Finite-size effects in a field-theoretic model with long-range exchange interaction

We consider the random-field O($N$) spin model with long-range exchange interactions which decay with distance $r$ between spins as $r^{-d-\sigma}$ and/or random fields which correlate with distance $r$ as $r^{-d+\rho}$, and reexamine the critical phenomena near the lower critical dimension by use of the perturbative functional renormalization group. We compute the analytic fixed points in the one-loop beta functions, and study their stability. We also calculate the critical exponents at the analytical fixed points. We show that the analytic fixed point which governs the phase transition in the system with the long-range correlations of random fields can be destabilized by the nonanalytic perturbation in both cases where the exchange interactions between spins are short ranged and long ranged. For the system with the long-range exchange interactions and uncorrelated random fields, we show that the $d\to d-\sigma$ dimensional reduction at the leading order of the $d-2\sigma$ expansion holds only for $N>2(4+3{\sqrt{3}})\simeq 18.3923\cdots$. Our investigation into the system with the long-range exchange interactions and uncorrelated random fields also gives the value of the boundary between critical behaviors in systems with long-range and short-range exchange interactions, which is identical to that predicted by Sak [Phys. Rev. B {\bf{8}}, 281 (1973)]. For the system with the long-range exchange interactions and the long-range correlated random fields, we show that the $d\to d-\sigma-\rho$ dimensional reduction does not hold within the present framework, as far as $N$ is finite.

Long-range corrected (LC) density functional theories (DFTs) were applied to the isomerization energy calculations of organic molecules to make clear why conventional DFTs including B3LYP have given poor isomerization reaction energies. Combining with local response dispersion (LRD) method, we performed LC-DFT calculations for the benchmark set of isomerization reactions. Consequently, we found that LC-DFT + LRD methods give accurate reaction energies equivalent to up-to-date DFTs containing many semi-empirical parameters. This result indicates that long-range exchange and intramolecular dispersion correlation interactions, which have been neglected in conventional DFTs, play prominent roles in isomerization reactions. However, we also found that these interactions are not sufficient to give accurate isomerization energies especially for cyclization reactions. Considering that Gaussian-attenuated LC-DFTs (LCgau-DFTs) give better isomerization reaction energies than LC-DFTs, we suggested that the isomerization energies will be further improved by correcting the short-range part of exchange functionals in DFT with keeping the whole long-range exchange interactions.

Long-range interactions in triple quantum dots (TQDs) in Kondo regime are investigated by accurately solving the three-impurity Anderson model. For the occupation configuration of (N1,N2,N3) = (1, 0, 1), a long-range antiferromagnetic exchange interaction (JAF) is demonstrated and induces a continuous phase transition from the separated Kondo singlet (KS) to the long-range spin singlet (LSS) state between edge dots. The expression of JAF is analytically derived and numerically verified, according to which JAF can be conveniently manipulated via gate control of the detuning energy. The long-range entanglement of Kondo clouds are proved to be quite robust at strong inter-dot coupling limit. Under equilibrium condition, it induces an unexpected peak in the spectral function of the middle dot whose singly occupied level keeps much higher than the Fermi level. Under nonequilibrium condition, higher inter-dot tunneling barrier induces an anomalous enhancement of current. These novel features can be observed in routine experiments.

We investigate the valley depolarization due to the electron-hole exchange interaction in monolayer MoS$_{2}$. Both the long- and short-range parts of the intra- and inter-valley electron-hole exchange interactions are calculated. We find that both the long- and short-range exchange interactions can cause the inter- and intra-valley bright exciton transitions. With the intra-valley bright exciton transition channel nearly forbidden due to the large splitting of the valence bands, the inter-valley channel due to the exchange interaction can cause the valley depolarization efficiently by the Maialle-Silva-Sham mechanism [Phys. Rev. B {\bf 47}, 15776 (1993)]. With only the long-range exchange interaction, the calculations show good agreement with the recent valley polarization experiments, including the time-resolved valley polarization measurement, the pump-probe experiment and the steady-state PL polarization measurement. We further show that for the A-exciton with large (small) center-of-mass momentum, the long-range exchange interaction can cause the {\em fast} ({\em slow}) inter-valley exciton transition.

