Dynamics of successive minor hysteresis loops

Abstract

Cumulative growth of successive minor hysteresis loops in Co/Pd multilayers with perpendicular anisotropy was studied in the context of time dependent magnetization reversal dynamics. We show that in disordered ferromagnets, where magnetization reversal involves nucleation, domains' expansion and annihilation, differences between the time dependencies of these processes are responsible for accumulation of nuclei for rapid domain expansion, for the asymmetry of forward and backward magnetization reversals and for the respective cumulative growth of hysteresis loops. Loops stop changing and become macroscopically reproducible when populations of upward and downward nucleation domains balance each other and the respective upward and downward reversal times stabilize. PACS: 75.60.Jk, 75.70.Cn, IntroductionReproducibility of cycling processes under identical external conditions attracts particular attention in studies of magnetic hysteresis for at least two reasons: the effect is fundamental to all magnetic storage technologies, and it can serve as a model for a wide range of type-I phase transitions. Two types of hysteresis loops are distinguished."Major" loops are obtained by sweeping the applied field beyond the saturation field H sat , above which the system is said to be fully saturated and its magnetization M(H) is a single-valued function of the applied field H; "minor" loops are obtained when the cycle is limited to fields near and below H sat . Many studies were devoted to the macroscopic and microscopic repeatability of minor and major hysteresis loops and effects of disorder on cycle-to-cycle memory [1,2]. Macroscopically the major loops repeat themselves in successive cycles, however it was appreciated [3,4] that disorder induces memory in the microscopic magnetic domain configurations from one cycle of the hysteresis loop to the next, even when H sat was crossed. Successive minor loops are usually reasonably reproducible, although changes of size and shape were observed [5][6][7]. Nevertheless these finite perturbations did not undermine a generally accepted view that macroscopic hysteresis loops are repeatable. It came therefore as a surprise when Berger et al. [8] reported major cumulative expansion of successive minor hysteresis loops in Co/Pt and Co/Pd multilayers even up to four times their initial area. The phenomenon was explained in terms of successive accumulation of small nucleation domains, i.e. microscopic areas of reversed magnetization that act as nuclei for the subsequent macroscopic magnetization reversal [8,9]. The reversals at all but the first cycle do not start anew from a fully saturated state but from a preconfigured state in which nuclei for domain expansion are locally conserved. Conservation and accumulation of the nuclei can happen if the system responds asymmetrically in forward and reverse field orientations such that small domains appear to be substantially more stable toward annihilation in an opposite field than toward expansion in a forward field.In this paper we shall de...

Analysis of Magnetic Relaxation With Pre-Existing Nucleation Sites Based on the Fatuzzo–Labrune Model

“…According to the Fatuzzo-Labrune model, the magnetization as a function of time is given by [9]: This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.…”

“…In such PMA films, understanding the relaxation behavior is basically crucial for utilizing the magnetization switching and reversal in a spin-transfer system. In describing the magnetic relaxation behavior of such systems, it has been known that the Fatuzzo-Labrune model [3,4] is well explaining the magnetic relaxation process involved with a thermally activated magnetization reversal in various magnetic thin films [5,6]. However, so far, little has been known for the validity of the Fatuzzo-Labrune model for a relaxation behavior starting not only from the saturated state but also from the partially saturated state with non-reversed preexisting domains.…”

Creeping of minor hysteresis loops in Co thin films

“…4,5,8 That state corresponds to the practically complete magnetic saturation. In view of the spatial non-uniformity (defects of the composition or crystal structure, surface roughness and so on), various regions are remagnetized (after switching the magnetic field) with different characteristic times.…”

“…8 However, in that work the emphasis has been done on studying the magnetization relaxation under fast periodical switching the field direction (instead of observing hysteresis loops.) Herewith, as well as in Refs.…”

Analysis of magnetic relaxation with pre-existing nucleation sites based on the Fatuzzo-Labrune model

“…Full details of the relaxation behavior and subsequent microscopic domain patterns evolving from the pre-existing nucleation sites originated from the sub-structured magnetic domains are discussed. It has been well known that the Fatuzzo-Labrune model is applicable in explaining magnetic relaxation processes involved with a thermally activated magnetization reversal in various magnetic thin films [3,4]. According to the model, the magnetic relaxation is quantied by a reversal parameter k = v/Rr c , where v is the domain wall velocity, R the nucleation rate, and r c the initial domain radius.…”