Hysteresis loop areas in kinetic Ising models : Effects of the switching mechanism

Experiments on ferromagnetic thin films have measured the dependence of the hysteresis loop area on the amplitude and frequency of the external field, A=A(H 0 , ω), and approximate agreement with numerical simulations of Ising models has been reported. Here we present numerical and theoretical calculations of A in the low-frequency regime for two values of H 0 , which bracket a temperature and system-size dependent crossover field. Our previous Monte Carlo studies have shown that the hysteretic response of the kinetic Ising model is qualitatively different for amplitudes above and below this crossover field. Using droplet theory, we derive analytic expressions for the low-frequency asymptotic behavior of the hysteresis loop area. In both field regimes, the loop area exhibits an extremely slow approach to an asymp-totic, logarithmic frequency dependence of the form A ∝ −[ln(H 0 ω)] −1. Our results are relevant to the interpretation of data from experiments and simulations , on the basis of which power-law exponents for the hysteresis-loop area have been reported. 1 When a ferromagnet is subject to an oscillating external field, H(t)=H 0 sin ωt, the time-dependent magnetization, m(t), typically lags behind the field. The area of the resulting hysteresis loop, A=− m(H) dH, equals the energy dissipated per period. It is therefore frequently measured in studies of periodically driven magnetic systems. Recent experiments on ultrathin ferromagnetic films, 1,2 as well as numerical simulations of two-dimensional Ising models, 3–6 have been interpreted in terms of a low-frequency power law, A ∝ H a 0 ω b , with a range of exponent values having been reported. 4–6 This interpretation is not fully consistent with the fluctuation-free mean-field result, 7,8 A = A 0 + const[ω 2 (H 2 0 − H 2 sp)] 1/3 with positive constants A 0 and H sp , which has been successfully applied to analyze experiments on ul-trathin films of Co on Cu(001). 9 Nor does the single power-law dependence agree with the logarithmic dependence expected if thermally activated nucleation is the rate-determining process. 10–12 Here we present analytical and numerical results that indicate a resolution of this puzzling situation. Theoretical arguments and numerical simulations reveal parameter regimes in which, following instantaneous field reversal, a uniaxial single-domain ferromagnet switches to the stable magnetization direction via two distinct mechanisms. This magnetization reversal occurs either by nucleation of a single critical droplet of the stable phase [the single-droplet (SD) regime] …