Metamagnetic Anomalies near Dynamic Phase Transitions

Dynamical phase transitions in the XY model: A Monte Carlo and mean-field-theory study

We investigate the dynamical phases and phase transitions arising in a classical two-dimensional anisotropic XY model under the influence of a periodically driven temporal external magnetic field in the form of a symmetric square wave. We use a combination of finite temperature classical Monte Carlo simulation, implemented within a CPU+GPU paradigm, utilizing local dynamics provided by the Glauber algorithm and a phenomenological equation-of-motion approach based on relaxational dynamics governed by the time-dependent free energy within a mean-field approximation to study the model. We investigate several parameter regimes of the variables (magnetic field, anisotropy, and the external drive frequency) that influence the anisotropic XY system. We identify four possible dynamical phases: Ising-SBO, Ising-SRO, XY-SBO, and XY-SRO. Both techniques indicate that only three of them (Ising-SRO, Ising-SBO, and XY-SRO) are stable dynamical phases in the thermodynamic sense. Within the Monte Carlo framework, a finite-size scaling analysis, shows that XY-SBO does not survive in the thermodynamic limit giving way to either an Ising-SBO or a XY-SRO regime. The finite-size scaling analysis further shows that the transitions between the three remaining dynamical phases either belong to the two-dimensional Ising universality class or are first-order in nature. Within the mean-field calculations yield three stable dynamical phases, i.e., Ising-SRO, Ising-SBO and XY-SRO, where the final steady state is independent of the initial condition chosen to evolve the equations of motion, as well as a region of bistability where the system flows to either Ising-SBO or XY-SRO (Ising-SRO) depending on the initial condition. Unlike the stable dynamical phases, the XY-SBO represents a transient feature that is eventually lost to either Ising-SBO or XY-SRO. Our mean-field analysis highlights the importance of the competition between switching of the stationary point(s) of the free energy after each half cycle of the external field and the two-dimensional nature of the phase space for the equations of motion.

Numerical simulation of a two-dimensional Blume-Capel ferromagnet in an oscillating magnetic field with a constant bias

We perform a numerical study of the kinetic Blume-Capel (BC) model to find if it exhibits the metamagnetic anomalies previously observed in the kinetic Ising model for supercritical periods [P. Riego et al., Phys. Rev. Lett. 118, 117202 (2017)0031-900710.1103/PhysRevLett.118.117202; G. M. Buendía et al., Phys. Rev. B 96, 134306 (2017)2469-995010.1103/PhysRevB.96.134306]. We employ a heat-bath Monte Carlo (MC) algorithm on a square lattice in which spins can take values of ±1,0, with a nonzero crystal field, subjected to a sinusoidal oscillating field in conjunction with a constant bias. In the ordered region, we find an equivalent hysteretic response of the order parameters with its respective conjugate fields between the kinetic and the equilibrium model. In the disordered region (supercritical periods), we observed two peaks, symmetrical with respect to zero bias, in the susceptibility and scaled variance curves, consistent with the numerical and experimental findings on the kinetic Ising model. This behavior does not have a counterpart in the equilibrium model. Furthermore, we find that the peaks occur at higher values of the bias field and become progressively smaller as the density of zeros, or the amplitude of the oscillating field, increases. Using nucleation theory, we demonstrate that these fluctuations, as in the Ising model, are not a critical phenomenon, but that they are associated with a crossover between a single-droplet (SD) and a multidroplet (MD) magnetization switching mechanism. For strong (weak) bias, the SD (MD) mechanism dominates. We also found that the zeros concentrate on the droplets' surfaces, which may cause a reduced interface tension in comparison with the Ising model [M. Schick et al., Phys. Rev. B 34, 1797 (1986)0163-182910.1103/PhysRevB.34.1797]. Our results suggest that metamagnetic anomalies are not particular to the kinetic Ising model, but rather are a general characteristic of spin kinetic models, and provide further evidence that the equivalence between dynamical phase transitions and equilibrium ones is only valid near the critical point.