We consider the spin-glass (SG) with long-range (LR) random exchange interaction varying with distance $R$ as ${R}^{\ensuremath{-}\frac{d}{2}\ensuremath{-}\frac{\ensuremath{\sigma}}{2}}$, where $d$ is the space dimensionality and $\ensuremath{\sigma}>0$. It is shown that the LR fixed point is stable if $\ensuremath{\sigma}<2$. The nonclassical ($d<3\ensuremath{\sigma}$) LR critical exponents in powers of $3\ensuremath{\sigma}\ensuremath{-}d$ are not continuous at $\ensuremath{\sigma}=2$ when the transition to short-range (SR) exchange is made.

Exciton fine structures in cubic III-V semiconductor GaAs, InAs and GaN quantum dots are investigated systematically and the exciton spin relaxation in GaN quantum dots is calculated by first setting up the effective exciton Hamiltonian. The electron-hole exchange interaction Hamiltonian, which consists of the long- and short-range parts, is derived within the effective-mass approximation by taking into account the conduction, heavy- and light-hole bands, and especially the split-off band. The scheme applied in this paper allows the description of excitons in both the strong- and weak-confinement regimes. The importance of treating the direct electron-hole Coulomb interaction unperturbatively is demonstrated. We show in our calculation that the light-hole and split-off bands are negligible when considering the exciton fine structure, even for GaN quantum dots, and the short-range exchange interaction is irrelevant when considering the optically active doublet splitting. We point out that the long-range exchange interaction, which is neglected in many previous works, contributes to the energy splitting between the bright and dark states, together with the short-range exchange interaction. Strong dependence of the optically active doublet splitting on the anisotropy of dot shape is reported. Large doublet splittings up to 600 $\ensuremath{\mu}$eV, and even up to several meV for small dot size with large anisotropy, are shown in GaN quantum dots. The spin relaxation between the lowest two optically active exciton states in GaN quantum dots is calculated, showing a strong dependence on the dot anisotropy. Long exciton spin relaxation time is reported in GaN quantum dots. These findings are in good agreement with the experimental results.

Understanding high ordering temperature in Gd6FeBi2 magnet: Critical behavior, electronic structure and crystal-field analysis

Long-range exchange interactions

Simulations of cold nuclear matter at sub-saturation densities

To resolve the discrepancies in the exciton fine structure of aluminum nitride (AlN), polarization- and angle-resolved photoluminescence (PL) spectroscopies are performed. The excitonic PL spectra strongly depend on the optical polarization and detection angle. We propose that both the long-range and short-range electron-hole exchange interaction should be used to interpret the luminescence spectra. The theoretical framework fully explains the present and previous experimental results. The large longitudinal-transverse splitting energy obtained in this study suggests that AlN has strong light-matter coupling without quantum-confined structures.

Magnetic-field splitting of the ground state of a shallow direct exciton in a cubic semiconductor makes it possible to determine the electron–hole exchange interaction. The short-range exchange interaction is diagonal in the representation of the total angular momentum of an electron and a hole. The long-range exchange interaction is taken into account by the linear dielectric response formalism. The frequency–wave vector dispersion relationships of an exciton polariton in the presence of a magnetic field are derived for the Voigt and Faraday configurations.

The layered LiMO2 (M = Co, Ni, and Mn) materials are commonly used as the cathode materials in the lithium-ion battery due to the distinctive layer structure for lithium extraction and insertion. Although their electrochemical properties have been extensively studied, the structural and magnetic properties of LiNiO2 are still under considerable debate, and the magnetic properties of monoclinic LiMnO2 are seldom reported. In this work, a detailed study of LiNiO2, LiMnO2, and a half-doped material LiNi0.5Mn0.5O2 is performed via both first-principles calculations and Monte Carlo simulations based on the effective spin Hamiltonian model. Through considering different structures, it is verified that a structure with a zigzag-type pattern is the most stable one of LiNiO2. Moreover, in order to figure out the magnetic properties, the spin exchange interactions are calculated, and then magnetic ground states are predicted in these three systems. The results show that LiNiO2 forms a spiral order that is caused by the competition from both the short-range and long-range spin exchange interactions, whereas the magnetic ground state of LiMnO2 is collinearly antiferromagnetic due to its nearest and next-nearest neighbor antiferromagnetic spin exchange interactions. However, LiNi0.5Mn0.5O2 is collinearly ferrimagnetic because of the ferromagnetic nearest neighbor Ni-Ni and Mn-Mn exchange interactions. Our work demonstrates the competition between the different exchange interactions in these cathode materials, which may be relevant to the performance of the lithium-ion battery.

