Two-dimensional Heisenberg model with material-dependent superexchange interactions

We investigate the two-dimensional classical Heisenberg model with a nonlinear nearest-neighbor interaction V(s,s') = 2K[(1+s x s')/2]p. The analogous nonlinear interaction for the XY model was introduced by Domany, Schick, and Swendsen, who find that for large p the Kosterlitz-Thouless transition is preempted by a first-order transition. Here we show that, whereas the standard (p = 1) Heisenberg model has no phase transition, for large enough p a first-order transition appears. Both phases have only short-range order, but with a correlation length that jumps at the transition.

It is known that magnetic vortices in two-dimensional Heisenberg models with easy-plane anisotropy exhibit an instability depending on the anisotropy strength. In this paper, we study the statistic behavior of the two-dimensional easy-plane Heisenberg models with distance-dependent interactions ${J}_{xy}(r)$ and ${J}_{z}(r)$ for in-plane and out-of-plane components. We develop analytical and numerical methods for accurate determination of critical anisotropy, above which out-of-plane vortices become stable. In particular, we explore the vortex formation of the Gaussian-type interaction model and determine the critical anisotropy accurately for square, hexagonal, and triangular lattices.

Binding and unbinding of vortices drives Kosterlitz-Thouless phase transition in two-dimensional XY model. Here we investigate whether similar mechanism works in two-dimensional Heisenberg model, by using the fluctuation of skyrmion number inside a loop to characterize the nature of binding vs. unbinding of defects. Through Monte Carlo simulations, we find that the fluctuation is proportional to the perimeter of the loop at low temperatures while it is proportional to the area of the loop at high temperatures, implying binding of the defects at low temperatures and unbinding at high temperatures.

Using a classical Monte Carlo simulation on the two-dimensional Heisenberg model with exchange anisotropy, we have obtained reliable results for several properties: spontaneous magnetization, total energy, self-correlation, susceptibility, and correlation functions. An improved algorithm has been used in order to eliminate artifacts in such quantities below the critical temperature. The present results allow us to confirm the validity of spin-wave theory up to temperatures of 0.5 T c and, simultaneously, to predict the phase-transition temperature according to an Ising-like model with a renormalized exchange constant

Two-dimensional (2D) van der Waals (vdW) heterostructures have attracted much attention due to their unique properties in photocatalysis, electronics, and energy storage. This work comprehensively analyzed the electronic properties and photocatalytic efficiency properties of 2D vdW MoS2/Hf2CO2 heterostructure by first-principles calculations and molecular dynamics simulation. An ideal band gap of 1.44 eV was found for visible light absorption. Meanwhile, a high solar-to-hydrogen efficiency of 17.14% is obtained from the calculated band-edge positions, and a high power conversion efficiency of 13.84% is also confirmed by spectroscopy limited maximum efficiency simulation. We estimate the time scale for electron–hole transfer and recombination times using a combination of non-adiabatic molecular dynamics and time-dependent density functional theory. A suitable e-h recombination time of 1.86 ns and electron (hole) transfer time of 331 (978) fs are obtained in the 2D MoS2/Hf2CO2 heterostructure, which is expected to ensure high photocatalytic efficiency. Therefore, the constructed MoS2/Hf2CO2 heterostructures provide a new example for the prediction of high-performance nano optoelectronic devices.

We have studied the relation between the resonating-valence-bond (RVB) state and the exact ground state for the two-dimensional antiferromagnetic (AF) Heisenberg model on a few small lattices. We describe a method to obtain the state of minimum energy within a family of RVB states. Based on the insight provided by the RVB states, and supported by our numerical results, we argue in favor of the existence of long-range order at T=0 for the two-dimensional AF Heisenberg model.

