Critical Order Parameter Research Articles

Terahertz field-induced metastable magnetization near criticality in FePS3.

Controlling the functional properties of quantum materials with light has emerged as a frontier of condensed-matter physics, leading to the discovery of various light-induced phases of matter, such as superconductivity1, ferroelectricity2,3, magnetism4-6 and charge density waves7. However, in most cases, the photoinduced phases return to equilibrium on ultrafast timescales after the light is turned off, limiting their practical applications. Here we use intense terahertz pulses to inducea metastable magnetization with a remarkably long lifetime of more than 2.5 milliseconds in the van der Waals antiferromagnet FePS3. The metastable state becomes increasingly robust as the temperature approaches the antiferromagnetic transition point, suggesting that critical order parameter fluctuations play an important part in facilitating the extended lifetime. By combining first-principles calculations with classical Monte Carlo and spin dynamics simulations, we find that the displacement of a specific phonon mode modulates the exchange couplings in a manner that favours a ground state with finite magnetization near the Néel temperature. This analysis also clarifies how the critical fluctuations of the dominant antiferromagnetic order can amplify both the magnitude and the lifetime of the new magnetic state. Our discovery demonstrates the efficient manipulation of the magnetic ground state in layered magnets through non-thermal pathways using terahertz light and establishes regions near critical points with enhanced order parameter fluctuations as promising areas to search for metastable hidden quantum states.

Phase separation in ordered polar active fluids: A completely different universality class from that of equilibrium fluids.

It has recently been shown that large collections of self-propelled entities (a.k.a. "flocks" or, more technically, polar-ordered active fluids), all spontaneously moving in the same direction, can undergo phase separation in the presence of sufficiently strong attractive interactions (which can be caused by, e.g., autochemotaxis). At this transition, the system spontaneously separates into a high-density band and a low-density band, moving parallel to each other, and to the direction of mean flock motion, at different speeds. We show here that phase separation in ordered polar active fluids belongs to a new universality class, completely different from that of phase separation in equilibrium fluids. The upper critical dimension for this transition is d_{c}=5, in contrast to the well-known d_{c}=4 of equilibrium phase separation. With a dynamical renormalization group analysis, we obtain the large-distance, long-time scaling laws of the velocity and density fluctuations, which are characterized by universal critical correlation length and order parameter exponents ν_{⊥},ν_{∥}, and β, respectively. We calculate these to O(ε) in a d=5-ε expansion.

Features of the formation of the rotationally ordered phases in perovskites

Based on the phenomenological theory, the conditions for the formation of a sequences of the rotationally ordered phase states observed in orthoaluminates, orthoferrites and several other ABX3 compounds with a perovskite structure have been studied. It was shown that the specificity of the phase state formation is due to the competition between two critical order parameters characterizing the in-phase and antiphase rotations of the octahedra. The condensation of one order parameter blocks the appearance of the other. The blocking can be overcome by the interaction of the competing order parameters with the displacements of the cation A. In this case, the degree of stretching of the A–X bonds is of great importance. The consequence of the removal of the blocking is the formation of the phase states described by two competing order parameters. The conditions under which a change in the critical order parameter occurs have discussed.

Enhanced explosive synchronization in heterogeneous oscillator populations with higher-order interactions

Explosive synchronization underlying many realistic dynamic processes has attracted great attention in the various fields. Here, we generalize the Kuramoto model with heterogeneous coupling incorporating the higher-order interactions encoded with the simplicial complexes. We show that the introduced nonlinear couplings can significantly enhance the emergence of explosive synchronization in addition to the pairwise interactions. In particular, we uncover that the critical thresholds manifesting the onset or vanishing of the abrupt synchronization are enlarged as the fraction of the higher-order interactions increases. As a consequence, the backward critical order parameter characterizing the desynchronization transition and the width of hysteresis supporting the bistability are remarkably improved. More importantly, we provide an analytical treatment for untangling the stability properties of the equilibrium states at different levels, which allows us to understand the bifurcation mechanism and locate the associated critical points. This study is a step forward in highlighting the importance of higher-order interactions among dynamical units, which might provide control strategies for the induced abrupt emergent phenomena in networked system.

Collective variable estimation with SEEKR.

