Two-component Spin Research Articles

The two-component spin–fermion model for high-Tc cuprates: its applications in neutron scattering and ARPES experiments

Motivated by neutron scattering experiments in high-Tc cuprates, we propose the two-component spin–fermion model as a minimal phenomenological model, which has both local spins and itinerant fermions as independent degrees of freedom (d.o.f.). Our calculations of the dynamic spin correlation function provide a successful description of the puzzling neutron experiment data and show that: (i) the upward dispersion branch of magnetic excitations is mostly due to local spin excitations; (ii) the downward dispersion branch is from collective particle–hole excitations of fermions; and (iii) the resonance mode is a mixture of both d.o.f. Using the same model with the same set of parameters, we calculated the renormalized quasiparticle (q.p.) dispersion and successfully reproduced one of the key features of the angle-resolved photoemission spectroscopy (ARPES) experiments, namely the high-energy kink structure in the fermion q.p. dispersion, thus supporting the two-component spin–fermion phenomenology.

Finite-temperature phase diagram of two-component bosons in a cubic optical lattice: Three-dimensionalt-Jmodel of hard-core bosons

We study the three-dimensional bosonic t-J model, i.e., the t-J model of "bosonic electrons", at finite temperatures. This model describes the $s={1 \over 2}$ Heisenberg spin model with the anisotropic exchange coupling $J_{\bot}=-\alpha J_z$ and doped {\it bosonic} holes, which is an effective system of the Bose-Hubbard model with strong repulsions. The bosonic "electron" operator $B_{r\sigma}$ at the site $r$ with a two-component (pseudo-)spin $\sigma (=1,2)$ is treated as a hard-core boson operator, and represented by a composite of two slave particles; a "spinon" described by a Schwinger boson (CP$^1$ boson) $z_{r\sigma}$ and a "holon" described by a hard-core-boson field $\phi_r$ as $B_{r\sigma}=\phi^\dag_r z_{r\sigma}$. By means of Monte Carlo simulations, we study its finite-temperature phase structure including the $\alpha$ dependence, the possible phenomena like appearance of checkerboard long-range order, super-counterflow, superfluid, and phase separation, etc. The obtained results may be taken as predictions about experiments of two-component cold bosonic atoms in the cubic optical lattice.

Apparent diffusion behaviors of spins in the presence of distant dipolar field in two-component solution NMR

The diffusion behaviors of spins in the presence of distant dipolar field in two-component spin systems during the second evolution period of a modified CRAZED sequence before acquisition were investigated. Theoretical formulas were deduced based on the distant dipolar field model. The simulation results and experimental observations are consistent with the theoretical predictions. This study shows that the relative intensities of signals from intermolecular zero-quantum coherences (iZQCs) and intermolecular double-quantum coherences (iDQCs) have the same diffusion attenuation characteristic under the combined effect of diffusion weighting gradients and distant dipolar field during the second evolution period. This diffusion attenuation may be different from that of conventional single-quantum coherence signal, depending on the relative orientation of the diffusion weighting gradients to the coherence selection gradients. The results presented herein are helpful for understanding the effect of distant dipolar field from a spin system on the diffusion behavior of other spin system and the signal properties in the iZQC or iDQC magnetic resonance imaging.

Cavity-enhanced detection of magnetic order in lattice spin models

We develop a general scheme for detecting spin correlations inside a two-component lattice gas of bosonic atoms, stimulated by the recent theoretical and experimental advances on analogous systems for a single component quantum gas. Within a linearized theory for the transmission spectra of the cavity mode field, different magnetic phases of a two-component (spin $1∕2$) lattice bosons become clearly distinguishable. In the Mott-insulating (MI) state with unit filling for the two-component lattice bosons, three different phases: antiferromagnetic, ferromagnetic, and the $XY$ phases are found to be associated with drastically different cavity photon numbers. Our suggested study can be straightforwardly implemented with current cold atom experiments.