Exploring emerging two-dimensional (2D) van der Waals (vdW) semiconducting materials and precisely tuning their electronic properties at the atomic level have long been recognized as crucial issues for developing their high-end electronic and optoelectronic applications. As a III-VI semiconductor, ultrathin layered hexagonal GaTe (h-GaTe) remains unexplored in terms of its intrinsic electronic properties and band engineering strategies. Herein, we report the successful synthesis of ultrathin h-GaTe layers on a selected graphene/SiC(0001) substrate, via molecular beam epitaxy (MBE). The widely tunable quasiparticle band gaps (∼2.60-1.55 eV), as well as the vdW quantum well states (QWSs) that can be strictly counted by the layer numbers, are well characterized by onsite scanning tunneling microscopy/spectroscopy (STM/STS), and their origins are clearly addressed by density functional theory (DFT) calculations. More intriguingly, distinctive 8|8E and 4|4P (Ga) mirror twin boundaries (MTBs) are identified in the ultrathin h-GaTe flakes, which can induce decreased band gaps and prominent p-doping effects. This work should deepen our understanding on the electronic tunability of 2D III-VI semiconductors by thickness control and line defect engineering, which may hold promise for fabricating atomic-scale vertical and lateral homojunctions toward ultrascaled electronics and optoelectronics.

Two-dimensional (2D) van der Waals (vdW) antiferromagnets (AFMs) have emerged as promising candidates for spintronic applications due to their fast spin dynamics and robustness against external magnetic perturbations. However, their intrinsically low electrical conductivity challenges their integration into electronic devices. A possible path to overcome this limitation is to form vdW heterostructures with highly conductive materials such as graphene, which can sensitively respond to interfacial magnetic interactions. Such an interplay is, however, far from being understood. In this work, we investigate vdW heterostructures composed of single-layer graphene and the antiferromagnet FePS3 (FEPS). Electron transport measurements in a field-effect transistor geometry reveal a sharp change in graphene resistance precisely at the Néel temperature of FEPS. Temperature-dependent Raman spectroscopy and gate-dependent transport suggest a distinct interfacial charge transfer driven by the antiferromagnetic ordering. Density functional theory (DFT) calculations support this mechanism, showing a significant modulation of charge transfer across the interface linked to the magnetic phase. These findings unveil a strong interplay between magnetism and electron transport in 2D vdW heterostructures and pave the way toward integrating antiferromagnetic vdW materials into future electronic and spintronic technologies.

Josephson junctions (JJs) and their tunable properties, including their nonlinearities, play an important role in superconducting qubits and amplifiers. JJs together with the circuit quantum electrodynamics architecture form many key components of quantum information processing1. In quantum circuits, low-noise amplification of feeble microwave signals is essential, and Josephson parametric amplifiers (JPAs)2 are the widely used devices. The existing JPAs are based on Al-AlOx-Al tunnel junctions realized in a superconducting quantum interference device geometry, where magnetic flux is the knob for tuning the frequency. Recent experimental realizations of two-dimensional (2D) van der Waals JJs3-5 provide an opportunity to implement various circuit quantum electrodynamics devices6-8 with the added advantage of tuning the junction properties and the operating point using a gate potential. While other components of a possible 2D van der Waals circuit quantum electrodynamics architecture have been demonstrated, a quantum-noise-limited amplifier, an essential component, has not been realized, to the best of our knowledge. Here we implement a quantum-noise-limited JPA using a graphene JJ, that has a linear resonance gate tunability of 3.5 GHz. We report 24 dB amplification with 10 MHz bandwidth and -130 dBm saturation power, a performance on par with the best single-junction JPAs2,9. Importantly, our gate-tunable JPA works in the quantum-limited noise regime, which makes it an attractive option for highly sensitive signal processing. Our work has implications for novel bolometers; the low heat capacity of graphene together with JJ nonlinearity can result in an extremely sensitive microwave bolometer embedded inside a quantum-noise-limited amplifier. In general, this work will open up the exploration of scalable device architectures of 2D van der Waals materials by integrating a sensor with the quantum amplifier.

Near the 100th anniversary of the discovery of ferroelectricity, so-called sliding ferroelectricity has been proposed and confirmed recently in a series of experiments that have stimulated remarkable interest. Such ferroelectricity exists widely and exists only in two-dimensional (2D) van der Waals stacked layers, where the vertical electric polarization is switched by in-plane interlayer sliding. Reciprocally, interlayer sliding and the “ripplocation” domain wall can be driven by an external vertical electric field. The unique combination of intralayer stiffness and interlayer slipperiness of 2D van der Waals layers greatly facilitates such switching while still maintaining environmental and mechanical robustness at ambient conditions. In this perspective, we discuss the progress and future opportunities in this behavior. The origin of such ferroelectricity as well as a general rule for judging its existence are summarized, where the vertical stacking sequence is crucial for its formation. This discovery broadens 2D ferroelectrics from very few material candidates to most of the known 2D materials. Their low switching barriers enable high-speed data writing with low energy cost. Related physics like Moiré ferroelectricity, the ferroelectric nonlinear anomalous Hall effect, and multiferroic coupling are discussed. For 2D valleytronics, nontrivial band topology and superconductivity, their possible couplings with sliding ferroelectricity via certain stacking or Moiré ferroelectricity also deserve interest. We provide critical reviews on the current challenges in this emerging area.