In biomolecular simulation, enhanced sampling methods improve the variety of states visited by the molecular system. Some enhanced sampling methods require the definition of a collective variable (CV) of interest - which often represents a slow or critical variable within the system, such as a reaction coordinate. Automated computational methods to identify the CV have been developed based on machine learning, principal component analysis, and mutual information - examples include the Automated Mutual Information and Noise Omission (AMINO) and Spectral Gap Optimization of Order Parameters (SGOOP) software. The SEEKR method is an approach to estimate the kinetics and thermodynamics of binding and requires the definition of a CV describing the process of interest. In this work we aim to develop a workflow for calculating single- or multi-dimensional CVs using algorithms that require minimal interaction or input from the user. This workflow consists of the production of MD trajectories through SEEKR using a weighing approach to recover the probability distributions. Trajectories are then analyzed using the AMINO algorithm for the identification of critical order parameters and the SGOOP algorithm to weigh the selected order parameters in a linear combination to form the CV. We test this method on a model two-well potential, a muller potential and real biomolecular systems.

Variance induced decoupling of spin, lattice, and charge ordering in perovskite nickelates

Perovskite nickelates possess an intimate connection among the structural, electronic, and magnetic orders. We investigate how crystal-field disorder induced by cation size variance impacts the emergence of macroscopic magnetic, structural, and electronic behaviors in single crystal high-entropy oxide nickelate films. The degree of variation in cation sizes hosted on the lattice is found to strongly influence critical ordering temperatures. Resonant x-ray scattering and density functional theory describe how high-variance systems produce local lattice distortions that can be used to manipulate charge disproportionation. The disorder induced shifts to local structure are shown to function as a critical order parameter capable of decoupling the nickelates' distinctive magnetic ground state and metal-insulator transition from its charge ordered state, making it possible to stabilize room-temperature ordered phases not observed in low-variance ternary compounds.

Kinetics of the chiral phase transition in a quark–meson [formula omitted]-model

In this study an effective description in the 2PI effective-action formalism for systems of quarks and mesons in and out of equilibrium within a numerical approach is developed, allowing to approximate the complexity of QCD by taking only the lightest and most relevant degrees of freedom into account. In particular the temporarily building up of fluctuations of the net-baryon number encoded by the fourth-order cumulant (or the rescaled curtosis) for lower momenta is being demonstrated when the phase transition occurs near the critical point, or even stronger when the phase transition is of first order, although the initial system is prepared with purely Gaussian fluctuations in the net baryon number. This is the result of the evolving slow and critical order parameter, i.e., the σ-field. On the other hand, depending on the speed of the (Hubble-)expansion scale, the final dissipative evolution due to the collisions among the mesons, the quarks and anti-quarks and the order field weakens the final fluctuations considerably.

Pairing by a Dynamical Interaction in a Metal

We consider pairing of itinerant fermions in a metal near a quantum-critical point (QCP) towards some form of particle-hole order (nematic, spin-density-wave, charge-density-wave, etc). At a QCP, the dominant interaction between fermions comes from exchanging massless fluctuations of a critical order parameter. At low energies, this physics can be described by an effective model with the dynamical electron-electron interaction $V(\Omega_m) \propto 1/|\Omega_m|^\gamma$, up to some upper cutoff $\Lambda$. The case $\gamma =0$ corresponds to BCS theory, and can be solved by summing up geometric series of Cooper logarithms. We show that for a finite $\gamma$, the pairing problem is still marginal (i.e., perturbation series are logarithmic), but one needs to go beyond logarithmic approximation to find the pairing instability. We discuss specifics of the pairing at $\gamma >0$ in some detail and also analyze the marginal case $\gamma = 0+$, when $V(\Omega_m) = \lambda \log{(\Lambda/|\Omega_m|)}$. We show that in this case the summation of Cooper logarithms does yield the pairing instability at $\lambda \log^2{(\Lambda/T_c)} = O(1)$, but the logarithmic series are not geometrical. We reformulate the pairing problem in terms of a renormalization group (RG) flow of the coupling, and show that the RG equation is different in the cases $\gamma=0$, $\gamma = 0+$, and $\gamma >0$.

