Magnetic hysteresis dynamics of thin Co films on Cu(001)

Hysteresis properties of ultrathin (2--4 monolayers) epitaxial Co films grown on Cu(001) surfaces are studied as a function of film thickness, temperature and the strength (H₀), in-plane direction, and frequency ({Ω}) of applied sinusoidal magnetic field. Scaling of the hysteresis loop area (power loss) of the form A=A₀+H₀^αΩ^βζ(H,Ω) where {ζ} is a scaling function is explored. All films exhibit a threshold field (Hₜ) where switching between equivalent magnetized states is initiated. Hysteresis loop areas measured over five decades in frequency exhibit very weak power-law dependence (β~0.02). No evidence of a dynamic phase transition is observed and no indication of a low-frequency (Ω₀~10²Hz) characteristic resonance is apparent over the drive frequency range covered. The observed weak power-law scaling does not support results of prior experiments that have been interpreted as corroborating the mean-field Ising model (α=β=2/3) and continuum spin models of thin-film hysteresis energy-loss scaling. The measured frequency and applied field-dependent scaling of the dynamic coercive force (Hc*) also appears to be inconsistent with recent phenomenological models of hysteresis behavior based on domain-wall motion that predict that Hc* scales as lnH ̇ \.. The results of this study of Co on Cu(001) and a corresponding study of Fe on W(110) suggest that the dynamics of magnetization reversal in real ultrathin film systems do not exhibit universal behavior in the low-field low-frequency limit. Recent theoretical results based on a more realistic model that accounts for thermal noise and spatial fluctuations in the dynamics yield logarithmic scaling at low {Ω} and effective exponents {β} that are compatible with the experiments. A simple physical picture of low drive-frequency energy-loss scaling is described that accounts for the experimental observations.