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

Abstract

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 ${(H}_{0}),$ in-plane direction, and frequency (\ensuremath{\Omega}) of applied sinusoidal magnetic field. Scaling of the hysteresis loop area (power loss) of the form ${A=A}_{0}{+H}_{0}^{\ensuremath{\alpha}}{\ensuremath{\Omega}}^{\ensuremath{\beta}}\ensuremath{\zeta}(H,\ensuremath{\Omega})$ where \ensuremath{\zeta} is a scaling function is explored. All films exhibit a threshold field ${(H}_{t})$ where switching between equivalent magnetized states is initiated. Hysteresis loop areas measured over five decades in frequency exhibit very weak power-law dependence $(\ensuremath{\beta}\ensuremath{\sim}0.02).$ No evidence of a dynamic phase transition is observed and no indication of a low-frequency $({\ensuremath{\Omega}}_{0}\ensuremath{\sim}{10}^{2}\mathrm{Hz})$ 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 $(\ensuremath{\alpha}=\ensuremath{\beta}=\frac{2}{3})$ and continuum spin models of thin-film hysteresis energy-loss scaling. The measured frequency and applied field-dependent scaling of the dynamic coercive force ${(H}_{c}^{*})$ also appears to be inconsistent with recent phenomenological models of hysteresis behavior based on domain-wall motion that predict that ${H}_{c}^{*}$ scales as $\mathrm{ln}\mathrm{H\ifmmode \dot{}\else \.{}\fi{}}.$ 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 \ensuremath{\Omega} and effective exponents \ensuremath{\beta} 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.