CrVI6 is a recently proposed van der Waals topological magnetic material derived from its parent compounds, CrI3 and VI3, via elemental substitution. However, beyond initial proposals of its topological nature, the fundamental characteristics of its magnetic ordering remain largely unexplored. Investigating the critical behaviors of a magnet provides deep insight into its underlying spin interactions and universality class. In this work, we synthesized high-quality CrVI6 single crystals, demonstrating strong perpendicular magnetic anisotropy below the Curie temperature (∼58.2 K) via DC magnetization and heat capacity measurements. The critical magnetic behavior in the vicinity of the paramagnetic to ferromagnetic phase transition region has been systematically analyzed using multiple approaches, yielding the critical exponents β = 0.294(8), γ = 0.947(9), and δ = 4.21(5). These values do not conform to any single universality class but instead demonstrate a distinct crossover behavior between the three-dimensional Ising and tricritical mean-field models. This crossover is indicative of complex magnetic ordering, characterized by the coexistence of short-range and long-range exchange interactions. Further analysis using renormalization group theory quantifies the decay of the exchange interaction J(r)≈r−4.80, confirming the behavior consistent with the crossover model. Our findings establish a comprehensive picture of the fundamental spin correlations in CrVI6, highlighting it as a fertile platform for developing future quantum and spintronic applications.

The exchange interaction governs static and dynamic magnetism. This fundamental interaction comes in two flavours-symmetric and antisymmetric. The symmetric interaction leads to ferro- and antiferromagnetism, and the antisymmetric interaction has attracted significant interest owing to its major role in promoting topologically non-trivial spin textures that promise fast, energy-efficient devices. So far, the antisymmetric exchange interaction has been found to be rather short ranged and limited to a single magnetic layer. Here we report a long-range antisymmetric interlayer exchange interaction in perpendicularly magnetized synthetic antiferromagnets with parallel and antiparallel magnetization alignments. Asymmetric hysteresis loops under an in-plane field reveal a unidirectional and chiral nature of this interaction, which results in canted magnetic structures. We explain our results by considering spin-orbit coupling combined with reduced symmetry in multilayers. Our discovery of a long-range chiral interaction provides an additional handle to engineer magnetic structures and could enable three-dimensional topological structures.

Low-lying excited states of planarly extended nanographenes are investigated using the long-range corrected (LC) density functional theory (DFT) and the spin-flip (SF) time-dependent density functional theory (TDDFT) by exploring the long-range exchange and double-excitation correlation effects on the excitation energies, band gaps, and exciton binding energies. Optimizing the geometries of the nanographenes indicates that the long-range exchange interaction significantly improves the CC bond lengths and amplify their bond length alternations with overall shortening the bond lengths. The calculated TDDFT excitation energies show that long-range exchange interaction is crucial to provide accurate excitation energies of small nanographenes and dominate the exciton binding energies in the excited states of nanographenes. It is, however, also found that the present long-range correction may cause the overestimation of the excitation energy for the infinitely wide graphene due to the discrepancy between the calculated band gaps and vertical ionization potential (IP) minus electron affinity (EA) values. Contrasting to the long-range exchange effects, the SF-TDDFT calculations show that the double-excitation correlation effects are negligible in the low-lying excitations of nanographenes, although this effect is large in the lowest excitation of benzene molecule. It is, therefore, concluded that long-range exchange interactions should be incorporated in TDDFT calculations to quantitatively investigate the excited states of graphenes, although TDDFT using a present LC functional may provide a considerable excitation energy for the infinitely wide graphene mainly due to the discrepancy between the calculated band gaps and IP-EA values. © 2017 Wiley Periodicals, Inc.