Nonequilibrium Dynamical Behavior Research Articles

Magnetic frustration driven by conduction carrier blocking in Nd2Co0.85Si2.88

The intermetallic compound ${\mathrm{Nd}}_{2}{\mathrm{Co}}_{0.85}{\mathrm{Si}}_{2.88}$ having a triangular lattice could be synthesized in single phase only with defect crystal structure. Investigation through different experimental techniques indicate the presence of two magnetic transitions in the system. As verified experimentally and theoretically, the high-temperature transition ${T}_{\mathrm{H}}\ensuremath{\sim}$ 140 K is associated with the development of ferromagnetic interaction between itinerant Co moments, whereas the low-temperature transition at ${T}_{\mathrm{L}}\ensuremath{\sim}$ 6.5 K is due to the coupling among $\text{Nd}\text{\ensuremath{-}}4f$ and $\mathrm{Co}\text{\ensuremath{-}}3d$ moments, which is antiferromagnetic in nature. Detailed studies of temperature-dependent dc magnetic susceptibility, field dependence of isothermal magnetization, nonequilibrium dynamical behavior, viz., magnetic relaxation, aging effect, magnetic-memory effect, and temperature dependence of heat capacity, along with density functional theory (DFT) calculations, suggest that the ground state is magnetically frustrated spin glass in nature, having competing magnetic interactions of equivalent energies. DFT results further reveal that the $3d/5d$-conduction carriers are blocked in the system and act as a barrier for the $4f\text{\ensuremath{-}}4f$ RKKY interactions, resulting in spin frustration. Presence of vacancy defects in the crystal are also conducive to the spin frustration. This is an unique mechanism of magnetic frustration, not emphasized so far in any of the ternary ${R}_{2}T{X}_{3}$ ($R$ = rare earth, $T$ = transition elements, and $X$ = Si, Ge, In) type compounds. Due to the competing character of the itinerant $3d$ and localized $4f$ moments, the compound exhibits anomalous field dependence of magnetic coercivity. The system also exhibits a considerable magnetic entropy change of $\ensuremath{-}\mathrm{\ensuremath{\Delta}}{S}_{\mathrm{M}}\ensuremath{\sim}$ 13.3 J/kg K with a relative cooling power (RCP) of 220 J/kg and adiabatic temperature change $\mathrm{\ensuremath{\Delta}}{T}_{\mathrm{ad}}$ of 6 K for magnetic field change of 70 kOe.

Nonequilibrium dynamical behavior in noncoplanar magnets with chiral spin texture

We observe nonequilibrium dynamical magnetic behavior in the magnetically ordered phase of a Tsai-type Tb-Au-Si quasicrystal approximant system. The magnetic texture in the ordered phase is found to exhibit scalar spin chirality (SSC) order, inferring that SSC is the order parameter of the present magnetic system. We further find that the introduction of ``pseudo-Tsai'' clusters, associated with additional Tb atoms in the structure, induces spin-glass dynamics. We discuss the observed dynamical magnetic behavior in the Tb-Au-Si systems, considering the effect of the pseudo-Tsai clusters on the magnetic configuration and local spin chirality.

Detecting the out-of-time-order correlations of dynamical quantum phase transitions in a solid-state quantum simulator

Quantum many-body systems in equilibrium can be effectively characterized using the framework of quantum statistical mechanics. However, there still exist a lot of questions regarding how to understand the nonequilibrium dynamical behavior of quantum many-body systems, which are not accessible with the thermodynamic description. Experiments in quantum simulators are opening up a route toward the generation of quantum states beyond the equilibrium paradigm. As an example, in closed quantum many-body systems, dynamical quantum phase transitions act as phase transitions in time, with physical quantities becoming nonanalytic at a critical time, extending important principles such as universality to the nonequilibrium realm. Here, in a solid-state quantum simulator, we report the experimental detection of out-of-time-order correlators in the presence of nonequilibrium phase transitions with the transverse field Ising model, which are a central concept to quantify quantum information scrambling and quantum chaos. Through measuring the multiple quantum spectra, we eventually observe the buildup of quantum correlation. Further applications of this protocol could potentially enable studies of other exotic phenomena such as many-body localization and tests of the holographic duality between quantum and gravitational systems.

