the fitting set. We discuss both how the class of well-described systems has grown along with constraint satisfaction and the possibilities for future functional development.

Paramagnetic NMR Shielding Tensors Based on Scalar Exact Two-Component and Spin-Orbit Perturbation Theory.

The temperature-dependent Fermi-contact and pseudocontact terms are important contributions to the paramagnetic NMR shielding tensor. Herein, we augment the scalar-relativistic (local) exact two-component (X2C) framework with spin-orbit perturbation theory including the screened nuclear spin-orbit correction for the EPR hyperfine coupling and g tensor to compute these temperature-dependent terms. The accuracy of this perturbative ansatz is assessed with the self-consistent spin-orbit two-component and four-component treatments serving as reference. This shows that the Fermi-contact and pseudocontact interaction is sufficiently described for paramagnetic NMR shifts; however, larger deviations are found for the EPR spectra and the principle components of the EPR properties of heavy elements. The impact of the perturbative treatment is further compared to that of the density functional approximation and the basis set. Large-scale calculations are routinely possible with the multipole-accelerated resolution of the identity approximation and the seminumerical exchange approximation, as shown for [CeTi6O3(OiPr)9(salicylate)6].

Neutrino spin operator and dispersion in moving matter

We found the spin integral of motion for neutrinos propagating in moving and polarized matter. Contrary to all previous studies this is the exact spin operator commuting with the Hamiltonian for a neutrino in matter which moves in an arbitrary direction relative to the direction of neutrino propagation. The operator obtained opens up the possibility of consistent classification of neutrino states in such a medium and, as a consequence, a systematic description of the related physical phenomena. Using the operator, we obtain a dispersion relation for neutrinos in arbitrary moving matter and consider its particular cases.

Spin solitons in spin-1 Bose–Einstein condensates

Vector solitons in Bose–Einstein condensates are usually investigated analytically with identical intra- and interatomic interactions (for an integrable model). We obtain six families of exact spin soliton solutions for nonintegrable cases, which can be used to describe spin-1 Bose–Einstein condensates. The stability analyses and numerical simulations indicate that three families of spin solitons are robust against spin-dependent interactions and white noise. We further investigate the motion of these stable spin solitons driven by external linear potentials. Their moving trajectories demonstrate that the spin solitons admit a negative–positive mass transition. Some splitting and diffusing behaviors can emerge during the motion of a spin soliton that are absent in spin-1/2 systems. The collisions between spin solitons are exhibited with varying relative velocity and phase. The nonintegrable properties of the systems can give rise to weak amplitude and location oscillations after collision. These stable spin soliton excitations can be used to study the negative inertial mass of solitons, the dynamics of soliton-impurity systems, and the spin dynamics in Bose–Einstein condensates.

Exact spin states and analytic formulas for nonequilibrium spin transport in a three-site one-dimensional system with interacting electrons

Exact spin states and analytic formulas for nonequilibrium spin transport in a three-site one-dimensional system with interacting electrons

Exact spin states and analytic formulas for nonequilibrium spin transport in a three-site one-dimensional system with interacting electrons

Представлен аналитический вывод точных выражений для спиновых состояний и характеристик неравновесного спинового транспорта в типичной одномерной квантовой цепочке с тремя узлами. Из полученного выражения для основного состояния в предположении о половинном заполнении узлов цепочки найдены начальные заряды электронов со спинами вверх и вниз в каждом узле. На основе формализма Келдыша в приближении Хартри-Фока выведены некоторые аналитические формулы для дифференциальной спиновой проводимости, тока спинового переноса и распределения спинового заряда электронов в модели с кулоновским взаимодействием. Учитываются процессы рассеяния, включая кулоновское отталкивание электронов со спинами вверх и вниз, а также спин-спиновые взаимодействия, обусловленные наличием спиновых степеней свободы. Представлены результаты численных расчетов характеристик неравновесного спинового транспорта для некоторых частных значений параметров.