Collective spin behavior of NiGe thin films on MgO substrate

The results of the magnetic and structural properties of epitaxially grown NiGe thin films on (001) oriented MgO substrate by using molecular beam epitaxy (MBE) have been presented. The XRD measurements showed that the NiGe thin films grown on MgO substrate epitaxially with four-fould rotational crystalline symmetry. In addition, the measurements indicate that the NiGe films were grown on (110)-crystalliographic orientation with respect to (100) direction of the MgO substrate. It has been revealed that the saturation magnetization (Ms) decreases with increasing Ge concentration up to the critical value and then start to increases again at the rate of x = 0.14 in sample of Ni(1-x)Gex. With increasing of the relative Ge concentration, the structural and the magnetic properties of the films evolved into a new pahase with a critical structural order parameter. Also, ferromagnetic resonance measurements show that all magneto-crystalline anisotropy parameters are consistent with this structural critical order. We compared these results with our previous studies about the structural and magnetic properties of the NiGe thin films grown on native oxide Si (001) substrate.

On the fractal structure of soil moisture fields

We study the spatial structure of soil moisture fields within savanna ecosystems, whose persistence is vital because it is the driver of the entire ecological structure and function. These include changes in the physical and biogeochemical conditions of the landscape, affecting vegetation state, soil composition, water fluxes, and solar radiation. We focus on computations of the probabilistic structure of islands of soil moisture, known empirically to be related to that of tree clusters, defined as crossing properties of simulated soil moisture fields. Rainfall is modelled via Cox-Isham space-time fields endowed with characteristic scales. Results show that clusters of soil moisture islands are characterized by robust scale-free structures in the region of a phase transition whose order parameter depends on mean soil moisture. Signatures of this fractal structure are well-defined power laws of size distributions of soil moisture clusters; their perimeters-vs-area relations; variance-vs- area of the fields. These characteristics allow for the estimation of the fractal dimension of the field, and its Hurst coefficient. From the general covariance equation of a fractal field, spatial simulations are possible because its mean and variance are known from the probabilistic structure of soil moisture at a point. Our results identify the statistics of hotspots of microbial activity deduced from proper moisture islands, unattainable otherwise, and thus may guide the design of field and remote observations. The critical order parameter characterizing the phase transition establishes where the fractal structure of soil moisture fields exists as a function of the climatic drivers, and the thresholds reflecting where vegetation survives in the field. An example of application of the phase transition diagram presented here is carried out with reference to the Nylsvley savanna in South Africa.

Quantum-critical scaling properties of the two-dimensional random-singlet state

We use QMC simulations to study effects of disorder on the $S=1/2$ Heisenberg model with exchange constant $J$ on the square lattice supplemented by multispin interactions $Q$. It was found recently [L. Lu et al., Phys. Rev. X 8, 041040 (2018)] that the ground state of this $J$-$Q$ model with random couplings undergoes a quantum phase transition from the N\'eel state into a randomness-induced spin-liquid-like state that is a close analogue to the well known random-singlet (RS) state of the random Heisenberg chain. The 2D RS state arises from spinons localized at topological defects. The interacting spinons form a critical state with mean spin-spin correlations decaying with distance $r$ as $r^{-2}$, as in the 1D RS state. The dynamic exponent $z \ge 2$, varying continuously with the model parameters. We here further investigate the properties of the RS state in the $J$-$Q$ model with random $Q$ couplings. We study the temperature dependence of the specific heat and various susceptibilities for large enough systems to reach the thermodynamic limit and also analyze the size dependence of the critical magnetic order parameter and its susceptibility in the ground state. For all these quantities, we find consistency with conventional quantum-critical scaling when the condition implied by the $r^{-2}$ form of the spin correlations is imposed. All quantities can be explained by the same value of the dynamic exponent $z$ at fixed model parameters. We argue that the RS state identified in the $J$-$Q$ model corresponds to a generic renormalization group fixed point that can be reached in many quantum magnets with random couplings, and may already have been observed experimentally.

Thermodynamic Properties of Heisenberg Spin Systems

We present the simulation results of magnetic 2D and 3D structures with direct (for both of them) and Dzyaloshinskii-Moriya (DMI) (for 2D lattice) interactions in the frame of the Heisenberg model. We have adapted the multipath Metropolis algorithm for systems with complex types of exchange interactions and rough energy landscapes. We show the temperature behavior of magnetization, energy, and heat capacity, and reveal its critical temperatures and order parameter.

