Crossover Transition Research Articles

Transition metal centers with anharmonic elastic interactions in one-dimensional spin-crossover solids

An exact examination of a one-dimensional (1D) anharmonic elastic model describing the thermodynamic properties of spin-crossover (SCO) solids is presented. This elastic model incorporates both intra-chain and mean field inter-chain interactions, providing a more understanding of 1D SCO materials. Numerical findings for a linear chain of spins unveil intriguing features, such as a two-step-like transition. Extending the model to interacting chains leads to an additional term in the effective ligand field of the system’s Hamiltonian, thereby enhancing its predictive power by accounting for more elastic constants of interactions. This augmentation reinforces the model’s validity in capturing the spin-crossover phenomenon. Numerical results in this extended framework elucidate clearer two-step-like spin crossover transitions, with the HS_LS fraction of spins approaching maximum values at equilibrium temperature Teq.

Understanding Pressure Effects on Structural, Optical, and Magnetic Properties of CsMnF4 and Other 3dn Compounds.

The pressure dependence of structural, optical, and magnetic properties of the layered compound CsMnF4 are explored through first-principles calculations. The structure at ambient pressure does not arise from a Jahn-Teller effect but from an orthorhombic instability on MnF63- units in the tetragonal parent phase, while there is a P4/n → P4 structural phase transition at P = 40 GPa discarding a spin crossover transition from S = 2 to S = 1. The present results reasonably explain the evolution of spin-allowed d-d transitions under pressure, showing that the first transition undergoes a red-shift under pressure following the orthorhombic distortion in the layer plane. The energy of such a transition at zero pressure is nearly twice that observed in Na3MnF6 due to the internal electric field and the orthorhombic distortion also involved in K2CuF4. The reasons for the lack of orthorhombic distortion in K2MF4 (M = Ni, Mn) or CsFeF4 are also discussed in detail. The present calculations confirm the ferromagnetic ordering of layers in CsMnF4 at zero pressure and predict a shift to an antiferromagnetic phase for pressures above 15 GPa consistent with the reduction of the orthorhombicity of the MnF63- units. This study underlines the usefulness of first-principles calculations for a right interpretation of experimental findings.

Frustration—no frustration crossover and phase transitions in 2D spin models with zig-zag structures

Three 2D spin models made of frustrated zig-zag chains with competing interactions which, by exact summation with respect to some degrees of freedom, can be replaced by an effective temperature-dependent interaction, were considered. The first model, exactly solvable Ising chains coupled by only four-spin interactions, does not exhibit any finite temperature phase transition; nevertheless, temperature can trigger a frustration–no frustration crossover accompanied by gigantic specific heat. A similar effect was observed in several two-leg ladder models (Weiguo 2020 arXiv:2006.08921v2; 2020 2006.15087v1). The anisotropic Ising chains coupled by a direct interchain interaction and, competing with it, indirect interaction via spins located between chains, are analyzed using the exact Onsager’s equation and linear perturbation renormalization group (LPRG). Depending on the parameter set, such a model exhibits one antiferromagnetic (AF) or ferromagnetic (FM) phase transition or three phase transitions with a re-entrant disordered phase between AF and FM ones. The LPRG method was also used to study coupled uniaxial XXZ chains which, for example, can be a minimal model to describe the magnetic properties of compounds in which uranium and rare earth atoms form zig-zag chains. As with the Ising model, for a certain set of parameters, the model can undergo three phase transitions. However, both intrachain and interchain plain interactions si,jxsk,lx+si,jysk,ly can eliminate the re-entrant disordered phase, and then only one transition takes place. Additionally, the XXZ model can undergo temperature-induced metamagnetic transition.

Temperature-scan-rate dependent SCO hysteresis found in a tetramethylphosphonium tripodal ferrate(II) salt

A new compound (Me4P)[Fe(py3COH)(NCS)3]•MeOH was prepared and structurally characterized, where py3COH stands for tris(2-pyridyl)methanol. After annealed at 400 K, desolvated (Me4P)[Fe(py3COH)(NCS)3] displayed an abrupt spin-crossover (SCO) at T1/2↑ = 255 K and T1/2↓ = 234 K. Namely, 21 K-wide hysteresis was recorded at a temperature scan rate of 5 K min−1. The χmT vs T profile was temperature-scan rate dependent; the wider hysteresis with the slower scan. The secondary SCO with T1/2↑ = 275 K emerged, and a new concomitant hysteresis loop overlapped the primary one. The total hysteresis width became 39 K at a slow scan with 0.1 K min−1. A mechanism of interplaying spin crossover and structural phase transition is described. Combining a similar result on the corresponding Me4N+ analog, we supposed that the tripod py3COH ligand would have an advantage for hysteretic SCO and possibly for double SCO behavior.