Dynamic magnetic characteristics of the kinetic Ising model under the influence of randomness

In this paper, we propose to solve the issues of long-range or next-neighbor interactions by introducing randomness. This approach is applied to the square lattice Ising model. The Monte Carlo method with the Metropolis algorithm is utilized to calculate the critical temperature T_{C}^{*} under equilibrium thermodynamic phase transition conditions and to investigate the characterization of randomness in terms of magnetization. In order to further characterize the effect of this randomness on the magnetic system, clustering coefficients C_{p} are introduced. Furthermore, we investigate a number of dynamic magnetic behaviors, including dynamic hysteresis behaviors and metamagnetic anomalies. The results indicate that noise has the effect of destabilizing the system and promoting the dynamic phase transition. When the system is subjected to noise, the effect of this noise can be mitigated by the addition of a time-oscillating magnetic field. Finally, the evolution of anomalous metamagnetic fluctuations under the influence of white noise is examined. The relationship between the bias field corresponding to the peak of the curve h_{b}^{peak} and the noise parameter σ satisfies the exponential growth equation, which is consistent with other results.

Verification of scaling behavior near dynamic phase transitions for nonantisymmetric field sequences

We investigate the scaling behavior of the magnetic dynamic order parameter Q in the vicinity of the dynamic phase transition (DPT) in the presence of temporal field sequences H(t) that are periodic with period P but lack half-wave antisymmetry. We verify by means of mean-field calculations that the scaling of Q is preserved in the vicinity of the second-order phase transition if one defines a suitable generalized conjugate field H^{*} that reestablishes the proper time-reversal symmetry. For the purpose of our quantitative data analysis, we employ the dynamic equivalent of the Arrott-Noakes equation of state, which allows for a simultaneous scaling analysis of the period P and the conjugate-field H^{*} dependence of Q. By doing so, we demonstrate that both the scaling behavior and universality are preserved, even if the dynamics is driven by a more general applied field sequence that lacks antisymmetry.

Complex phase diagram and supercritical matter

The supercritical region is often described as uniform with no definite transitions. The distinct behaviors of the matter therein, e.g., as liquidlike and gaslike, however, suggest "supercritical boundaries." Here we provide a mathematical description of these phenomena by revisiting the Yang-Lee theory and introducing a complex phase diagram, specifically a four-dimensional (4D) one with complex T and p. While the traditional 2D phase diagram with real temperature T and pressure p values (the physical plane) lacks Lee-Yang (LY) zeros beyond the critical point, preventing the occurrence of criticality, the off-plane zeros in this 4D scenario still induce critical anomalies in various physical properties. This relationship is evidenced by the correlation between the Widom line and LY edges in van der Waals, 2D Ising model, and water. The diverged supercritical boundaries manifest the high-dimensional feature of the phase diagram: e.g., when LY zeros of complex T or p are projected onto the physical plane, boundaries defined by isobaric heat capacity C_{p} or isothermal compression coefficient K_{T} emanates. These results demonstrate the incipient phase transition nature of the supercritical matter.

Dynamic Phase Transition in 2D Ising Systems: Effect of Anisotropy and Defects

We investigate the dynamic phase transition in two-dimensional Ising models whose equilibrium characteristics are influenced by either anisotropic interactions or quenched defects. The presence of anisotropy reduces the dynamical critical temperature, leading to the expected result that the critical temperature approaches zero in the full-anisotropy limit. We show that a comprehensive understanding of the dynamic behavior of systems with quenched defects requires a generalized definition of the dynamic order parameter. By doing so, we demonstrate that the inclusion of quenched defects lowers the dynamic critical temperature as well, with a linear trend across the range of defect fractions considered. We also explore if and how it is possible to predict the dynamic behavior of specific magnetic systems with quenched randomness. Various geometric quantities, such as a defect potential index, the defect dipole moment, and the properties of the defect Delaunay triangulation, prove useful for this purpose.