Relativistic two-component calculations of electronic g-tensor for oxo-molybdenum(V) and oxo-tungsten(V) complexes: The important role of higher-order spin-orbit contributions

In an effort towards the reliable calculation of EPR parameters of molybdenum and tungsten enzyme active sites, the effect of higher-order spin-orbit effects and of exchange–correlation functional on the electronic g-tensors of small [MVOCl5]2− and medium-sized [MVO(bdt)2]− (bdt=benzene-1,2-dithiolate), [MVOCl3(bpy)] (bpy=bipyridine) complexes (M=Mo or W) has been evaluated. Comparison of one-component calculations with perturbational treatment of spin-orbit coupling and two-component non-collinear spin density functional calculations indicate the substantial importance of higher-order spin-orbit effects, in particular for the tungsten species. Pseudopotential calculations tend to underestimate the spin-orbit effects compared to all-electron calculations based on the Douglas–Kroll–Hess Hamiltonian. Hybrid functionals with somewhat enhanced exact-exchange admixture tend to provide better agreement with experiment than pure gradient-corrected functionals.

Basis-set extensions for two-component spin–orbit treatments of heavy elements

The accuracy of standard basis sets of quadruple-zeta and lower quality for the use in two-component self-consistent field procedures including spin-orbit coupling is investigated for the elements In-I and Au-At. Spin-orbit coupling leads to energetic and spatial splittings of inner shells, which are not described accurately with standard basis sets optimized for scalar relativistic calculations. This results in large errors in total atomic energies and significant errors in atomization energies of compounds containing these atoms. We show how these errors can be corrected by adding just a few steep sets of basis functions and demonstrate the quality of the resulting extended basis sets.

Spin–orbit density functional theory calculations for IX (X=F, Cl, Br and I) molecules

Two-component spin–orbit density functional theory (SODFT) calculations for spectroscopic constants of IX (X=F, Cl, Br and I) molecules have been performed with several functionals using shape-consistent relativistic effective core potentials (RECPs) with effective one-electron spin–orbit operator. The SODFT results obtained with the B3LYP functional are in very good accord with the results of previous two-component CCSD(T) calculations with the same RECP and basis sets. Results of two-component SODFT calculations with RECPs are also in good agreement with reported all-electron relativistic DFT calculations with the same functionals. The spectroscopic constants obtained with ACM and PBE0 functionals display the best agreement with the experimental values among the functionals tested. Spin–orbit effects from the SODFT calculations result in increases of bond lengths and decreases of dissociation energies and harmonic vibrational frequencies and the magnitudes are in reasonable agreement with those from two-component CCSD(T) calculations. Spin–orbit effects appear to be quite insensitive to the choice of functionals for the bond lengths and harmonic vibrational frequencies, but those of the dissociation energies somewhat deviate with the differing class of functionals.

The spin−orbit energy estimated from two-component spin−orbit calculations as correction terms for the Gaussian-2 (G2) theory

Two-component relativistic effective core potential (RECP) approaches are employed to derive spin–orbit energies from the energy difference of spin–orbit two-component RECP and spin averaged RECP calculations. These spin–orbit energies include both the spin–orbit splitting of open-shell species and the higher order spin–orbit contributions for all species. The present spin–orbit energies, which can be estimated from the single reference configuration calculations at various levels of theory such as Hartree–Fock and coupled-cluster methods, are utilized as additional correction terms in the Gaussian-2 (G2) theory for Br and I containing species. The improvement in reaction energies due to the present scheme is similar to those reported for other types of spin–orbit calculations based on multireference configuration interaction calculations. The present scheme straightforwardly provides spin–orbit correction terms for the compounded methods such as the G2 theory. Even the spin–orbit corrections at the HF level are reliable enough to improve the performance of the G2 theory, reducing the error to the chemical accuracy (±0.1 eV or 2 kcal mol−1) that is the target prescribed in G2 theory.