Uncovering the hidden structure of small-world networks

The small-world (SW) network model introduced by Watts and Strogatz has significantly influenced the study of complex systems, spurring the development of network science as an interdisciplinary field. The Newman-Watts model is widely applied to analyze SW networks by adding several randomly placed shortcuts to a regular lattice. We meticulously examine related previous works and conclude that the scaling of various pertinent quantities lacks convincing evidence. We demonstrate that the SW property primarily stems from the existence of clusters of nodes linked by shortcuts rather than just the mean number of shortcuts. Introducing the mean degree of clusters linked by shortcuts as a new key parameter resolves the scaling ambiguity, yielding a more precise characterization of the network. Our findings provide a new framework for analyzing SW networks, highlighting the significance of considering emergent structures in complex systems. We also develop a phase diagram of the crossover transition from the small to the large world, offering profound insights into the nature of complex networks and highlighting the power of emergence in shaping their behavior.

Effect of finite volume on thermodynamics of quark-hadron matter

The effects of a finite system volume on thermodynamic quantities, such as the pressure, energy density, specific heat, speed of sound, conserved charge susceptibilities, and correlations, in hot and dense strongly interacting matter are studied within the parity-doublet chiral mean field model. Such an investigation is motivated by relativistic heavy-ion collisions, which create a blob of hot QCD matter of a finite volume, consisting of strongly interacting hadrons and potentially deconfined quarks and gluons. The effect of the finite volume of the system is incorporated by introducing lower momentum cutoffs in the momentum integrals appearing in the model, the numerical value of the momentum cutoff being related to the de Broglie wavelength of the given particle species. It is found that some of these quantities show a significant volume dependence, in particular, those sensitive to pion degrees of freedom, and the crossover transition is generally observed to become smoother in finite volume. These findings are relevant for the effective equation of state used in fluid dynamical simulations of heavy-ion collisions and efforts to extract the freeze-out properties of heavy-ion collisions with susceptibilities involving electric charge and strangeness. Published by the American Physical Society 2024

Toward a universal description of hadronic phase of QCD

Mean-field model quantum field theories of hadrons were traditionally developed to describe cold and dense nuclear matter and are by now very well constrained from the recent neutron star merger observations. We show that when augmented with additional known hadrons and resonances but not included earlier, these mean-field models can be extended beyond its regime of applicability. Calculating some specific ratios of baryon number susceptibilities for finite temperature and moderate values of baryon densities within mean-field approximation, we show that these match consistently with the lattice QCD data available at lower densities, unlike the results obtained from a noninteracting hadron resonance gas model. We also estimate the curvature of the line of constant energy density, fixed at its corresponding value at the chiral crossover transition in QCD, in the temperature-density plane. The number density at low temperatures and high density is found to be about twice the nuclear saturation density. Moreover from this line we can indirectly constrain the critical endpoint of QCD to be beyond μB=596 MeV for temperature ∼125 MeV. Published by the American Physical Society 2024

Probing the nature of the QCD phase transition with higher-order net-proton number fluctuation and local parton density fluctuation measurements at RHIC-STAR

The moments of proton and net-proton multiplicity distributions are observables expected to be sensitive to the QCD critical point and the nature of the QCD phase transition from QGP to hadron gas. Hyper-order cumulants are measured in wide centrality bins in STAR BES-I data and found to be qualitatively consistent with trends predicted by lattice QCD which finds a cross-over phase transition at low μB. Data collected at √SNN = 3 GeV in BES-II exhibit trends opposite of those observed in higher energy collisions which may suggest the dominance of hadronic interactions at this energy. The variance of proton multiplicity distributions in azimuthal partitions is measured to search for signals of clustering indicative of a first-order phase transition. A strong dependence on the event multiplicity is observed. This dependence is independent of energy in AMPT while in STAR data a significant trend with energy is observed.

Thermodynamics of spin crossover in a bis(terpyridine) cobalt(II) complex featuring a thioether functionality.