Metamagnetic fluctuation characteristics near dynamic phase transitions

We experimentally explore the magnetization dynamics of thin ferromagnetic Co films with uniaxial in-plane anisotropy near the dynamic phase transition (DPT) and, in particular, we study the temporal characteristics of anomalous metamagnetic fluctuations that occur in its vicinity, and for which no thermodynamic equivalent exists. For this purpose, we measure the real-time evolution of magnetization trajectories in the relevant dynamic phase space, conduct a Fourier analysis of these experimental results and compare it to a model, in which the fluctuating metamagnetic behavior occurs in a purely random manner, following individual state probability distributions. We find excellent quantitative agreement in between our experimental results and the random state model, clearly indicating that multiperiod time-correlations of magnetic states are not relevant in our DPT system, not even for the occurrence of the anomalous metamagnetic fluctuations that are nonetheless associated with nonperiodic magnetic state evolutions.

Experimental Observation of Critical Scaling in Magnetic Dynamic Phase Transitions

We explore the critical behavior of dynamic phase transitions in ultrathin uniaxial Co films. Our data demonstrate the occurrence of critical fluctuations, which define the critical regime, and in which we conduct a scaling analysis of the dynamic order parameter Q, utilizing a dynamic analog to the Arrott-Noakes equation of state. Our results show dynamic critical exponents that agree with the 2D Ising model as theoretically predicted. However, equilibrium critical exponents of our sample agree with the 3D Ising model. We argue that these differences between dynamic and thermodynamic behavior are due to fundamentally different length scales at which dimensional crossovers occur.

Exploring the equilibrium and dynamic phase transition properties of the Ising ferromagnet on a decorated triangular lattice

We study the equilibrium and dynamic phase transition properties of a two-dimensional Ising model on a decorated triangular lattice under the influence of a time-dependent magnetic field composed of a periodic square wave part plus a time-independent bias term. Using Monte Carlo simulations with a standard Metropolis algorithm, we determine the equilibrium critical behavior in zero field. At a fixed temperature corresponding to the multidroplet regime, we locate the relaxation time and the dynamic critical half period at which a dynamic phase transition takes place between ferromagnetic and paramagnetic states. Benefiting from finite-size scaling theory, we estimate the dynamic critical exponent ratios for the dynamic order parameter and its scaled variance, respectively. The response function of the average energy is found to follow a logarithmic scaling as a function of lattice size. At the critical half period and in the vicinity of a small bias field regime, the average of the dynamic order parameter obeys a scaling relation with a dynamic scaling exponent which is very close to the equilibrium critical isotherm value. Finally, in the slow critical dynamics regime, investigation of metamagnetic fluctuations in the presence of bias field reveals a symmetric double-peak behavior for the scaled variance contours of the dynamic order parameter and average energy. Our results strongly resemble those previously reported for kinetic Ising models.

Disorder effects on the metastability of classical Heisenberg ferromagnets

In the present paper, we investigate the effects of disorder on the reversal time (τ) of classical anisotropic Heisenberg ferromagnets in three dimensions by means of Monte Carlo simulations. Starting from the pure system, our analysis suggests that τ increases with increasing anisotropy strength. On the other hand, for the case of randomly distributed anisotropy, generated from various statistical distributions, a set of results is obtained: (i) For both bimodal and uniform distributions, the variation of τ with the strength of anisotropy strongly depends on temperature. (ii) At lower temperatures, the decrement in τ with increasing width of the distribution is more prominent. (iii) For the case of normally distributed anisotropy, the variation of τ with the width of the distribution is nonmonotonic, featuring a minimum value that decays exponentially with the temperature. Finally, we elaborate on the joint effect of longitudinal (h_{z}) and transverse (h_{x}) fields on τ, which appear to obey a scaling behavior of the form τh_{z}^{n}∼f(h_{x}).

General existence and determination of conjugate fields in dynamically ordered magnetic systems

We investigate experimentally as well as theoretically the dynamic magnetic phase diagram and its associated order parameter Q upon the application of a non-antisymmetric magnetic field sequence composed of a fundamental harmonic component H_{0}, a constant bias field H_{b}, and a second-harmonic component H_{2}. The broken time antisymmetry introduced by the second-harmonic field component H_{2} leads to an effective bias effect that is superimposed onto the influence of the static bias H_{b}. Despite this interference, we can demonstrate the existence of a generalized conjugate field H^{*} for the dynamic order parameter Q, to which both the static bias field and the second-harmonic Fourier amplitude of the field sequence contribute. Hereby, we observed that especially the conventional paramagnetic dynamic phase is very susceptible to the impact of the second-harmonic field component H_{2}, whereas this additional field component leads to only very minor phase-space modifications in the ferromagnetic and anomalous paramagnetic regions. In contrast to prior studies, we also observe that the critical point of the phase transition is shifted upon introducing a second-harmonic field component H_{2}, illustrating that the overall dynamic behavior of such magnetic systems is being driven by the total effective amplitude of the field sequence.