Separation and characterization of different signals from intermolecular three-spin orders in solution NMR

In this paper, signals originating from a pure specific coherence of intermolecular three-spin orders were separated and characterized experimentally in highly polarized two-component spin systems. A modified CRAZED sequence with selective radio-frequency excitation was designed to separate the small signals from the strong conventional single-spin single-quantum signals. General theoretical expressions of the pulse sequence with arbitrary flip angle pulses were derived using dipolar field treatment. The expressions were used to predict the relaxation and diffusion properties and optimal experimental parameters such as flip angles. For the first time, relaxation and diffusion properties of pure intermolecular single-quantum, double-quantum, and triple-quantum coherences of three-spin orders were characterized and analyzed in one-dimensional experiments. All experimental observations are in excellent agreement with the theoretical predictions. The theoretical results show that the quantum-mechanical treatment leads to exactly the same predictions as the dipolar field treatment. The quantitative study of intermolecular multiple-quantum coherences of three-spin orders presented herein provides a better understanding of their mechanisms.

Two-component spin–orbit calculations for the hetero diatomic molecules TlAt and (1 1 3)(1 1 7) with relativistic effective core potentials

Bond lengths, harmonic vibrational frequencies and dissociation energies of TlAt and (1 1 3)(1 1 7) are calculated at the highly correlated level of theory with and without spin–orbit interactions. Spin–orbit effects of Group 13 and Group 17 elements almost cancel out for R e . The spin–orbit effects on D e of TlAt(−1.20 eV) and (1 1 3)(1 1 7)(−2.05 eV) are roughly the sum of those of the corresponding element hydrides. Element 113 becomes more electronegative than Element 117 upon inclusion of spin–orbit interactions in the (1 1 3)(1 1 7) molecule. Electron correlations and spin–orbit effects are almost additive in the TlAt molecule, but the nonadditivity is quite pronounced for the (1 1 3)(1 1 7) molecule.

Quantitative characterization of intermolecular dipolar interactions of two-component systems in solution nuclear magnetic resonance

Liquid nuclear magnetic resonance behaviors related to intermolecular dipolar interactions were investigated theoretically and experimentally in highly polarized two-component spin systems. A modified CRAZED pulse sequence was designed to investigate relative signal intensities with considerations of spin transverse relaxation, longitudinal relaxation, molecular diffusion, and optimal radio-frequency flip angles. The dissipation of the demagnetizing field due to relaxation and diffusion processes during the detection period was taken into account as well. For the first time, vigorous analytical expressions of the spin dynamics, including all the effects mentioned above, were derived from the combination of the demagnetizing field model and product operator formalism. In the regime where the linear approximation (γμ0M0t≪1) is valid, these explicit analytical expressions can quantitatively describe the signal behaviors related to intermolecular dipolar interactions. All the theoretical predictions based on the analytical expressions for the directly excited component are in excellent agreement with experimental observations reported previously. Several valuable insights for the indirectly excited component were gained from the analytical expressions and verified by experimental measurements, including optimal radio-frequency flip angles, unusual relative signal intensities for n=−2 and n=2, and unconventional diffusion and multi-exponential longitudinal relaxation processes, where n is the ratio of the coherence-selection gradient areas in the CRAZED pulse sequence. In addition, n-order diffusion coefficients of the directly and indirectly excited spins during the evolution period predicted by the demagnetizing field picture are found to be the same as those obtained with the combination of the intermolecular multiple-quantum picture and Gaussian phase distribution approximation which is valid in the case of unrestricted isotropic diffusion. These results suggest that a combination of the demagnetizing field model and product operator formalism provides excellent predictive power and computational convenience for diffusion and relaxation behaviors in two-component systems. These quantitative studies may also provide an opportunity to probe specific sources of new contrast for medical MR imaging.