Superconductivity above a quantum critical point in a metal: Gap closing versus gap filling, Fermi arcs, and pseudogap behavior

We consider a quantum-critical metal with interaction mediated by fluctuations of a critical order parameter. This interaction gives rise to two competing tendencies -- pairing and non-Fermi liquid behavior. Due to competition, the pairing develops below a finite $T_p $, however its prominent feedback on the fermionic self-energy develops only at a lower $ T_{cross}$. At $T<T_{cross}$ the system behavior is similar to that of a BCS supercoductor -- the density of states (DOS) and the spectral function (SF) have sharp gaps which close as $T$ increases. At higher $T_{cross}<T<T_{p}$ the DOS has a dip, which {\it fills in} with increasing $T$. The SF in this region shows either the same behavior as the DOS, or has a peak at $\omega =0$ (the Fermi arc), depending on the position on the Fermi surface. We argue that phase fluctuations are strong in this $T$ range, and the actual $T_c \sim T_{cross}$, while $T_p$ marks the onset of pseugogap behavior. We compare our theory with the behavior of optimally doped cuprates.

Group-Theoretical Classification of Aristotypes of Cation and Anion Orders in Perovskites

A group-theoretical classification of cation and anion orders of crystals with a perovskite structure is presented. Aristotypes are idealized structures (phases), from which the low-symmetry ordered modifications of perovskites are formed as a result of rotations and deformation of octahedra, as well as the cooperative Jahn–Teller effect and other physical phenomena. Seven aristotype classes have been distinguished, which are characterized by the atomic ordering in each of Wyckoff positions and simultaneous atomic ordering in several positions. The critical and secondary (improper) order parameters, describing the formation of ordered structures, are determined. The classification proposed makes it possible to systematize a variety of known phases, establish genetic structural links between low-symmetry ordered structures, and design new materials.

Size effects of critical temperatures and order parameter distributions under four-fold symmetry of nano-structured superconductors

We investigate size and shape dependences of critical temperatures Tc’s and order parameter distributions for nano-structured superconductors. We use the finite element method to solve the Gor’kov equations. We find that order parameter distributions hold four-fold symmetry for square superconductors. It is different from order parameter distributions of rectangular superconductors, which have two-fold symmetry. We show that the difference comes from symmetry of the superconductor and degeneracy of states of Cooper pairs, by investigating size dependences of order parameter distributions and those of eigen-energies of quasi-particles.

Vanadium clusters formation in geometrically frustrated spinel oxide AlV2O4.

The spinel oxide AlV2O4 is a unique material, in which the formation of clusters is accompanied by atomic, charge and orbital ordering and a rhombohedral lattice distortion. In this work a theory of the structural phase transition in AlV2O4 is proposed. This theory is based on the study of the order-parameter symmetry, thermodynamics, electron density distribution, crystal chemistry and mechanisms of formation of the atomic and orbital structures of the rhombohedral phase. It is established that the critical order parameter is transformed according to irreducible representation k9(τ4) (in Kovalev notation) of the Fd \bar{3}m space group. Knowledge of the order-parameter symmetry allows us to show that the derived AlV2O4 rhombohedral structure is a result of displacements of all atom types and the ordering of Al atoms (1:1 order type in tetrahedral spinel sites), V atoms (1:1:6 order type in octahedral sites) and O atoms (1:1:3:3 order type), and the ordering of dxy, dxz and dyz orbitals. Application of the density functional theory showed that V atoms in the Kagomé sublattice formed separate trimers. Also, no sign of metallic bonding between separate vanadium trimers in the heptamer structure was found. The density functional theory study and the crystal chemical analysis of V-O bond lengths allowed us to assume the existence of dimers and trimers as main clusters in the structure of the AlV2O4 rhombohedral modification. The trimer model of the low-symmetry AlV2O4 structure is proposed. Within the Landau theory of phase transitions, typical diagrams of possible phase states are built. It is shown that phase states can be changed as a first-order phase transition close to the second order in the vicinity of tricritical points of the phase diagrams.

