Number Of Spins Research Articles

Optical spectroscopy of an excited Laughlin liquid

Neutral excitations with zero momentum in a Laughlin liquid at an electron filling factor of 1/3 have been studied. It was found that the lowest in energy are spin-magnetogravitons, excitations with a simultaneous change in the electron density in the Laughlin liquid and the spin quantum number of the electron system. The experimental possibility of the formation of new quasi-equilibrium states of anionic matter – Laughlin solutions of spin-magnetogravitons – is demonstrated. A new type of optical scattering is observed in Laughlin solutions.

Projective Spin Adaptation for the Exact Diagonalization of Isotropic Spin Clusters

Spin Hamiltonians, like the Heisenberg model, are used to describe the magnetic properties of exchange-coupled molecules and solids. For finite clusters, physical quantities, such as heat capacities, magnetic susceptibilities or neutron-scattering spectra, can be calculated based on energies and eigenstates obtained by exact diagonalization (ED). Utilizing spin-rotational symmetry SU(2) to factor the Hamiltonian with respect to total spin S facilitates ED, but the conventional approach to spin-adapting the basis is more intricate than selecting states with a given magnetic quantum number M (the spin z-component), as it relies on irreducible tensor-operator techniques and spin-coupling coefficients. Here, we present a simpler technique based on applying a spin projector to uncoupled basis states. As an alternative to Löwdin’s projection operator, we consider a group-theoretical formulation of the projector, which can be evaluated either exactly or approximately using an integration grid. An important aspect is the choice of uncoupled basis states. We present an extension of Löwdin’s theorem for s=12 to arbitrary local spin quantum numbers s, which allows for the direct selection of configurations that span a complete, linearly independent basis in an S sector upon the spin projection. We illustrate the procedure with a few examples.

Spin-wave resonance frequency and quantum fluctuation of the (anti)ferri-(anti)ferrimagnetic double-layer superlattice

The Hamiltonian of a four-sublattice simple cubic superlattice was solved by applying the linear spin-wave theory and the retarded Green's function technique. This study focused on the spin-wave resonance frequency, energy gap, sublattice magnetization, and quantum fluctuations of the system. The results show that the spin quantum number, interlayer (intralayer) exchange couplings, and intralayer anisotropy have a significant influence. In the ground state, the magnetizations of the sublattices are smaller than their spin quantum numbers, indicating the existence of quantum zero-point vibrations in the (anti)ferrimagnetic-(anti)ferrimagnetic bilayer system.

Peculiarities in Rabi oscillations for fast-relaxing electron spins

Rabi oscillations (transient nutations) are a phenomenon that has proven itself well in EPR for identifying electron spin quantum numbers and electron-spin transitions. They are successfully applied when the Rabi frequency significantly exceeds the spin relaxation rates and therefore does not depend on these rates. However, the short transverse relaxation time, being comparable to or even shorter than the dead time of EPR spectrometers, makes it difficult to observe Rabi oscillations and their frequency depends not only on the intensity of the short microwave pulse, but also on its shape and relaxation rates. Two techniques are considered that are suitable for this case, in which Rabi oscillations are detected by monitoring the FID amplitude as a function of pulse duration or microwave field amplitude. We describe the FID-detected Rabi oscillations analytically or numerically for rectangular or shaped pulses, respectively. The description is confirmed by EPR experiments using DPPH as a model sample.

Gadolinium-Based NMR Spin Relaxation Measurements of Near-Surface Electrostatic Potentials of Biomolecules.

NMR spectroscopy is an important tool for the measurement of the electrostatic properties of biomolecules. To this point, paramagnetic relaxation enhancements (PREs) of 1H nuclei arising from nitroxide cosolutes in biomolecular solutions have been used to measure effective near-surface electrostatic potentials (ϕENS) of proteins and nucleic acids. Here, we present a gadolinium (Gd)-based NMR method, exploiting Gd chelates with different net charges, for measuring ϕENS values and demonstrate its utility through applications to a number of biomolecular systems. The use of Gd-based cosolutes offers several advantages over nitroxides for ϕENS measurements. First, unlike nitroxide compounds, Gd chelates enable electrostatic potential measurements on oxidation-sensitive proteins that require reducing agents. Second, the large electron spin quantum number of Gd (7/2) results in notably larger PREs for Gd chelates when used at the same concentrations as nitroxide radicals. Thus, it is possible to measure ϕENS values exclusively from + and - charged compounds even for highly charged biomolecules, avoiding the use of neutral cosolutes that, as we further establish here, limits the accuracy of the measured electrostatic potentials. In addition, the smaller concentrations of cosolutes required minimize potential binding to sites on macromolecules. Fourth, the closer proximity of the paramagnetic center and charged groups within Gd chelates, in comparison to the corresponding nitroxide compounds, enables more accurate predictions of ϕENS potentials for cross-validation of the experimental results. The Gd-based method described here, thus, broadens the applicability of studies of biomolecular electrostatics using solution NMR spectroscopy.