Relaxational dynamics study of the classical Heisenberg spinXYmodel in spherical coordinate representation

The two- and three-dimensional classical Heisenberg spin $\mathrm{XY}$ $(\mathrm{CHS}XY)$ models, with the spherical coordinates of spins taken as dynamic variables, are numerically investigated. We allow the polar \ensuremath{\theta} and azimuthal $\ensuremath{\varphi}$ angles to have uniform values in $[0,\ensuremath{\pi})$ and $[\ensuremath{-}\ensuremath{\pi},\ensuremath{\pi}),$ respectively, and the static universality class is shown to be identical to the classical $\mathrm{XY}$ model with two-component spins, as well as the $\mathrm{CHS}\mathrm{XY}$ model with a different choice of dynamic variables, conventionally used in the literature. The relaxational dynamic simulation reveals that the dynamic critical exponent z is found to have the value $z\ensuremath{\approx}2.0$ for both two and three dimensions, in contrast to $z\ensuremath{\approx}d/2$ $(d=$ spatial dimension) found previously with spin dynamics simulation of the conventional $\mathrm{CHS}\mathrm{XY}$ model. Comparisons with the usual two-component classical $\mathrm{XY}$ model are also made.

Quantitative study of longitudinal relaxation related to intermolecular dipolar interactions in solution NMR

Longitudinal relaxation related to intermolecular dipolar interactions was investigated by solution NMR. A novel pulse sequence with selective pre-saturation and selective excitation was designed for a highly polarized two-component spin system. A general analytical expression for the longitudinal relaxation was derived from a combination of the demagnetizing field theory and product operator formalism. The analytical expression suggests that the longitudinal relaxation is not a mono-exponential process. The predicted relaxation relationship is in excellent agreement with the experimental recovery curves.

Diffusion of intermolecular zero- and double-quantum coherences in two-component spin systems

An NMR pulse sequence was designed to accurately measure the diffusion rates of intermolecular zero-quantum coherences (ZQCs) and double-quantum coherences (DQCs) in two-component spin systems. The Gaussian phase distribution approximation was employed to describe the behavior of intermolecular ZQCs and DQCs as they underwent unrestricted isotropic diffusion. Our experimental and theoretical results demonstrate that intermolecular ZQCs and DQCs evolve with the same diffusion rates. Uncorrelated phases between individual spins on different molecules in intermolecular ZQCs and DQCs are suggested as the cause for their unconventional diffusion behavior. The differences in diffusion rates between inter- and intramolecular ZQCs or DQCs are explained.

Nuclear spin–spin coupling constants from regular approximate relativistic density functional calculations. II. Spin–orbit coupling effects and anisotropies

Based on our recently published two-component relativistic formulation of the nuclear spin–spin coupling hyperfine terms, we present a full implementation into the Amsterdam Density Functional program. The scalar relativistic code has been extended to include the relativistic analogue of the spin–dipole operator in the coupling calculations, which can now in addition be based on two-component spin–orbit coupled Kohn–Sham orbitals. One-bond coupling constants for some plumbanes are in good agreement with experiment, slightly improving the scalar relativistic values. Coupling constants and anisotropies for the XF (X=Cl, Br, I) and TlX (X=F, Cl, Br, I) series are compared to experimental data and for ClF additionally to recently published ab initio calculations. The spin–dipole term contributes largely to the coupling constants in XF. Spin–orbit effects are essential for the TlX couplings, where they can yield the most important contributions. In addition, data is reported for the benchmark systems ethane, ethene, and ethyne.