Continuously varying critical order-parameter fluctuations in a parity conserving absorbing-state transition with long-range diffusion

We study the critical order parameter fluctuations of the absorbing-state phase-transition exhibited by branching and annihilating random walkers performing anomalous diffusion in a linear chain. The diffusion process is considered to follow a power-law distribution of jump lengths with a typical decay exponent α. We focus in the case of parity conserving dynamics for which deviations from the usual directed percolation universality class have been previously demonstrated even for the limiting cases of normal diffusion. Anomalous diffusion induces a continuous change of the critical exponents. By performing a finite-size scaling analysis of simulation data, we show that the critical order parameter moment ratio also varies continuously with α. We unveil that the critical order parameter distribution evolves from a nearly Gaussian to an exponential form as the range of the jump distribution is increased up to the limit on which the active state predominates for any finite branching probability.

Unique hyper-kagome atomic order in the noncentrosymmetric structure of Na3Ir3O8

The formation of a unique hyper-kagome atomic order in the structure of the ordered spinel phase Na3Ir3O8 has been analyzed in terms of the Landau theory of phase transitions. We have identified a critical six-component order parameter generating a phase transformation of the spinel parent phase to ordered P4132 (P4332) spinel-like enantiomorphs and examined the structural mechanism behind the development of hyper-kagome order and the detailed crystal chemistry of Na3Ir3O8.

Phenomenological thermodynamics and the structure formation mechanism of the CuTi₂S₄ rhombohedral phase.

The theory of structural phase transition in CuTi2S4 is proposed. The symmetry of order parameters, thermodynamics and the mechanism of the atomic structure formation of the rhombohedral Cu-Ti-thiospinel have been studied. The critical order parameter inducing the phase transition has been found. Within the Landau theory of phase transitions, it is shown that the phase state may change from the high-symmetry cubic disordered Fd3[combining macron]m phase to the low-symmetry ordered rhombohedral R3[combining macron]m phase as a result of phase transition of the first order close to the second order. It is shown that the rhombohedral structure of CuTi2S4 is formed as a result of the displacements of all types of atoms and the ordering of Cu-atoms (1 : 1 order type in tetrahedral spinel sites), Ti-atoms (1 : 1 : 6 order type in octahedral spinel sites), and S-atoms (1 : 1 : 3 : 3 order type). The Cu- and Ti-atoms form metal nanoclusters which are named a "bunch" of dimers. The "bunch" of dimers in CuTi2S4 is a new type of self-organization of atoms in frustrated spinel-like structures. It is shown that Ti-atoms also form other types of metal nanoclusters: trimers and tetrahedra.

Unique atom hyper-kagome order in Na4Ir3O8 and in low-symmetry spinel modifications.

Group-theoretical and thermodynamic methods of the Landau theory of phase transitions are used to investigate the hyper-kagome atomic order in structures of ordered spinels and a spinel-like Na4Ir3O8 crystal. The formation of an atom hyper-kagome sublattice in Na4Ir3O8 is described theoretically on the basis of the archetype (hypothetical parent structure/phase) concept. The archetype structure of Na4Ir3O8 has a spinel-like structure (space group Fd\bar 3m) and composition [Na1/2Ir3/2](16d)[Na3/2](16c)O(32e)4. The critical order parameter which induces hypothetical phase transition has been stated. It is shown that the derived structure of Na4Ir3O8 is formed as a result of the displacements of Na, Ir and O atoms, and ordering of Na, Ir and O atoms, ordering dxy, dxz, dyz orbitals as well. Ordering of all atoms takes place according to the type 1:3. Ir and Na atoms form an intriguing atom order: a network of corner-shared Ir triangles called a hyper-kagome lattice. The Ir atoms form nanoclusters which are named decagons. The existence of hyper-kagome lattices in six types of ordered spinel structures is predicted theoretically. The structure mechanisms of the formation of the predicted hyper-kagome atom order in some ordered spinel phases are established. For a number of cases typical diagrams of possible crystal phase states are built in the framework of the Landau theory of phase transitions. Thermodynamical conditions of hyper-kagome order formation are discussed by means of these diagrams. The proposed theory is in accordance with experimental data.