Chaotic study on a multibody interacting particle system with trajectory of variable curvature radius

Multibody interacting particle system is one of the most important driven-diffusive systems, which can well describe stochastic dynamics of self-driven particles unidirectionally updating along one-dimensional discrete lattices controlled by hard-core exclusions. Such determined nonlinear dynamic system shows the chaos, a complicated motion that is similar to random and can’t determine future states according to given initial conditions. Derived from the study of randomness in the framework of determinism, chaos effectively unifies determinacy and randomness of nonlinear physics, which also embodies the randomness and uncertainty of multi-body particle motions. Besides, chaos often presents complex ordered phenomena like aperiodic ordered motion state etc., which indicates it’s a stable coordination of local random and global mode. Different with previous work, a mesoscopic multibody interacting particle system considering the trajectory of variable curvature radius is proposed, which is more reliable to depict true driven-diffusive systems. Nonlinear dynamical master equations are established. Linear and nonlinear stability analyses are performed to test system robustness, which lead to linear stable region, metastable region, unstable region, triangular wave, solitary wave and kink-antikink wave. Complete numerical simulations under quantitatively changing characteristic order parameters are performed to reveal intrinsic chaotic dynamics mechanisms. By comparing fruitful chaotic patterns, double periodic convergence in stable limit cycles is observed due to attractors folding. System states tend to be limit cycles with the passage of time. The longer time is, the higher density is near attractors. The number of main components of attractors and the shape of them are found to drastically change with these parameters. Hereafter, the chaotic formation mechanism is explained by performing Fourier spectrums analyses. High and low frequency elements are obtained, whose module lengths are found to change periodically with time and nonperiodically with space. Our results show the sensitivity of the chaotic system to initial conditions, which mean slight changes of initial states in one part of system can lead to disproportionate consequences in other parts. The sensitivity is directly related to uncertainty and unpredictability. Moreover, calculations also show that three kinds of attractors (namely, point attractor, limit-cycle attractor and strange attractor) exist in the proposed chaotic system, which control particle motions. The first two attractors are convergence attractors playing a limiting role, which lead to static and balanced features of system. Oppositely, strange attractor makes the system deviate from regions of convergent attractors and creates unpredictability by inducing the vitality of the system and turning it into a non-preset mode. Furthermore, interactions between convergence attractors and strange attractors trigger such locally fruitful modes. This work will be helpful to understand mesoscopic dynamics, stochastic dynamics and non-equilibrium dynamical behaviors of multibody interacting particle systems.

Spatially limited antiferromagnetic order in a cluster glass compound Tb2Ni0.90Si2.94

In the present study, the synthesis of a new ternary intermetallic compound Tb2Ni0.90Si2.94 has been reported. The detailed studies on structure, static and dynamical magnetic properties of the compound have been investigated by means of powder x-ray diffraction, compositional analysis, dc & ac magnetization, non-equilibrium dynamics, heat capacity and neutron diffraction measurements. The dc & ac magnetic susceptibility reveal that the compound undergoes spin cluster-glass behaviour below 9.9 K. The frequency dependence of the freezing temperature have been analysed on the basis of dynamic scaling laws such as power-law divergence and Vogel-Fulcher law, which further confirm the cluster-glass state formation for the compound. A detailed study on non-equilibrium dynamical behaviour associated with cluster-glass state has been carried out through magnetic relaxation behaviour along with magnetic memory effect in zero-field-cooled (ZFC) as well as field-cooled (FC) conditions and associated aging effect. The zero-field neutron diffraction study reveals the presence of a spatially limited antiferromagnetic phase in addition to the magnetically frustrated cluster-glass state. This result has also been supported through zero-field heat capacity studies. The variation in local electronic environment among the magnetic rare-earth ions caused by the structural disorder associated with Ni/Si ions have been argued to be responsible for the coexistence of different magnetic phases.