Exchange Energy of the Ferromagnetic Electronic Ground State in a Monolayer Semiconductor.

Mobile electrons in the semiconductor monolayer MoS_{2} form a ferromagnetic state at low temperature. The Fermi sea consists of two circles: one at the K point, the other at the K[over ˜] point, both with the same spin. Here, we present an optical experiment on gated MoS_{2} at low electron density in which excitons are injected with known spin and valley quantum numbers. The resulting trions are identified using a model which accounts for the injection process, the formation of antisymmetrized trion states, electron-hole scattering from one valley to the other, and recombination. The results are consistent with a complete spin polarization. From the splittings between different trion states, we measure the exchange energy Σ, the energy required to flip a single spin within the ferromagnetic state, as well as the intervalley Coulomb exchange energy J. We determine Σ=11.2 meV and J=5 meV at n=1.5×10^{12} cm^{-2} and find that J depends strongly on the electron density n.

Space-time description of atoms, part I: Electronic structures, dark matter, and g-factors of electron, muon and tau

The description of atoms is based on 3D time and some relativistic effects about spinning bodies have been published previously. The time displacement of the electrons also plays an important role. While the principal quantum number [Formula: see text] refers to the angular momentum [Formula: see text] observed by external observer, the azimuth quantum number [Formula: see text] refers to the angular momentum [Formula: see text] observed from the electron itself. The intrinsic angular momentum observed by the electron is [Formula: see text] according to Stern–Gerlach experiment, but the angular momentum observed by external observer is about [Formula: see text]. The magnetic quantum numbers are deduced from the mentioned effects and the trajectories of electrons are non-probabilistic and geometrically well determined. The spin quantum number indicates the time arrow toward the future or toward the past. So, the electrons with opposite time arrows can be grouped in pairs, where the nucleus is in the middle. Descriptions of the dark matter particles and the electrons are given. Using the value [Formula: see text] suggested from the QED, the [Formula: see text]-factors of the electron and muon are [Formula: see text]; [Formula: see text], which give excellent agreements with the experiments. So, if we equalize the formulas for [Formula: see text]-factor from QED and this approach, it determines the theoretical value of [Formula: see text], without experiment.

Quantum Magnetism of the Iron Core in Ferritin Proteins-A Re-Evaluation of the Giant-Spin Model.

The electron-electron, or zero-field interaction (ZFI) in the electron paramagnetic resonance (EPR) of high-spin transition ions in metalloproteins and coordination complexes, is commonly described by a simple spin Hamiltonian that is second-order in the spin S: H=D[Sz2-SS+1/3+E(Sx2-Sy2). Symmetry considerations, however, allow for fourth-order terms when S ≥ 2. In metalloprotein EPR studies, these terms have rarely been explored. Metal ions can cluster via non-metal bridges, as, for example, in iron-sulfur clusters, in which exchange interaction can result in higher system spin, and this would allow for sixth- and higher-order ZFI terms. For metalloproteins, these have thus far been completely ignored. Single-molecule magnets (SMMs) are multi-metal ion high spin complexes, in which the ZFI usually has a negative sign, thus affording a ground state level pair with maximal spin quantum number mS = ±S, giving rise to unusual magnetic properties at low temperatures. The description of EPR from SMMs is commonly cast in terms of the 'giant-spin model', which assumes a magnetically isolated system spin, and in which fourth-order, and recently, even sixth-order ZFI terms have been found to be required. A special version of the giant-spin model, adopted for scaling-up to system spins of order S ≈ 103-104, has been applied to the ubiquitous iron-storage protein ferritin, which has an internal core containing Fe3+ ions whose individual high spins couple in a way to create a superparamagnet at ambient temperature with very high system spin reminiscent to that of ferromagnetic nanoparticles. This scaled giant-spin model is critically evaluated; limitations and future possibilities are explicitly formulated.

Collective long-lived zero-quantum coherences in aliphatic chains.

