Kinetic Ising model in an oscillating field: Avrami theory for the hysteretic response and finite-size scaling for the dynamic phase transition

Abstract

Hysteresis is studied for a two-dimensional, spin-1/2, nearest-neighbor, kinetic Ising ferromagnet in a sinusoidally oscillating field, using Monte Carlo simulations and analytical theory. Attention is focused on large systems and moderately strong field amplitudes at a temperature below Tc. In this parameter regime, the magnetization switches through random nucleation and subsequent growth of many droplets of spins aligned with the applied field. Using a time-dependent extension of the Kolmogorov-Johnson-Mehl-Avrami (KJMA) theory of metastable decay, we analyze the statistical properties of the hysteresis-loop area and the correlation between the magnetization and the field. This analysis enables us to accurately predict the results of extensive Monte Carlo simulations. The average loop area exhibits an extremely slow approach to an asymptotic, logarithmic dependence on the product of the amplitude and the field frequency. This may explain the inconsistent exponent estimates reported in previous attempts to fit experimental and numerical data for the low-frequency behavior of this quantity to a power law. At higher frequencies we observe a dynamic phase transition. Applying standard finite-size scaling techniques from the theory of second-order equilibrium phase transitions to this nonequilibrium transition, we obtain estimates for the transition frequency and the critical exponents (β/ν ≈ 0.11, γ/ν ≈ 1.84 and ν ≈ 1.1). In addition to their significance for the interpretation of recent experiments on switching in ferromagnetic and ferroelectric nanoparticles and thin films, our results provide evidence for the relevance of universality and finite-size scaling to dynamic phase transitions in spatially extended nonstationary systems. PACS number(s): 05.40.+j, 77.80.Dj, 64.60.Qb

Conjugate field and fluctuation-dissipation relation for the dynamic phase transition in the two-dimensional kinetic Ising model

“…[9,10,23]. We have established two distinct but related results about the field conjugate to the dynamic order parameter.…”

“…The square-wave form not only allows for more efficient KMC simulation, but also reduces the critical period and the finite-size effects for the DPT [23]. Other symmetric field shapes, such as sinusoidal [9,10] and sawtooth [34], yield essentially the same results, but with a larger critical period and with stronger finite-size effects. The Glauber single-spin-flip MC algorithm with updates at randomly chosen sites is used, in which each attempted spin flip is accepted with probability…”

“…It was then studied further, both in mean-field models [3,4,5,6] and in kinetic Monte Carlo (KMC) simulations [5,6,7,8,9,10]. A review of this early work can be found in Ref.…”

Modeling the role of oxygen vacancy on ferroelectric properties in thin films

“…The conclusion with regard to these effects has been well established both experimentally and theoretically. 10,24 Generally speaking, both the loop area and the coercive field are increased by either the amplitude or frequency, or both. Conversely, both of them are reduced by increasing the temperature as the ''hardness'' of the ferroelectricity is reduced by thermal energy.…”

Hysteresis loop area of the Ising model

“…Some illustrations of the resonance at peak I can be found in, e.g., Ref. [11,9]. In the following we focus on peak II, as 1 An exception is that, in the MF Ising model, with temperature T above Tc = 1, and H0 very small, it is analytically obtained…”