In this contribution, a terpyridine-based ligand bearing a thioether functionality is used to prepare a new cobalt(II) spin crossover complex: [Co(TerpyPhSMe)2](PF6)2 (1), where TerpyPhSMe is 4'-(4-methylthiophenyl)-2,2':6',2''-terpyridine. Its structure, determined by single crystal X-ray diffraction, reveals a mer coordination of the tridentate terpyridine ligands, leading to a tetragonally compressed octahedron. Intermolecular interactions in the crystal lattice freeze the complex in the high spin state in the solid state at all temperatures, as indicated by magnetometry and Electron Paramagnetic Resonance (EPR) spectra. When dissolved in acetonitrile, however, temperature dependent electronic, 1H-NMR and EPR spectra highlight an entropy-driven spin crossover transition, whose thermodynamics parameters have been determined. This is the first report of a cobalt(II) SCO complex featuring a thioether group, allowing its implementation in chemically grown bistable monolayers and may open important perspectives for the use of such systems in molecular spintronics.

Thermal transport and phonon localization in periodich-GaN/h-AlN superlattices.

The widely observed non-diffusive phonon thermal transport phenomenon in nanostructures is largely attributed to classical size effects, which ignore the characteristic of phonon wave. In this context, the crossover transition process from incoherent to coherent phonon transport in two-dimensional heterogeneous periodic h-GaN/h-AlN superlattices is demonstrated using a non-equilibrium molecular dynamics approach, where the localization behavior of thermal phonons is particularly significant. The results show that the thermal transport of the superlattice structure is affected by a combination of structural parameters and temperature. The thermal conductivity (TC) of the superlattice decreases and then increases as the interface density increases. Phonon-interface scattering dominates the incoherent phonon transport, while local phonons modulate the transport in the coherent region. Thus, the competition between phonon wave and particle properties causes the transition from incoherent to coherent phonon transport. In addition, as the TC valley depth slows down with increasing system temperature, the scattering of medium and high frequency phonons is enhanced and the phonon lifetime decreases. Research on localized phonons in superlattices provides theoretical support for thermal transport regulation in basal low-dimensional materials.

Advancing frequency locking: Modified FPGA-Guided direct modulation spectroscopy for laser stabilization

In this paper, we propose a cost-effective laser frequency locking scheme based on frequency modulation spectroscopy (FMS) for precision measurements and experiments in various fields. We demonstrate that by digitally modulating the detected signal frequency using a Field-Programmable-Gate-Array (FPGA) driven by a home-built lock-in and a proportional–integral–derivative (PID) control system, our system achieves higher precision, user-friendliness, and versatility. Our system generates a 20 V peak-to-peak amplified voltage to a piezo transducer (PZT), which enables a mode-hop free laser scan of approximately 2 ±0.2 GHz. We directly modulate the detected saturation absorption signal with a sinusoidal waveform, then demodulate it to obtain multiple zero crossing locking points on the D2 transition of Cs at 852.35 nm. We optimized the system for three commonly used atomic transitions and found that researchers can select any of the zero crossing peaks for frequency stabilization depending on their experimental requirements, we locked the laser at the crossover transition. We measured the long-time frequency fluctuation and power spectral density and found that the frequency fluctuation of the laser is much less than the natural line width of the D2 transition of Cs. Our results demonstrate that our laser frequency locking scheme is effective and practical for precision measurements and experiments in various fields.

Binary Neutron-Star Mergers with a Crossover Transition to Quark Matter

This paper summarizes recent work on the possible gravitational-wave signal from binary neutron-star mergers in which there is a crossover transition to quark matter. Although this is a small piece of a much more complicated problem, we discuss how the power spectral density function may reveal the presence of a crossover transition to quark matter.

Hysteretic Spin Crossover with High Transition Temperatures in Two Cobalt(II) Complexes.

Cooperative spin crossover transitions with thermal hysteresis loops are rarely observed in cobalt(II) complexes. Herein, two new mononuclear cobalt(II) complexes with hysteretic spin crossover at relatively high temperatures (from 320 to 400 K), namely, [Co(terpy-CH2OH)2]·X2 (terpy-CH2OH = 4'-(hydroxymethyl)-2,2';6',2″-terpyridine, X = SCN-(1) and SeCN- (2)), have been synthesized and characterized structurally and magnetically. Both compounds are mononuclear CoII complexes with two chelating terpy-CH2OH ligands. Magnetic measurements revealed the existence of the hysteretic SCO transitions for both complexes. For compound 1, a one-step transition with T1/2↑= 334.5 K was observed upon heating, while a two-step transition is observed upon cooling with T1/2↓(1) = 329.3 K and T1/2↓(2) = 324.1 K (at a temperature sweep rate of 5 K/min). As for compound 2, a hysteresis loop with a width of 5 K (T1/2↓ = 391.6 K and T1/2↑ = 396.6 K, at a sweep rate of 5 K/min) can be observed. Thanks to the absence of the crystallized lattice solvents, their single crystals are stable enough at high temperatures for the structure determination at both spin states, which reveals that the hysteretic SCO transitions in both complexes originate from the crystallographic phase transitions involving a thermally induced order-disorder transition of the dangling -CH2OH groups in the ligand. This work shows that the modification of the terpy ligand has an important effect on the magnetic properties of the resulting cobalt(II) complexes.