In nuclear magnetic resonance, long-lived coherences constitute a class of zero-quantum (ZQ) coherences that have lifetimes that can be longer than the relaxation lifetimes T2 of transverse magnetization. So far, such coherences have been observed in systems with two coupled spins with spin quantum numbers I = 1/2, where a term S0T0+T0S0 in the density operator corresponds to a coherent superposition between the singlet S0 and the central triplet T0 state. Here, we report on the excitation and detection of collective long-lived coherences in AA'MM'XX' spin systems in molecules containing a chain of at least three methylene (-CH2-) groups. Several variants of excitation by polychromatic spin-lock induced crossing (poly-SLIC) are introduced that can excite a non-uniform distribution of the amplitudes of terms such as S0S0T0S0S0T0, S0T0S0S0T0S0, and T0S0S0T0S0S0. Once the radio frequency fields are switched off, these are not eigenstates, leading to ZQ precession involving all six protons, a process that can be understood as a propagation of spin order along the chain of CH2 groups before the reconversion into observable magnetization by a second poly-SLIC pulse that can be applied to any one or several of the CH2 groups. In the resulting 2D spectra, the ω2 domain shows SQ spectra with the chemical shifts of the CH2 groups irradiated during the reconversion, while the ω1 dimension shows ZQ signals in absorption mode with linewidths on the order of 0.1Hz that are not affected by the inhomogeneity of the static magnetic field but can be broadened by chemical exchange as occurs in drug screening. The ZQ frequencies are primarily determined by differences ΔJ between vicinal J-couplings.

Fractional and Unitary Electric Charges I: Classical Foundations of Quantum Effects

Numerical value of the atom’s electrical/electromotive charge emerges naturally upon expressing its definitive e-m oscillation frequency ν as an exponent of eight, 8ν  (‘octave quantum’). This simple procedure realizes, for each element, accurate values of the established quantum numbers. It is revealed that unlike others, the spin quantum number ±½ is not an ‘octave quantum’, it actually turns out an exponent of a field coupling that manifests atomic mass. Octave quanta of frequencies of atoms of the second and third (invisible unknown) elements of nature’s chemical periodicity, “blackton” Bl and “boston” Bs, (8⅓, 8⅔)  manifest observational fractional one-third 1/3  and two-third 2/3  electrical charges normally associated with ‘quarks’. Based on the concept of ‘octave quantum’ the author uses periodic arrangement of the chemical elements to present a unique account of established quantum numbers, it facilitates a deeper insight into factors responsible for unusual valences commonly encountered among transition elements. It is concluded that the ease with which the procedure reproduces established quantum numbers strongly suggests an intrinsic classical origin of observational quantum characteristics.

Slow magnetic relaxation in a europium(II) complex.

Single-ion anisotropy is vital for the observation of Single-Molecule Magnet (SMM) properties (i.e., a slow dynamics of the magnetization) in lanthanide-based systems. In the case of europium, the occurrence of this phenomenon has been inhibited by the spin and orbital quantum numbers that give way to J = 0 in the trivalent state and the half-filled population of the 4f orbitals in the divalent state. Herein, by optimizing the local crystal field of a quasi-linear bis(silylamido) EuII complex, the [EuII(N{SiMePh2}2)2] SMM is described, providing an example of a europium complex exhibiting slow relaxation of its magnetization. This behavior is dominated by a thermally activated (Orbach-like) mechanism, with an effective energy barrier of approximately 8 K, determined by bulk magnetometry and electron paramagnetic resonance. Ab initio calculations confirm second-order spin-orbit coupling effects lead to non-negligible axial magnetic anisotropy, splitting the ground state multiplet into four Kramers doublets, thereby allowing for the observation of an Orbach-like relaxation at low temperatures.

Theory for magnetic impurity modes in two-dimensional van der Waals ferromagnetic films

A spin-wave analysis is developed to calculate the energies of the localized excitations occurring in two-dimensional ferromagnetic van der Waals monolayers when a substitutional magnetic impurity is introduced. The magnetic ions lie on a bipartite honeycomb lattice (similar to that for graphene) and the theory includes the effects of both Ising anisotropy and single-ion anisotropy to stabilize the magnetic ordering perpendicular to the atomic plane at low temperatures. A Dyson-equation formalism, together with the spin-dependent Green’s functions derived for van der Waals monolayers, is employed to evaluate the existence conditions and energies for the impurity modes, which lie above the band of spin-wave states of the pure host material. For realistic parameter values it is found that typically two impurity modes may exist, depending on the spin quantum number for the magnetic impurity atom. Numerical applications are made to CrI3 and Cr2Ge2Te6 as the host materials.