Spin relaxation inGaAs/AlxGa1−xAsquantum wells

Spin dynamics of photoexcited carriers in ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ quantum wells have been investigated in a wafer containing twelve different single quantum wells, allowing full investigation of well-width and temperature dependences with minimal accidental variations due to growth conditions. The behavior at low temperatures is dominated by excitonic effects, confirming results described in detail by others. Between 50 and 90 K there is a transition from excitonic to free-carrier-dominated behavior; both the temperature and time scale of the transition are in excellent agreement with a theoretical model for exciton dissociation. Above 90 K we find two-component spin decays consisting of an unresolved component (faster than 2 ps) associated with exciton dissociation and hole spin-relaxation and a longer-lived component that yields the electron spin-relaxation time. In the free-carrier regime, the electron spin-relaxation rate in wide wells follows that for bulk GaAs, which varies approximately as ${T}^{2}.$ For narrow wells the rate is approximately independent of temperature and varies quadratically with confinement energy. This behavior is consistent with dominance of the D'yakonov-Perel mechanism of electron-spin relaxation and the expected behavior of the electron mobility. The data show evidence of the influence of electron scattering by interface roughness.

Plane-rotator lattice gas in an external orienting field

We consider a lattice gas of particles that carry a two-component classical spin (i.e., a two-component unit vector). The pair interaction, restricted to nearest neighbors, implicitly includes hard-core repulsion, since each site can host one particle at most, and also contains ferromagnetic interaction between spins as well as nonmagnetic attraction between particles. We study thermodynamic properties and phase diagrams of the model by means of mean-field and two-site cluster approximations, and also by grand-canonical Monte Carlo simulations carried out for one value of the chemical potential; these aim at a quantitative check of the named approximations, as well as a more detailed description. Both mean-field and two-site cluster approximations were found to provide a qualitatively correct description for the thermodynamics of the model with nearest-neighbor interactions, and the predictions of the two-site cluster approximation were in satisfactory quantitative agreement with simulation results. According to both mean-field and two-site cluster treatments, the temperature-density phase diagrams of the model at zero external field are similar to those of the Ising lattice gas, but the effect of external field is quite different. In particular, at zero nonmagnetic attraction the field effect on the gas-liquid critical temperature becomes nonmonotonic. Having compared the field effects in the Ising, plane-rotator, and Heisenberg spin fluids, we conclude that the ability of the external field to decrease the gas-liquid critical temperature weakens with increasing number of spin components.

Long range order in two-dimensional spin models with long range interactions

We show that simple spin wave theory does not provide a reliable indication of long range order or no long range order in two-dimensional square models of two-component spins coupled by long range interactions. This failure occurs when accidental soft modes are provided by harmonic approximation owing to accidental infinite degeneracy of the ground state configuration. Indeed simple spin wave theory gives no long range order both for isotropic long range antiferromagnetic interaction decaying as 1/r3 and for dipolar interaction. On the contrary renormalized spin wave theory replaces accidental soft modes by temperature dependent gaps, so providing no long range order in the former case and long range order in the latter case in agreement with Monte Carlo simulation.

The singlet–triplet magnetism in the cuprates

The spin subsystem of the copper oxides within the polar Jahn–Teller CuO 4 center model is a two-component spin liquid and corresponds to a singlet–triplet magnet with, in general, multiparametric (non)collinear spin configurations. In the framework of a modified mean field approximation several collinear spin orders are discussed including both quite trivial singlet or triplet states and a purely quantum singlet–triplet mixed state. The spectrum of the elementary excitations is calculated by the Green's function method. We conjecture that charge fluctuations in a singlet–triplet magnet are accompanied by a modulation of the on-site spin density that results in a possibility to observe the charge fluctuations in the inelastic neutron scattering and the spin lattice relaxation experiments. The suggested model represents a new approach to the description of the spin system of the cuprates.

The infinite-range two-real-Ising replicas spin glass

A spin-glass model, with two Ising coupled systems (real replicas), is investigated in the limit of infinite-range interactions, through the replica method. Besides the Ising representation, the model is also considered as a discrete two-component four-state clock spin glass. The phase diagram of the model is obtained, within the replica-symmetry approximation, exhibiting a collinear spin-glass phase, i.e., no transverse four-state clock ordering. The order parameter conjugated to the coupling field presents a discontinuity along the spin-glass phase, when the field is reversed. The validity limits of the replica-symmetry solution are analysed.