Analytical and simulation studies of driven diffusive system with asymmetric heterogeneous interactions

Totally asymmetric simple exclusion process (namely, TASEP) is one of the most vital driven diffusive systems, which depicts stochastic dynamics of self-driven particles unidirectional updating along one-dimensional discrete lattices controlled by hard-core exclusions. Different with pre-existing results, driven diffusive system composed by multiple TASEPs with asymmetric heterogeneous interactions under two-dimensional periodic boundaries is investigated. By using detailed balance principle, particle configurations are extensively studied to obtain universal laws of characteristic order parameters of such stochastic dynamic system. By performing analytical analyses and Monte-Carlo simulations, local densities are found to be monotone increase with global density and spatially homogeneous to site locations. Oppositely, local currents are found to be non-monotonically increasing against global density and proportional to forward rate. Additionally, by calculating different cases of topologies, changing transition rates are found to have greater effects on particle configurations in adjacent subsystems. By intuitively comparing with pre-existing results, the improvement of our work also shows that introducing and considering totally heterogeneous interactions can improve the total current in such multiple TASEPs and optimize the overall transport of such driven-diffusive system. Our research will be helpful to understand microscopic dynamics and non-equilibrium dynamical behaviors of interacting particle systems.

Unusual bidirectional frequency dependence of dynamical susceptibility in hexagonal intermetallic Pr2Ni0.95Si2.95

In this study, the synthesis of a novel ternary intermetallic compound Pr2Ni0.95Si2.95 forming in single phase only by deliberately introducing vacancies in Ni/Si site is reported. The detailed studies on dc magnetization, heat capacity, ac magnetization & associated dynamical scaling, different types of non-equilibrium dynamical behaviour, viz., magnetic relaxation behaviour as a function of wait time and temperature, aging phenomena, and magnetic memory effect firmly establish that the compound exhibits spin freezing behaviour below 3.3 K (Tf). However, below Tf, temperature dependence of ac susceptibility data exhibit an additional peak that shows reverse frequency dependence to that generally observed in a glassy system. The unusual bidirectional frequency dependence in a single magnetic system is of significant interest and rarely reported in literature. Competing exchange interaction arising from c/a ~ 1 and crystallographic randomness driven magnetic phase separation has been argued to be responsible for such observation. The reverse frequency shift of the low temperature peak has been described on the basis of a simple phenomenological model proposed in this work.

Magnetic phase inhomogeneity in frustrated intermetallic compound Sm2Ni0.87Si2.87

A new ternary compound Sm2Ni0.87Si2.87, belonging to intermetallic R2TX3 family (R = rare-earth, T = transition metals, X = Si, Ge, etc.), could be synthesized in single phase only by the deliberate introduction of lattice vacancies in the Ni and Si sites. The detailed studies of heat capacity as well as dc and ac magnetization including different non-equilibrium dynamical behaviour, viz., aging effect, temperature and field dependent magnetic relaxation and magnetic memory effect establish the compound to be a cluster-glass material having a spin freezing temperature ∼6.6 K. To understand the nature of the glassy phase, experimental results have been analysed using a few different theoretical models and found that the observed magnetic memory effect favours the hierarchical model over the droplet model. Competing exchange interaction driven magnetic phase inhomogeneity could be further confirmed through exchange bias effect. The observed magnetic phase inhomogeneity has been attributed to random magnetic anisotropy that develops due to local environmental variations between the rare-earth ions.

Chemical disorder driven reentrant spin cluster glass state formation and associated magnetocaloric properties of Nd2Ni0.94Si2.94.

In this work, we report the synthesis of a new ternary intermetallic compound, Nd2Ni0.94Si2.94, that forms in single phase only in a defect crystal structure. The compound exhibits an antiferromagnetic transition below 7.2 K (TN) followed by a spin cluster freezing behaviour below 2.85 K (Tf), which makes the compound a reentrant spin cluster glass system. The detailed studies of dc and ac magnetization, heat capacity, non-equilibrium dynamical behaviour, viz., aging effect, temperature and field dependent magnetic relaxation and magnetic memory effect establish the compound to be a cluster-glass material below freezing temperature. The interplay between competing exchange coupling (c/a ≃ 1.04 ⇒ JNN ≃ JNNN) and chemical disorder driven variation in the electronic environment among the Nd ions has been argued to be responsible for such a metastable state formation. A considerable value of MCE parameters (-ΔS ∼ 11.4 J kg-1 K-1, RCP ∼ 160 J kg-1 and ΔTad ∼ 5.2 K for a field change of 70 kOe) is obtained for this magnetically frustrated glassy compound.