Multi-state quantum simulations via model-space quantum imaginary time evolution

We introduce the framework of model space into quantum imaginary time evolution (QITE) to enable stable estimation of ground and excited states using a quantum computer. Model-space QITE (MSQITE) propagates a model space to the exact one by retaining its orthogonality, and hence is able to describe multiple states simultaneously. The quantum Lanczos (QLanczos) algorithm is extended to MSQITE to accelerate the convergence. The present scheme is found to outperform both the standard QLanczos and the recently proposed folded-spectrum QITE in simulating excited states. Moreover, we demonstrate that spin contamination can be effectively removed by shifting the imaginary time propagator, and thus excited states with a particular spin quantum number are efficiently captured without falling into the different spin states that have lower energies. We also investigate how different levels of the unitary approximation employed in MSQITE can affect the results. The effectiveness of the algorithm over QITE is demonstrated by noise simulations for the H4 model system.

Metals (Ga, In) encapsulated aluminum nitride nanotubes (AlNNTs) as nonenzymatic sensors for biomarker volatiles of liver cirrhosis: A computational study

In the realm of scientific curiosity, the quest to develop groundbreaking biosensor technology and materials that cater to the urgent societal demands in healthcare, environment, food safety, and beyond has reached unprecedented heights. In this study, we delve into the captivating world of cutting-edge research, harnessing the power of density functional theory (DFT) at the B3LYP-GD3(BJ)/def2-SVP level of theory to investigate the adsorption, conductivity, reactivity, and dynamical stability of biomarker volatiles of liver cirrhosis: limonene (LMN), methanol (MTN), and pentanone (PTN) on aluminum nitride nanotube (AlNNT) and its metals doped Indium (In) and Gallium (Ga) designed surfaces. From the evolution in band gap analysis, PTN_Ga@AlNNT was noticed to have obtained least energy gap of 3.035 eV whereas, LMN_Ga@AlNNT system had the highest energy gap of 4.330 eV. The calculated fraction of electronic transfer for the studied systems were observed as thus; −2.48936, −0.798342 and −6.321428571 for LMN_Ga@AlNNT, MTN_Ga@AlNNT and PTN_Ga@AlNNT respectively. The perturbation energy analysis presents an increasing stabilization energy of Aluminum nanotube doped with Gallium (Ga) and indium (In) surface to followed the trend; In@ AINNT > Ga@ AINNT. Results from the Molecular Dynamic simulation suggest that the nanomaterials studied induced conformational changes in all six complexes during the simulation, as evidenced by the changes in energy and temperature. Also, from the UV– Vis analysis, the excited states in all three instances are single-A states, which implies they have spin quantum number S = 0. We hope this research work will contribute to the development efficient biosensor materials.

Isotope effects on radical pair performance in cryptochrome: A new hypothesis for the evolution of animal migration: The quantum biology of migration.

Mechanisms occurring at the atomic level are now known to drive processes essential for life, as revealed by quantum effects on biochemical reactions. Some macroscopic characteristics of organisms may thus show an atomic imprint, which may be transferred across organisms and affect their evolution. This possibility is considered here for the first time, with the aim of elucidating the appearance of an animal innovation with an unclear evolutionary origin: migratory behaviour. This trait may be mediated by a radical pair (RP) mechanism in the retinal flavoprotein cryptochrome, providing essential magnetic orientation for migration. Isotopes may affect the performance of quantum processes through their nuclear spin. Here, we consider a simple model and then apply the standard open quantum system approach to the spin dynamics of cryptochrome RP. We changed the spin quantum number (I) and g-factor of hydrogen and nitrogen isotopes to investigate their effect on RP's yield and magnetic sensitivity. Strong differences arose between isotopes with I=1 and I=1/2 in their contribution to cryptochrome magnetic sensitivity, particularly regarding Earth's magnetic field strengths (25-65µT). In most cases, isotopic substitution improved RP's magnetic sensitivity. Migratory behaviour may thus have been favoured in animals with certain isotopic compositions of cryptochrome.

Effects of odderon spin on helicity amplitudes in pp elastic scattering

In recent years, the discovery of the odderon, a colorless C-odd gluonic compound, has been confirmed in the TOTEM and D0 collaborations. However, the spin quantum number of the odderon remains unidentified. In this work, we aim to attribute a spin of J=3 to the odderon in pp elastic scattering by calculating the helicity amplitudes and the corresponding complex parameter r_5, the ratio of helicity’s single-flip to non-flip amplitudes, for the spin-3 tensor odderon with the standard spin-2 tensor pomeron exchanges. Then, we apply these results to the constraints obtained from the STAR experiment at RHIC. By comparing to the contributions of the spin-1 vector odderon and spin-2 tensor pomeron, we demonstrate that the spin-3 tensor odderon, i.e. J=3, provides a better explanation for the observable in pp elastic scattering.