Search for Weak Side Branches in the Electromagnetic Decay Paths of the 6526-keV 10+ Isomer in 54Fe

High-spin nuclear isomers in N≈Z nuclei between doubly magic 40Ca and 56Ni provide an excellent testing ground for the nuclear shell model and questions related to isospin symmetry breaking in the vicinity of the proton drip line. The purpose of the present study is to investigate the possibility of weak electromagnetic decay branches along the decay paths of the 6526-keV 10+ isomer in 54Fe. The isomer was strongly populated by means of the fusion-evaporation reaction 24Mg(36Ar,α2p)54mFe. The Gammasphere array was used to detect γ-ray cascades emitted from the isomeric state. By means of γγγ coincidences, weak non-yrast decay branches can be discriminated, with the isomer’s half-life confirmed at T1/2=363(4) ns. The yrast 61+→21+ E4 cross-over transition was interrogated. The observations are compared with shell-model calculations.

Implementation of cluster expansion for hot QCD matter

We present a cluster expansion EoS model for strongly-interacting matter based on the generalized Beth-Uhlenbeck formalism to describe hadrons as bound clusters of quarks. This formalism can describe both confined and deconfined phases. Our emphasis is on the region of vanishing baryon densities, where numerical solutions available from Lattice QCD predict a smooth crossover transition from hadron to quark matter. Medium effects are taken into account as self energies, which are motivated from both perturbative QCD calculations and phenomenological models. Parameters are tuned to Lattice QCD data and result in a good agreement of the thermodynamics.

Synthesis and Characterization of a One-Dimensional Malleable Spin-Crossover Polymer Complex Modified by Methoxy Polyethylene Glycol.

A novel one-dimensional malleable spin-crossover (SCO) complex {[Fe(MPEG-trz)3](BF4)2} has been successfully synthesized by molecular self-assembly between 4-amino-1,2,4-triazoles (MPEG-trz) grafted with a long flexible chain methoxy polyethylene glycol (MPEG) and metallic complex Fe(BF4)2•6H2O. The detailed structure information was illustrated by using FT-IR and 1H NMR measurements, while the physical behaviors of the malleable SCO complexes were systematically investigated by using magnetic susceptibility measurements using superconductivity quantum interference device (SQUID) and differential scanning calorimetry (DSC). This new metallopolymer exhibits a remarkable spin crossover transition behavior, between two spin quantum states (Fe2+ ions): high spin (HS) state (quintet state) and low spin (LS) state (singlet state), at a specific critical temperature with a slender hysteresis loop of 1 K. DFT computations revealed the partial rules of HOMO-LUMO energy levels and spin density distributions of different four-position substituted [Fe(1,2,4-triazole)3]2+ derivatives with different length of repeat units in polymer complexes. This can go a step further to depict the spin and magnetic transition behaviors of SCO polymer complexes. Furthermore, the coordination polymers possess an excellent processability due to an outstanding malleability, which can be easily shaped into a polymer film with spin magnetic switching properties.

Sweeping across the BCS-BEC crossover, reentrant, and hidden quantum phase transitions in two-band superconductors by tuning the valence and conduction bands

Two-band electronic structures with a valence and a conduction band separated by a tunable energy gap and with pairing of electrons in different channels can be relevant to investigate the properties of two-dimensional multiband superconductors and electron-hole superfluids, as monolayer FeSe, recently discovered superconducting bilayer graphene, and double-bilayer graphene electron-hole systems. This electronic configuration allows also to study the coexistence of superconductivity and charge density waves in connection with underdoped cuprates and transition metal dichalcogenides. By using a mean-field approach to study the system above mentioned, we have obtained numerical results for superconducting gaps, chemical potential, condensate fractions, coherence lengths, and superconducting mean-field critical temperature, considering a tunable band gap and different filling of the conduction band, for parametric choice of the pairing interactions. By tuning these quantities, the electrons redistribute among valence and conduction band in a complex way, leading to a new physics with respect to single-band superconductors, such as density induced and band-selective BCS-BEC crossover, quantum phase transitions, and hidden criticalities. At finite temperature, this phenomenon is also responsible for the non-monotonic behavior of the superconducting gaps resulting in a superconducting-normal state reentrant transition, without the need of disorder or magnetic effects.

