Richard A. Fry

Preisach-Arrhenius model for thermal aftereffect

Aftereffect - that is, decay of magnetization with time at a fixed holding field - is often linear in log-time for a limited time window. The slope of the decay at the holding field that maximizes the decay rate (normally near the field that maximizes the irreversible susceptibility) is often used as a measurement of the long-term stability of permanent magnet media. This paper demonstrates that this measurement alone does not indicate the stability at other fields. It shows theoretically, using the Preisach-Arrhenius model, and experimentally that for materials in which there is negligible particle interaction and negligible reversible magnetization, the shape of the thermal aftereffect curve is the same as that of the ascending major hysteresis curve. For these criteria, the ratio of the decay coefficient at one field to that at another is the same as the ratio of the susceptibilities at those two fields. The paper also discusses the effect of interaction on the decay process. In general, the full identification of the Preisach parameters is necessary and sufficient to estimate the decay rate.

Preisach modeling of aftereffect in a magneto-optical medium with perpendicular magnetization

Abstract The aftereffect of Co/Pt multilayer films with perpendicular magnetization has been measured with a magneto-optical Kerr effect (MOKE) magnetometer and calculated with a newly developed Preisach model. Compared to materials such as traditional magnetic recording media, Co/Pt multilayer films show a more complete picture of the progression of aftereffect because the magnetization of this material decays from saturation almost all the way to a ground state in a reasonable length of time. The magnetization measurements for times equal to negative and positive infinity are asymptotically horizontal, with a transition region that is linear on a logarithmic time scale. In contrast, typical published aftereffect analyses exhibit only a very small percentage of the total aftereffect that could be observed if time were not a factor in making measurements. A Preisach–Arrhenius model is used to calculate the magnetic aftereffect in the Co/Pt multilayer. Comparisons of the model to experimental results show not only the validity of the model, but also its value in predicting very short-time and long-time aftereffect behavior, and low levels of aftereffect occurring in noisy data, all of which are difficult to observe experimentally.

Kerr imaging of a Co/Pt bimodal magneto-optical medium

Spatially resolved magneto-optical (MO) images of a (0.3 nm Co/1.2 nm Pt)15 multilayer film with perpendicular magnetic anisotropy have been obtained by Kerr microscopy. This material exhibits a major hysteresis loop with two-step magnetization reversal. The MO images display four possible “stable” magnetic states distinguished by four different intensities. This behavior is explained by the presence of two different magnetic phases each which has a stable magnetization state either parallel or antiparallel to the applied field, and which may reverse quasi-independently from one another.

Identification of parameters in multilayer media

Multilayer media are of increasing importance as magneto-optic and perpendicular media. The properties of successive layers evolve as the layers are epitaxially deposited. This complicates both the model for these media and the identification of the model parameters. In this paper, the effect of the variation of the Preisach model parameters is discussed and an identification procedure is outlined. Reentrant-type hysteresis behavior, which is found to be necessary in order to accurately fit both major loop and first-order reversal curves in these multilayer materials, is also considered.

Preisach modeling of a magneto-optical medium with perpendicular magnetization

Magneto-optical Kerr effect measurements on a (0.3 nm Co/0.6 nm Pt)15 multilayer film with perpendicular magnetization showed Kerr rotation hysteresis loops that are very square, but asymmetric: on the descending major loop, while the magnetization decreases rapidly once the applied field approaches the coercive field, there is a long tail as saturation is approached. Modeling of this behavior was performed using a Preisach-based approach. To account for the known changes in magnetization behavior as a function of the number of bilayers, the Preisach density function was replaced by the sum of as many Gaussian distributions as there were bilayers in the material. The parameters of these Gaussian functions were systematically varied. The resulting model shows a good fit to both the experimental major loop and a first-order reversal curve.

Magneto-optical behavior in Co/Pt ultrathin film multilayers

Magneto-optical Kerr effect measurements performed on (0.3 nm Co/x Pt)15 multilayers with x=0.3–2.0 nm showed all samples to exhibit strong perpendicular magnetic anisotropy. Recent work has shown that for compositions near (0.3 nm Co/1.2 nm Pt)15, both polar Kerr rotation and ellipticity exhibit bimodal reversals in which the major hysteresis loops have two distinct field-dependent steps due to the contributions of two magnetic phases. To better understand this bimodal magnetization phenomenon, Kerr rotation and ellipticity were determined as a function of radial position from the center to the edge of this disk sample. These measurements exhibit a continuous variation from two-step (bimodal) behavior in the center to single-step (unimodal) behavior at the edge. Since these films were deposited via MBE with a heated substrate, it is believed that this phenomenon is related to thermally induced variations in interface effects such as alloying, abruptness, and morphology.