Insight into the magnetic behavior and magnetocaloric effect of a borophene monolayer

The successful discovery of borophene has opened a new door for the development of 2D materials. Due to its excellent chemical, electronic and thermal properties, borophene has shown considerable potential in supercapacitors, hydrogen storage and batteries. In this paper, the thermodynamic characteristics and magnetocaloric effect of borophene are specifically studied using the Monte Carlo method. We find that there is an opposite impact between the spin quantum number and the crystal field on the magnetization, magnetic susceptibility, specific heat and magnetic entropy of the system. Moreover, increasing the spin quantum number or decreasing the absolute value of the crystal field can improve the relative cooling power, the coercivity (h c), and the remanence (M R) and the area of the loop.

$\Delta$S$^z$=2 quantum magnetization discontinuities proportional in number to the spin s in C$_{60}$: Origin and the role of symmetry

The quantum antiferromagnetic Heisenberg model on the fullerene C_{60}60 in a magnetic field has 4s4s ground-state magnetization discontinuities with \Delta S^z=2ΔSz=2 as a function of the spin quantum number ss that disappear at the classical limit. The molecule can be seen as the fullerene C_{20}20 with interpentagon interactions that generate the discontinuities when sufficiently strong. The discontinuities originate from the antiferromagnetic Ising limit for both molecules. The results show how spatial symmetry dictates the magnetic response of the I_hIh fullerene molecules.

Magnetic quantum and spin-wave behavior of three-layer graphene-like materials

This study examines the spin-wave and magnetic quantum behavior of three-layer graphene-like based on the Heisenberg model. The system is diagonally solved for Hamiltonian quantities using the linear spin wave theory and postponed Green's functions. The effects of exchange coupling, anisotropy, and spin quantum number on the resonance frequency and quantum fluctuation are discussed, providing a basis for regulating resonance frequency and quantum fluctuation.

Survival of magnetic correlations above the ordering temperature in the ferromagnetically ordered classical kagome magnet Li9Cr3(P2O7)3(PO4)2

Motivated by the recent discovery of a semiclassical nematic spin liquid state in a Heisenberg kagom\'e antiferromagnet ${\mathrm{Li}}_{9}{\mathrm{Fe}}_{3}{({\mathrm{P}}_{2}{\mathrm{O}}_{7})}_{3}{({\mathrm{PO}}_{4})}_{2}$ (LFPO) with $S=5/2$ [Kermarrec $et\phantom{\rule{4pt}{0ex}}al$. Phys. Rev. Lett. 127, 157202 (2021)], we now investigate the impact of spin quantum number $S$ on the ground-state properties by studying the isostructural kagom\'e magnet ${\mathrm{Li}}_{9}{\mathrm{Cr}}_{3}{({\mathrm{P}}_{2}{\mathrm{O}}_{7})}_{3}{({\mathrm{PO}}_{4})}_{2}$ (LCPO) with active ${t}_{2g}$ orbitals and $S=3/2$. Thermodynamic measurements reveal that the ground-state properties of LCPO is dominated by the ferromagnetic interactions with a mean-field temperature $\mathrm{\ensuremath{\Theta}}\phantom{\rule{4pt}{0ex}}\ensuremath{\sim}3\phantom{\rule{0.28em}{0ex}}\text{K}(J<1\phantom{\rule{0.28em}{0ex}}\text{K})$ and the ordering temperature, ${T}_{c}$ \ensuremath{\sim}2.7 K, and the size of the ordered moment \ensuremath{\sim}$1.05\phantom{\rule{0.28em}{0ex}}\ifmmode\pm\else\textpm\fi{}0.25\phantom{\rule{0.28em}{0ex}}{\textmu{}}_{\mathrm{B}}$ is significantly reduced from that of a fully ordered moment. The ab initio electronic structure calculations nicely corroborate the thermodynamic results and suggest the presence of additional in- and out-of-plane further-neighbor antiferromagnetic couplings, although significantly weaker in comparison to the dominant first-nearest-neighbor ferromagnetic coupling. The spin-lattice relaxation rate measured with fields larger than the saturation field shows a magnetic field induced gap $(\mathrm{\ensuremath{\Delta}}\ensuremath{\propto}$ B) in the excitation spectrum, and in $B\ensuremath{\rightarrow}0$ limit the gap has a finite intercept \ensuremath{\sim}3 K, equivalent to the mean-field scale. We interpret the origin of this gap is associated with the magnetic interactions inherent to the material. With our experimental results, we establish the stabilization of a ferromagnetic like ground state and the persistence of magnetic correlations above the ordering temperature in LCPO.