Critical quench dynamics of random quantum spin chains: ultra-slow relaxation from initial order and delayed ordering from initial disorder

By means of free fermionic techniques combined with multiple precision arithmetic we study the time evolution of the average magnetization, , of the random transverse-field Ising chain after global quenches. We observe different relaxation behaviors for quenches starting from different initial states to the critical point. Starting from a fully ordered initial state, the relaxation is logarithmically slow described by , and in a finite sample of length L the average magnetization saturates at a size-dependent plateau here the two exponents satisfy the relation . Starting from a fully disordered initial state, the magnetization stays at zero for a period of time until with and then starts to increase until it saturates to an asymptotic value , with . For both quenching protocols, finite-size scaling is satisfied in terms of the scaled variable . Furthermore, the distribution of long-time limiting values of the magnetization shows that the typical and the average values scale differently and the average is governed by rare events. The non-equilibrium dynamical behavior of the magnetization is explained through semi-classical theory.

Large magnetic cooling power involving frustrated antiferromagnetic spin-glass state inR2NiSi3(R=Gd,Er)

The ternary intermetallic compounds ${\mathrm{Gd}}_{2}{\mathrm{NiSi}}_{3}$ and ${\mathrm{Er}}_{2}{\mathrm{NiSi}}_{3}$ are synthesized in chemically single phase, which are characterized using dc magnetization, ac magnetic susceptibility, heat capacity, and neutron diffraction studies. Neutron diffraction and heat capacity studies confirm that long-range magnetic ordering coexists with the frustrated glassy magnetic components for both compounds. The static and dynamical features of dc magnetization and frequency-dependent ac susceptibility data reveal that ${\mathrm{Gd}}_{2}{\mathrm{NiSi}}_{3}$ is a canonical spin-glass system, while ${\mathrm{Er}}_{2}{\mathrm{NiSi}}_{3}$ is a reentrant spin cluster-glass system. The spin freezing temperature merges with the long-range antiferromagnetic ordering temperature at 16.4 K for ${\mathrm{Gd}}_{2}{\mathrm{NiSi}}_{3}$. ${\mathrm{Er}}_{2}{\mathrm{NiSi}}_{3}$ undergoes antiferromagnetic ordering at 5.4 K, which is slightly above the spin freezing temperature at 3 K. The detailed studies of nonequilibrium dynamical behavior, viz., the memory effect and relaxation behavior using different protocols, suggest that both compounds favor the hierarchical model over the droplet model. A large magnetocaloric effect is observed for both compounds. Maximum values of isothermal entropy change $(\ensuremath{-}\mathrm{\ensuremath{\Delta}}{S}_{M})$ and relative cooling power (RCP) are found to be 18.4 J/kg K and 525 J/kg for ${\mathrm{Gd}}_{2}{\mathrm{NiSi}}_{3}$ and 22.6 J/kg K and 540 J/kg for ${\mathrm{Er}}_{2}{\mathrm{NiSi}}_{3}$, respectively, for a change in field from 0 to 70 kOe. The values of RCP are comparable to those of the promising refrigerant materials. A correlation between large RCP and magnetic frustration is discussed for developing new magnetic refrigerant materials.

Self-organization in suspensions of end-functionalized semiflexible polymers under shear flow.

The nonequilibrium dynamical behavior and structure formation of end-functionalized semiflexible polymer suspensions under flow are investigated by mesoscale hydrodynamic simulations. The hybrid simulation approach combines the multiparticle collision dynamics method for the fluid, which accounts for hydrodynamic interactions, with molecular dynamics simulations for the semiflexible polymers. In equilibrium, various kinds of scaffold-like network structures are observed, depending on polymer flexibility and end-attraction strength. We investigate the flow behavior of the polymer networks under shear and analyze their nonequilibrium structural and rheological properties. The scaffold structure breaks up and densified aggregates are formed at low shear rates, while the structural integrity is completely lost at high shear rates. We provide a detailed analysis of the shear- rate-dependent flow-induced structures. The studies provide a deeper understanding of the formation and deformation of network structures in complex materials.