Magnetic aftereffect in a bimodal Co/Pt magneto-optical medium

Magneto-optical Kerr effect measurements were used to perform magnetic aftereffect studies of the reversal behavior in a bimodal magneto-optical medium with perpendicular magnetic anisotropy. This (0.3 nm Co/1.2 nm Pt)15 multilayer film has shown both the Kerr rotation (θK) and ellipticity (eK) to exhibit major hysteresis loops with two distinct field-dependent steps. However, whereas both steps in the θK loop occur in the same direction, in the eK loop they occur in opposite directions. Thus, upon traversing the descending major loop, at the first magnetic reversal, eK increases even though the magnetization decreases. Magnetic aftereffect in this material was investigated in the vicinity of each magnetization step by measuring both θK and eK over time. The data clearly show the time dependence of each of the two separate reversals, including the changes in eK which occur in opposite directions.

Numerical Simulation of the Aftereffect of a Co/Pt Bimodal Magneto-Optical Medium

Moving version of the Preisach–Arrhenius (PA) model function is used to simulate aftereffect in bimodal Co/Pt multilayers. The Co/Pt multilayers are assumed to have two kinds of magnetic phases, each characterized by its own magnetic properties. The Co/Pt bimodal major loop is the sum of the conventional (unimodal) loops of each of the two constituent phases. The aftereffect of each of these loops is calculated separately using its own parameters obtained from the major loop. The individual models are then combined into a single bimodal aftereffect model.

Reversal behavior in a bimodal magneto-optical medium

Bimodal magnetic behavior, in which Kerr rotation (θK) and ellipticity (eK) each exhibit major magneto-optic hysteresis loops with two distinct field-dependent steps, was encountered in a (0.3 nm Co/1.2 nm Pt)15 multilayer film with perpendicular magnetization. A model is postulated in which there are two different interacting magnetic entities present in the layered structure of this material, each with a stable perpendicular magnetization state either parallel or antiparallel to the applied field, and which reverse quasi-independently from one another. Due to interactions between the two, the reversals occur at the intrinsic coercivities displaced by an interaction field, Hi, whose sign depends upon the magnetization of the other phase. Using major loop and first-order reversal measurements, the intrinsic coercivities, as well as Hi, were obtained.

The Preisach-Arrhenius model for aftereffect

Summary form only given. In the presence of large energy barriers, the magnetization decays very slowly towards its ground state. In most permanent magnetic materials this decay is immeasurable in zero field. In order to estimate the useful lifetime of a magnetic material, this decay is accelerated by applying a reverse field, that we call the holding field, that is approximately equal to the remanent coercivity. Unfortunately, unless we know how much we have accelerated the decay rate, this does not tell us anything about how long it will be useful at other fields. It is necessary to have a model built on physical principles that can address this issue. The Preisach-Arrhenius (PA) model is just such a model. Some of the predictions of this model have been verified experimentally. In particular, the shift in log-time of the after effect curve by an applied field and the shape of the after effect curve in bimodal media. In this paper we discuss the experimental verification of the correct location of the peak in the decay coefficient, and the shape of the after effect curve for multilayer media. We also discuss how to compute the expected lifetime of a recording. The magnetization of the ground state is the same as the magnetization achieved after an anhysteretic magnetizing process. However, the anhysteretic magnetic state differs from the true ground state where the populations of energy levels obey Maxwell-Boltzmann statistics in the ground state. As the material relaxes to the true ground state its magnetization does not change since for a given time constant there are as many negative hysterons changing to a positive state as there are positive hysterons changing to the negative state. Thus, this difference in states is difficult to detect and may be only of academic interest. Had we started from positive saturation, then applied field equal to the negative coercivity and finally reduced the field to zero, then the after effect would have started from zero magnetization, risen to a positive magnetization and then finally returned to zero. Although in this case, the same number of hysterons would have to change from positive magnetization to negative as the other way around, this time they do so with different time constants. The time required for the magnetization to start decreasing to zero is so long that we have not been able to observe this. However, this effect has been observed in nonzero holding fields.