Fractal analysis of time‐resolved magnetic domain patterns in Co/Pd multilayer with varying number of repeats

Abstract

We investigate the fractal behavior of magnetic domain together with analysis of dynamic reversal behavior in Co/Pd multilayer films prepared with different number of repeats n. We utilize a novel magnetooptical microscope magnetometer technique to visualize the time-resolved domain evolution patterns in these films. Quantitative analysis of the time-resolved domain evolution patterns allows us to determine the fractal dimension D f and the reversal ratio V/R depending on n, where V/R represents the counterbalance between the wall-motion speed V and the nucleation rate R. As n increases, domain shape becomes more ragged and complex and thus, D f increases. Interestingly enough, the change in D f clearly seems to be coupled to the change in V/R with varying n, which implies that the correlation between D f and V/R is mediated via the distributed defects.1 Introduction Understanding the shape of magnetic domain and domain dynamics during magnetization reversal in ferromagnetic nanothin films continues to be an intriguing issue in magnetism, greatly motivated by recent technological interest for upcoming magnetoelectric technology such as spintronics and quantum computing as well as for ultrahigh density magnetic and magneto-optical recording [1,2]. To meet the technological interest, it is so vital to understand domain properties, since the magnetic information is stored and controlled via the formation and the reversal of the domain. The size, irregularity, and stability of the written domain will affect the performance of the real magnetic devices. Recently, it has been reported that the detailed shape and the reversal behavior of the magnetic domain is closely correlated with varying the Co sublayer thickness in Co/Pd multilayers [3], where the fractal dimension D f characterizing the shape of the domain has been found to be inversely related to the reversal parameter V/R representing the counterbalance between the wall-motion speed V and the nucleation rate R of magnetic domain [4]. However, systematic investigation on the correlation between the shape and the reversal behavior of magnetic domain in the real ferromagnetic films are still lacking.Domain properties in the real films cannot be fully explained without considering the defect distributed in the film. Numerous efforts have been devoted to correlate the defect to the domain properties. It has been known that distributed defect may leads the motion of domain wall to be glassy creeping dominated by defect [5] or to be propagating with a deroughened shape competing with defect [6]. In this sense, it is not surprising to notice that there have been wide varieties of results reporting different and, in some cases, controversial domain properties depending on detailed fabrication conditions even among similar samples [7 -10]. Recently, domain dynamics has been investigated based on thermally activated

Morphogenesis of maze-like magnetic domains

“…39 Fractal nature of magnetic domains and domain walls has previously been studied both experimentally and theoretically. [16][17][18]36,[40][41][42][43][44][45][46][47][48][49][50] In particular, fractal or hierarchical nature of walls has been predicted to dominate magnetostrictive materials based on minimization of energy density. 46 Using a ruler method, it has been shown that the fractal dimension D in Tb-Fe films increases with an increase in temperature up to the Curie point.…”

Fractal Dimension of Magnetic Domain Walls in CoFe/Pt Multilayers

“…Magnetization reversal in ferromagnetic films with perpendicular magnetic anisotropy occurs by several distinct mechanisms − the wall-motion from existing domains and the nucleation of domains at random positions − depending on the film structure and composition as well as the fabrication conditions [4][5][6][7]. To understand these reversal processes with magnetic properties, many theoretical models, such as the random-field Ising model, the random-bond Ising model [8], the thermally activated relaxation model [9][10][11], and so on, have been proposed and tested. In these models, randomness plays a crucial role.…”

“…From a theoretical point of view, the magnetization reversal occurs through randomly distributed defects in amorphous or poly-crystallized materials and, consequently, such nonlinear stochastic effects result in the fractal nature of the magnetic domain patterns [12]. Many studies have examined the fractal properties of the magnetic domains [9][10][11][12][13][14] and domain walls [9,12]. The fractal dimension provides a unique characterization parameter for domain interface formation in accordance with non-uniformity.…”