Study of strange quark density fluctuations in Au + Au Collisions at $$\sqrt{\textrm{s}_{_{\textrm{NN}}}}$$ = 7.7–200 GeV from AMPT Model

The strangeness production is an important observable to study the QCD phase diagram. The yield ratios of strange quark can be helpful to search for the QCD critical end point (CEP) and/or first-order phase transition. In this work, we studied the production of $$K^{\pm }$$ , $$\Xi ^-({\bar{\Xi }}^{+})$$ , $$\phi $$ and $$\Lambda ({\bar{\Lambda }})$$ in Au + Au collisions at $$\sqrt{\textrm{s}_{_{\textrm{NN}}}}$$ = 7.7, 11.5, 14.5, 19.6, 27, 39, 54.4, 62.4, and 200 GeV from A Multi-Phase Transport model with string melting version (AMPT-SM). We calculated the invariant yield of these strange hadrons using a different set of parameters compared to those reported in earlier studies and also by varying the hadronic cascade time ( $$t_{max}$$ ) in the AMPT-SM model. We also calculated the yield ratios, $${\mathcal {O}}_{K^{\pm }-\Xi ^{-}({\bar{\Xi }}^{+})-\phi -\Lambda (\bar{\Lambda })}$$ which are reported as sensitive to the strange quark density fluctuations and found that the AMPT-SM model fails to describe the non-monotonic trend observed by the experimental data. The negative particle ratio are found to be higher than the ratio of positive particles which is consistent with the experimental data. A significant effect is also seen on these ratios by varying the $$t_{max}$$ . For a crossover transition between the Quark-Gluon Plasma (QGP) and hadronic matter, the double yield ratios considered in the present study based on AMPT-SM model do not show any non-monotonic behaviors and thus providing a baseline for the search of CEP, because there is no first-order or second-order phase transition in the AMPT model. The more realistic equation of state based dynamical modeling is still required for the heavy-ion collisions in order to extract the definite physics conclusion about the non-monotonic energy dependence behavior.

Phase Structure of Electroweak Vacuum in a Strong Magnetic Field: The Lattice Results.

Using first-principle lattice simulations, we demonstrate that in the background of a strong magnetic field (around 10^{20} T), the electroweak sector of the vacuum experiences two consecutive crossover transitions associated with dramatic changes in the zero-temperature dynamics of the vector W bosons and the scalar Higgs particles, respectively. Above the first crossover, we observe the appearance of large, inhomogeneous structures consistent with a classical picture of the formation of W and Z condensates pierced by vortices. The presence of the W and Z condensates supports the emergence of the exotic superconducting and superfluid properties induced by a strong magnetic field in the vacuum. We find evidence that the vortices form a disordered solid or a liquid rather than a crystal. The second transition restores the electroweak symmetry. Such conditions can be realized in the near-horizon region of the magnetized black holes.

Beam Energy Dependence of Fifth- and Sixth-Order Net-Proton Number Fluctuations in Au+Au Collisions at RHIC

We report the beam energy and collision centrality dependence of fifth and sixth order cumulants (C_{5}, C_{6}) and factorial cumulants (κ_{5}, κ_{6}) of net-proton and proton number distributions, from center-of-mass energy (sqrt[s_{NN}]) 3GeV to 200GeV Au+Au collisions at RHIC. Cumulant ratios of net-proton (taken as proxy for net-baryon) distributions generally follow the hierarchy expected from QCD thermodynamics, except for the case of collisions at 3GeV. The measured values of C_{6}/C_{2} for 0%-40% centrality collisions show progressively negative trend with decreasing energy, while it is positive for the lowest energy studied. These observed negative signs are consistent with QCD calculations (for baryon chemical potential, μ_{B}≤110 MeV) which contains the crossover transition range. In addition, for energies above 7.7GeV, the measured proton κ_{n}, within uncertainties, does not support the two-component (Poisson+binomial) shape of proton number distributions that would be expected from a first-order phase transition. Taken in combination, the hyperorder proton number fluctuations suggest that the structure of QCD matter at high baryon density, μ_{B}∼750 MeV at sqrt[s_{NN}]=3 GeV is starkly different from those at vanishing μ_{B}∼24 MeV at sqrt[s_{NN}]=200 GeV and higher collision energies.