The development of new routes for the synthesis of the magnetic nanostructures with low cost, simple and rapid growth has inspired as alternative materials in a wide range of applications. In this report, 3D-hierarchical MnO2 microspheres with an ultrathin nanosheet structure have been synthesized by microwave heating method. X-ray diffraction analysis exhibit the microcrystalline nature of microspheres and (211) is the major pattern with the highest intensity. High purity and surface adsorbed oxygen species have been detected by valance state of microspheres. The magnetic properties of microsphere α-MnO2 investigated experimentally and combined with density functional theory (DFT) calculations, suggest the coexistence of ferromagnetic (FM) and antiferromagnetic (AFM) interaction in their nanostructures. The observed FM state is arising from noncollinear magnetic field that tilts two AFM Mn spins consequently, which make a distortion through intermediate oxygen ion in the crystal structure. While, the canted angle between two Mn sublattices lead them to a weak FM state. Similarly, the superexchange interaction is also responsible for magnetic ordering in the adjacent O ion, that can help to exchange magnetic information by direct electron hops of Mn–Mn chain. This is further confirmed from our DFT calculations. They may be found the strong potential for alternative materials other than partially oxidized metal nanoparticles.

Single-layer CrI3 grown by molecular beam epitaxy

The authors present numerical simulation studies on the two-dimensional easy-plane classical ferromagnetic Heisenberg model with fourfold in-plane symmetry breaking. Continuum limit equations of motion are obtained and some non-linear particular solutions are discussed. Their simulation data are compared with experimental data obtained for Rb2CrCl4. They find evidence for two transition temperatures in this model.

We use the self-consistent harmonic approximation (SCHA) to study static properties of the two-dimensional quantum Heisenberg model with easy-axis anisotropy. We calculate the critical temperature as a function of the spin value, and compare with classical results. Specifically, we compare how the ratio of critical temperatures varies as a function of the spin S in the quantum and classical cases, for afixed anisotropy parameter. We see that, for values of spin near 5/2, the classical result approximates to the quantum results and the classical calculation is justified. We have also studied the behavior of the magnetization for very small anisotropies. We have shown that our magnetization curves do not present a plateau in the limit of very small anisotropies, as predicted by the real-space renormalization-group calculations.

We study how well magnetic models can be implemented with ultracold bosonic atoms of two different hyperfine states in an optical superlattice. The system is captured by a two-species Bose-Hubbard model, but realizes in a certain parameter regime actually the physics of a spin-1/2 Heisenberg magnet, describing the second-order hopping processes. Tuning of the superlattice allows for controlling the effect of fast first-order processes versus the slower second-order ones. Using the density-matrix renormalization-group method, we provide the evolution of typical experimentally available observables. The validity of the description via the Heisenberg model, depending on the parameters of the Hubbard model, is studied numerically and analytically. The analysis is also motivated by recent experiments [S. F\"olling et al., Nature (London) 448, 1029 (2007); S. Trotzky et al., Science 319, 295 (2008)] where coherent two-particle dynamics with ultracold bosonic atoms in isolated double wells were realized. We provide theoretical background for the next step, the observation of coherent many-particle dynamics after coupling the double wells. Contrary to the case of isolated double wells, relaxation of local observables can be observed. The tunability between the Bose-Hubbard model and the Heisenberg model in this setup could be used to study experimentally the differences in equilibration processes for nonintegrable and Bethe ansatz integrable models. We show that the relaxation in the Heisenberg model is connected to a phase averaging effect, which is in contrast to the typical scattering driven thermalization in nonintegrable models. We discuss the preparation of magnetic ground states by adiabatic tuning of the superlattice parameters.