Monte Carlo study of the two-dimensional kinetic Blume-Capel model in a quenched random crystal field

We investigate by means of Monte Carlo simulations the dynamic phase transition of the two-dimensional kinetic Blume-Capel model under a periodically oscillating magnetic field in the presence of a quenched random crystal-field coupling. We analyze the universality principles of this dynamic transition for various values of the crystal-field coupling at the originally second-order regime of the corresponding equilibrium phase diagram of the model. A detailed finite-size scaling analysis indicates that the observed nonequilibrium phase transition belongs to the universality class of the equilibrium Ising ferromagnet with additional logarithmic corrections in the scaling behavior of the heat capacity. Our results are in agreement with earlier works on kinetic Ising models.

Experimental exploration of dynamic phase transitions and associated metamagnetic fluctuations for materials with different Curie temperatures

We study dynamic magnetic behavior in the vicinity of the dynamic phase transition (DPT) for a suitable series of samples that have different Curie temperatures T_{C}, which thus enables us to experimentally explore the role of the reduced temperature T/T_{C} in the DPT. For this purpose, we fabricate Co_{1-x}Ru_{x} epitaxial thin films with uniaxial in-plane anisotropy by means of sputter deposition in the concentration range 0.0≤x≤0.26. All samples are ferromagnetic at room temperature, exhibit an abrupt magnetization reversal along their easy axis, and represent a unique T_{C} and thus T/T_{C} ratio according to their Ru concentration. The dynamic magnetic behavior is measured by using an ultrasensitive transverse magneto-optical detection method and the resulting dynamic states are explored as a function of the applied magnetic field amplitude H_{0} and period P, as well as an additional bias field H_{b}, which is the conjugate field of the dynamic order parameter Q. Our experimental results demonstrate that the qualitative behavior of the dynamic phase diagram is independent of the T/T_{C} ratio and that for all T/T_{C} values we observe metamagnetic anomalies in the dynamic paramagnetic state, which do not exist in the corresponding thermodynamic phase diagram. However, quantitatively, these metamagnetic anomalies are very strongly dependent on the T/T_{C} ratio, leading to an about 20-fold increase of large metamagnetic fluctuations in the paramagnetic regime as the T/T_{C} ratio increases from 0.37 to 0.68. Also, the phase space range in which these anomalous metamagnetic fluctuations occur extends closer and closer to the critical point as T/T_{C} increases.

Dynamic phase transitions in the presence of quenched randomness

We present an extensive study of the effects of quenched disorder on the dynamic phase transitions of kinetic spin models in two dimensions. We undertake a numerical experiment performing Monte Carlo simulations of the square-lattice random-bond Ising and Blume-Capel models under a periodically oscillating magnetic field. For the case of the Blume-Capel model we analyze the universality principles of the dynamic disordered-induced continuous transition at the low-temperature regime of the phase diagram. A detailed finite-size scaling analysis indicates that both nonequilibrium phase transitions belong to the universality class of the corresponding equilibrium random Ising model.

Dynamic phase transition of the Blume-Capel model in an oscillating magnetic field

We employ numerical simulations and finite-size scaling techniques to investigate the properties of the dynamic phase transition that is encountered in the Blume-Capel model subjected to a periodically oscillating magnetic field. We mainly focus on the study of the two-dimensional system for various values of the crystal-field coupling in the second-order transition regime. Our results indicate that the present nonequilibrium phase transition belongs to the universality class of the equilibrium Ising model and allow us to construct a dynamic phase diagram, in analogy with the equilibrium case, at least for the range of parameters considered. Finally, we present some complementary results for the three-dimensional model, where again the obtained estimates for the critical exponents fall into the universality class of the corresponding three-dimensional equilibrium Ising ferromagnet.