Measuring the spins of heavy binary black holes

An accurate and precise measurement of the spins of individual merging black holes is required to understand their origin. While previous studies have indicated that most of the spin information comes from the inspiral part of the signal, the informative spin measurement of the heavy binary black hole system GW190521 suggests that the merger and ringdown can contribute significantly to the spin constraints for such massive systems. We perform a systematic study into the measurability of the spin parameters of individual heavy binary black hole mergers using a numerical relativity surrogate waveform model including the effects of both spin-induced precession and higher-order modes. We find that the spin measurements are driven by the merger and ringdown parts of the signal for GW190521-like systems, but the uncertainty in the measurement increases with the total mass of the system. We are able to place meaningful constraints on the spin parameters even for systems observed at moderate signal-to-noise ratios, but the measurability depends on the exact six-dimensional spin configuration of the system. Finally, we find that the azimuthal angle between the in-plane projections of the component spin vectors at a given reference frequency cannot be well-measured for most of our simulated configurations even for signals observed with high signal-to-noise ratios.

Exact classical spin dynamics of high spin nanoscale molecular magnetic clusters

A common feature of many organic-based molecular magnets is that inter-molecular magnetic interactions are extremely weak compared to intra-molecular ones. As a result a bulk sample can be described in terms of independent individual molecular magnets made up of a cluster of a small finite number of coupled magnetic spins. Because of the large value of individual spins of several molecular magnetic compounds it turns out that such systems can be described to very high accuracy, at sufficiently high temperatures, by a classical Heisenberg spin model. Only for sufficiently low temperatures need one incorporate the quantum character of the spins. In this work we focus on the exact classical spin dynamics of small nanoscale molecular magnetic clusters of classical Heisenberg spins. The present study permits us to obtain analytical solutions for the time-dependent spin-spin autocorrelation function for certain clusters of classical Heisenberg spins coupled through exchange interaction. This study underscores the potential utility of a classical spin treatment of nanoscale magnetic clusters and provides results useful to interpret data obtained from experiments.

Discovery and characterization of a new type of domain wall in a row-wise antiferromagnet

Antiferromagnets have recently moved into the focus of application-related research, with the perspective to use them in future spintronics devices. At the same time the experimental determination of the detailed spin texture remains challenging. Here we use spin-polarized scanning tunneling microscopy to investigate the spin structure of antiferromagnetic domain walls. Comparison with spin dynamics simulations allows the identification of a new type of domain wall, which is a superposition state of the adjacent domains. We determine the relevant magnetic interactions and derive analytical formulas. Our experiments show a pathway to control the number of domain walls by boundary effects, and demonstrate the possibility to change the position of domain walls by interaction with movable adsorbed atoms. The knowledge about the exact spin structure of the domain walls is crucial for an understanding and theoretical modelling of their properties regarding, for instance, dynamics, response in transport experiments, and manipulation.

Magnetic order in XY-type antiferromagnetic monolayer CoPS3 revealed by Raman spectroscopy

Mermin-Wagner-Coleman theorem predicts no long-range magnetic order at finite temperature in the two-dimensional (2D) isotropic systems, but it does predict a quasi-long-range order with a divergent correlation length at the Kosterlitz-Thouless (KT) transition for planar magnets. As a representative of two-dimensional planar antiferromagnets, single-layer ${\mathrm{CoPS}}_{3}$ carries the promise of monolayer antiferromagnetic platforms for the ultimately thin spintronics. Here, with the aid of magnetostriction which is sensitive to the local magnetic order, we observe the signature phonon mode splitting of below ${T}_{\mathrm{KT}}$ in monolayer ${\mathrm{CoPS}}_{3}$. The two-magnon signal in the monolayer one manifests the associated magnetic transition. It indicates the quasi-long-range order in an exact 2D planar spin model below KT phase transition. The ratio ($J$\ensuremath{'}/$J$) between the interlayer and intralayer interactions, which characterizes the 2D behaviors, is evaluated to be around 0.03. Our results provide an efficient method to detect the quasi-long-range antiferromagnetic ordering in the two-dimensional magnets down to the monolayer limit.

