Analysis of Magnetic Domain Sizes in Ultrathin Ferromagnetic Films

Abstract

Ultrathin magnetic films are considered where the thickness-induced second order phase transition occurs due to surface magnetic anisotropy changes. By increasing the thickness, the easy magnetization axis state passes through the easy cone state (for film thickness t: t 1 < t < t 2 ) into the easy magnetization plane state. The characteristic material length l c (defined as the ratio of the domain wall energy density to the demagnetization energy) was calculated up to thickness t 2 . The exact determination of stripe domain period, p, was proposed, applying the transcendent Lerch functions to the classical Kooy-Enz model. Near t 2 where l c vanishes, the critical period, p c , was also discussed. Considering real sets of material parameters taken for ultrathin cobalt films, it was found that by increasing the thickness, the equilibrium domain period drastically decreases from practically infinity (many kilometers for t = 0.5 nm) into the nanometer scale near t 2 .The changes of magnetic domain sizes with film thickness and especially in the vicinity of the reorientation phase transition (RPT) are still of great and current interest [1][2][3][4]. For both application and theory it is important to understand the physical mechanisms leading to the formation of domain structures and determining the observed variety of their sizes. A sharp decrease in domain sizes was found experimentally in the vicinity of the RPT [3,4] in Co/Au ultrathin wedges. Small domains in the nanometer scale were observed in the reorientation region.Analysis of equilibrium stripe domain structures was based in the present work on calculations of: (i) the domain period considering the classical parameter, called the material length l c = g w /(m 0 M s 2 ), where M s is the saturation magnetization, and g w is the wall energy, and (ii) l c which is dependent on thickness-induced magnetic anisotropy changes.Let us consider a stripe domain structure in an ultrathin film where the easy axis is perpendicular to the surface. Stripe domain period, p, is usually determined minimizing the total surface energy density of the domain structure -the sum of the domain wall and the demagnetization energies E = E w + E m . The domain wall energy density one can easy calculate as E w = m 0 M s 2 l c x/y, where x = t/l c and y = p/l c . More complicated is the demagnetization energy calculation. The structure can be described by the classical Kooy-Enz theory [5,6] giving E m in the form of infinite series which are slowly convergent, especially for the smallest film thickness. This was the reason for making some approximations, e.g. [2]. We propose to perform exact E m calculations using the transcendent Lerch functions. These functions are easily available in typical program

Transformation of magnetic structure in amorphous microwires induced by temperature and high frequency magnetic field

“…In general, the main magnetic parameters that determine the equilibrium domain size and period are the domain wall width d = (A/K) 1/2 and the characteristic length l c = r/4pM S 2 , where r = 4(AK) 1/2 is the domain wall energy surface density and A is the exchange constant. For a wide range of magnetic materials, the characteristic length decreases as temperature increases [32].…”

“…9-11, both the domain size and period decrease when the temperature increases from room temperature up to 470 K, which is a consequence of the decreasing characteristic length. Indeed, the characteristic length is proportional to the square root of the anisotropy constant, which is a monotonically decreasing function of temperature [32]. In turn, the mean domain size and period decreases as the characteristic length decreases.…”

“…12), obeys that of the characteristic length, l c . In turn, the characteristic length depends upon temperature as a function of the quality factor, Q(T) [32], such that l c ðTÞ ¼ 2l ex QðTÞ ð 1Þ…”

Modification of Magnetic Properties of Pt/Co/Pt Films by Ga+ Ion Irradiation: Focused versus Uniform Irradiation

“…Domains size (B) decreases down to few hundreds nanometers (A) while approaching the border between out-of-plane and in-plane magnetization state (SRT region). Submicrometer domain sizes near SRT were theoretically predicted in [40][41][42]. This domains behavior is consistent with the fluence gradient present across the transitional zone between the two regions that involves intermediate fluences belonging to branch 1.…”

Employing soft x-ray resonant magnetic scattering to study domain sizes and anisotropy in Co/Pd multilayers

“…The result is an inverse-thickness dependence of the anisotropy which is expected for a thickness-driven spin reorientation. The results fit very well with data of previous investigations [25][26][27][28]. It has to be emphasized that the resolution of the small-angle scattering allows for the determination of anisotropies within a thickness range of only a few angstroms in the immediate vicinity of the SRT.…”