Local aging phenomena close to magnetic surfaces

Surface aging phenomena are discussed for semi-infinite systems prepared in a fully disordered initial state and then quenched to or below the critical point. In addition to solving exactly the semi-infinite Ising model in the limit of large dimensions, we also present results of an extensive numerical study of the nonequilibrium dynamical behavior of the two-dimensional semi-infinite Ising model undergoing coarsening. The studied models reveal a simple aging behavior where some of the nonequilibrium surface exponents take on values that differ from their bulk counterparts. For the two-dimensional semi-infinite Ising model we find that the exponent ${b}_{1}$ that describes the scaling behavior of the surface autocorrelation vanishes. These simulations also reveal the existence of strong finite-time corrections that to some extent mask the leading scaling behavior of the studied two-time quantities.

Nonequilibrium and nonlinear dynamics in Berea and Fontainebleau sandstones: Low‐strain regime

Members of a wide class of geomaterials are known to display complex and fascinating nonlinear and nonequilibrium dynamical behaviors over a wide range of bulk strains, down to surprisingly low values, e.g., 10−7. In this paper we investigate two sandstones, Berea and Fontainebleau, and characterize their behavior under the influence of very small external forces via carefully controlled resonant bar experiments. By reducing environmental effects due to temperature and humidity variations, we are able to systematically and reproducibly study dynamical behavior at strains as low as 10−9. Our study establishes the existence of two strain regimes separated by εM. At strains below εM the material is nonlinear and quasi‐equilibrium thermodynamics applies as evidenced by the success of Landau theory and a simple macroscopic description based on the Duffing oscillator. At strains above εM the behavior becomes truly nonequilibrium, as demonstrated by the existence of material conditioning, and Landau theory no longer applies. The main focus of this paper is the study of the first region, but we also comment on how our work clarifies and resolves previous experimental conflicts, as well as suggest new directions of research.

Linear time dependence of the surfactant effect: A local equilibrium under flux

We have investigated the dissolution kinetics of an A metal thin film deposited on a (100) B metal under thermal annealing for a system with a strong B segregation (e.g., Ni/Ag). The interdiffusion is described using both Monte Carlo and mean-field simulations with an effective exchange mechanism derived from the kinetic tight-binding Ising model. Surprisingly, the surface enrichment in substrate B element is found to increase linearly with time instead of following the usual $\sqrt{t}$ law. We demonstrate that this t law occurs when the diffusion coefficient of B atoms in the A deposit is high or when the deposit thickness decreases. Moreover it is shown that, in this surfactant regime, the usual local equilibrium rule which drives the kinetics has to be generalized under the flux of B atoms coming from the deposit/substrate interface. Consequences of this new formulation on nonequilibrium dynamical behaviors during thin film dissolutions are discussed.

Non-equilibrium dynamical behavior of exciton/biexciton in a diluted magnetic semiconductor asymmetric quantum well

Optical properties of a (Cd,Mg)Te/CdTe/(Cd,Mn)Te quantum well is investigated systematically using photoluminescence (PL) and time-resolved photoluminescence (TRPL). The PL intensity ratio of biexciton to exciton showed a linear dependence. The biexciton TRPL showed a longer lifetime as compared with that of the exciton. These results suggested an important role of dark excitons and their spin scattering by Mn localized spins in this system. The rate equations based on our model taking account of the dark exciton level ( J=±2) were used to analyze the time decay of the exciton and biexciton TRPL in various temperatures and excitation densities. Our analysis leads to a conclusion that the new channel from a dark exciton has an essential role when biexcitons are created in dilute magnetic semiconductor quantum wells containing Mn in the barrier.

Statistical neurodynamics of associative memory

A new statistical neurodynamical method is proposed for analyzing the non-equilibrium dynamical behaviors of an autocorrelation associative memory model. The theory explains strange dynamical behaviors in recalling processes which are observed by computer simulations: Starting with an initial state close to a memorized pattern, the state monotonically approaches the memorized one. Starting with an initial state which is not so close to a memorized one, the state once approaches it but then goes away from it. The theory not only gives the relative and absolute capacity of the memory network without using the spin glass analogy, but it explains the non-equilibrium or transient dynamical behaviors of the recalling process by taking the long-term correlation effects into account. It thus explains the strange behaviors due to strange shapes of the basins of attractors.