Multichannel nature of three-body recombination for ultracold K39

We develop a full multichannel spin model in momentum space to investigate three-body recombination of identical alkali-metal atoms colliding in a magnetic field. The model combines the exact three-atom spin structure and realistic pairwise atom-atom interactions. By neglecting the interaction between two particles when the spectating particle is not in its initial spin state we arrive at an approximate model. With this approximate model we achieve excellent agreement with the recent precise measurement of the ground Efimov resonance position in potassium-39 close to 33.58 G [Chapurin $et$ $al$., Phys. Rev. Lett. 123, 233402 (2019)]. We analyze the limitations of our approximation by comparing to the numerical results for the full system and find that it breaks down for Feshbach resonances at larger magnetic fields in the same spin channel. There the relevant three-body closed channel thresholds are much closer to the open channel threshold, which enhances the corresponding multichannel couplings. Therefore the neglected components of the interaction should be included for those Feshbach resonances.

Comprehensive study of the global phase diagram of the J−K−Γ model on a triangular lattice

The celebrated Kitaev honeycomb model provides an analytically tractable example with an exact quantum spin liquid ground state. While in real materials, other types of interactions besides the Kitaev coupling ($K$) are present, such as the Heisenberg ($J$) and symmetric off-diagonal ($\Gamma$) terms, and these interactions can also be generalized to a triangular lattice. Here, we carry out a comprehensive study of the $J$-$K$-$\Gamma$ model on the triangular lattice covering the full parameters region, using the combination of the exact diagonalization, classical Monte Carlo and analytic methods. In the HK limit ($\Gamma=0$), we find five quantum phases which are quite similar to their classical counterparts. Among them, the stripe-A and dual N\'{e}el phase are robust against the $\Gamma$ term, in particular the stripe-A extends to the region connecting the $K=-1$ and $K=1$ for $\Gamma<0$. Though the 120$^\circ$ N\'{e}el phase also extends to a finite $\Gamma$, its region has been largely reduced compared to the previous classical result. Interestingly, the ferromagnetic (dubbed as FM-A) phase and the stripe-B phase are unstable in response to an infinitesimal $\Gamma$ interaction. Moreover, we find five new phases for $\Gamma\ne 0$ which are elaborated by both the quantum and classical numerical methods. Part of the space previously identified as 120$^\circ$ N\'{e}el phase in the classical study is found to give way to the modulated stripe phase. Depending on the sign of the $\Gamma$, the FM-A phase transits into the FM-B ($\Gamma>0$) and FM-C ($\Gamma<0$) phase with different spin orientations, and the stripe-B phase transits into the stripe-C ($\Gamma>0$) and stripe-A ($\Gamma<0$). Around the positive $\Gamma$ point, due to the interplay of the Heisenberg, Kiatev and $\Gamma$ interactions, we find a possible quantum spin liquid with a continuum in spin excitations.

Fractons from a liquid of singlet pairs

Fracton phases of matter feature a variety of exciting phenomena stemming from the restricted mobility of their quasiparticles. Here we consider a model of interacting electrons in one dimension that describes hopping of spin-singlet pairs and obeys both charge and dipole conservation laws. The model contains Bethe ansatz integrable sectors which allow us to solve the ground state and calculate the exact spin and single-electron excitation gaps. We observe hallmarks of fractonic behavior, including localization of single-electron excitations and propensity to clustering. Our results demonstrate the important role of the dipole moment conservation law in a simple model of spin-1/2 fermions.

Pseudospin and spin symmetry in the relativistic generalized Woods-Saxon potential including Coulomb-like tensor potential

The Dirac Equation is solved approximately for relativistic generalized Woods-Saxon potential including Coulomb-like tensor potential in exact pseudospin and spin symmetry limits. The bound states energy eigenvalues are found by using wavefunction boundary conditions, and corresponding radial wavefunctions are obtained in terms of hypergeometric function. Some numerical examples are given for the dependence of bound states energy eigenvalues on quantum numbers and potential parameters.