Hysteresis properties of ultrathin (1.5 -4 monolayer) epitaxial Fe films grown on flat and stepped W(110) surfaces are studied as a function of film thickness, temperature, and the strength and frequency of the applied sinusoidal magnetic field. Power law scaling of the hysteresis loop area is observed over five decades in frequency. Measured exponents depart significantly from those reported based on prior experiments and existing theoretical models. An abrupt transition from switching behavior to a stable magnetic state is observed at a critical frequency where the dynamic coercivity exceeds the applied field strength. [S0031-9007(97)03008-1] PACS numbers: 75.60. Ej, 75.40.Gb, 75.70.Ak The dynamics of magnetization reversal has recently attracted considerable scientific interest based on new opportunities to explore concepts of universality and scaling [1][2][3][4][5][6][7][8][9][10][11][12]. Theoretical efforts have explored hysteresis phenomena in model magnetic systems based on a variety of approaches [1][2][3][4][5][6][7][8][9][10]. A general objective of these efforts has been to discover scale-invariant descriptions of the energy loss per cycle (area of the hysteresis loop) as a function of external parameters (applied magnetic field strength H, frequency V, and temperature T ) and intrinsic system parameters (dimensionality and symmetry, i.e., magnetic anisotropy). For example, in the low frequency limit, invariant functions of the hysteresis loop area have been shown to reduce to a power law function of the form(1) where a, b, and g are exponents that depend on the dimensionality and symmetry of the system. Two basic types of dynamical models have been explored theoretically: Ising-like models [4][5][6]9] in which an energy barrier separates the two equivalent magnetized states, and continuous spin models [1][2][3][4]7,8] having no barrier. Specific values of the exponents in Eq. (1) for various models are summarized in Table I with corresponding references to the literature.Dynamical properties of magnetization reversal have also been investigated experimentally in ultrathin film systems [11][12][13][14]. These systems offer unique opportunities to explore dynamical effects in well-characterized structures in which relevant intrinsic parameters (dimensionality, anisotropy) can be controlled. Studies of Fe on Au(001) [11] and Co on Cu(001) [12] have apparently revealed dynamical scaling effects corroborating general theoretical predictions based on the continuous spin and Ising-like models: power law scaling of the loop area (exponents in Table I); constant loop area characteristic of adiabatic magnetization reversal at very low frequencies [12]; and threshold field effects associated with a doublewell barrier in Ising-type models.In this Letter, we report hysteresis loop measurements of well-characterized ultrathin Fe films grown on flat and stepped W(110) surfaces as a function of H, V, and T. Our results are consistent with universal behavior (thickness invariant exponents) and clearly exhibit uni...

Hysteresis properties of ultrathin ͑2-4 monolayers͒ epitaxial Co films grown on Cu͑001͒ surfaces are studied as a function of film thickness, temperature and the strength (H 0), in-plane direction, and frequency ͑⍀͒ of applied sinusoidal magnetic field. Scaling of the hysteresis loop area ͑power loss͒ of the form AϭA 0 ϩH 0 ␣ ⍀ ␤ (H,⍀) where 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 (␤ϳ0.02). No evidence of a dynamic phase transition is observed and no indication of a low-frequency (⍀ 0 ϳ10 2 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 (␣ϭ␤ϭ 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 ln Ḣ. The results of this study of Co on Cu͑001͒ and a corresponding study of Fe on W͑110͒ 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 ⍀ and effective exponents ␤ 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. ͓S0163-1829͑99͒03505-5͔

No abstract