Theoretical analysis of magnetic force microscopy contrast in multidomain states of magnetic superlattices with perpendicular anisotropy

Abstract

Recently synthesized magnetic multilayers with strong perpendicular anisotropy exhibit unique magnetic properties including the formation of specific multidomain states. In particular, antiferromagnetically coupled multilayers own rich phase diagrams that include various multidomain ground states. Analytical equations have been derived for the stray-field components of these multidomain states in perpendicular multilayer systems. In particular, closed expressions for stray fields in the case of ferromagnetic and antiferromagnetic stripes are presented. The theoretical approach provides a basis for the analysis of magnetic force microscopy (MFM) images from this novel class of nanomagnetic systems. Peculiarities of the MFM contrast have been calculated for realistic tip models. [2,3,4,5]. These nanoscale synthetic antiferromagnets are characterized by new types of multidomain states, unusual demagnetization processes and other specific phenomena [2,3,5]. In contrast to other bulk and nanomagnetic systems, the multidomain states in perpendicular antiferromagnetic multilayers are determined by a strong competition between the antiferromagnetic interlayer exchange and magnetostatic couplings [3,6,7]. The remarkable role of stray-field effects in synthetic antiferromagnets and the peculiarities of their multidomain states are currently investigated by high resolution magnetic force microscopy (MFM)(for recent examples of successful experimental tests on domain theory by MFM see, e.g. Refs. [3,8]). From the theoretical side, only few results have been obtained on MFM images in antiferromagnetically coupled multilayers, mostly by numerical methods [2,5,9]. Here we present an analytical approach that provides a comprehensive description of stray-field distributions and MFM images in multidomain states of these nanostructures. We show that the stray-field components and their spatial derivatives, that are crucial for an analysis of MFM contrast, own distinctive features for different multidomain states. These features allow to recognize the particular distribution of the magnetization at the surfaces of domains and in the depth of the multilayers. The quantitative relations from theory for the MFM contrast can also serve to determine the values of magnetic interactions, i.e. materials parameters of an antiferromagnetic multilayer. We apply our results for an analysis of multidomain states observed in [Co/Pt]Ru As a model we consider strong stripes, i.e. so-called band domains in a superlattice composed of N identical layers of thickness h separated by spacers of thickness s, (see, Fig. 1). Note, that the term "stripe domains" is also commonly used to denote multidomain patterns consisting of stripes with weakly undulating magnetization which, however, stays predominantly in the layer plane [10]. On the other hand, the term band domains is used to describe structures of homogeneous domains with perpendicular magnetization that alternates between up and down direction. These two types of stripe domains should

Effect of magnetic field on domain-wall structures in two antiferromagnetically coupled Co∕Pt multilayers

“…4 trast band, which is much wider than the domain-wall width in pure Co/ Pt multilayer, has been shown to be created by the relative shifts of domain walls in top and bottom multilayers owing to the competition between magnetostatic and exchange interactions. [4][5][6][7] In the net FM stripes formed between the relatively shifted domain walls, the moments in the top and bottom multilayers align parallel to each other and give rise to the observed dark contrast bands. The inset of Fig.…”

“…The relative shifts of domain walls originate from the competition between the magnetostatic and exchange interactions between the adjacent FM layers. [4][5][6][7] The relative domain-wall shift d or the net FM stripe width is found to be inversely proportional to the AFM interlayer coupling strength. 5,6 The Co/ Pt multilayer with perpendicular anisotropy is one of the well-established magnetic layered systems used to investigate domain structures in FM films.…”

“…1-3 This expectation has stimulated increasing interests in the crucial roles of exchange and magnetostatic interactions in the domain formation of magnetic multilayers with perpendicular anisotropy. [4][5][6][7] The magnetostatic stray fields prefer the parallel alignment of magnetic domain moments in the separated multilayers, inducing the ferromagnetic ͑FM͒ interlayer coupling. Its competition with the antiferromagnetic ͑AFM͒ interlayer coupling results in interesting domain configurations.…”

Evolution of stripe and bubble domains in antiferromagnetically coupled[(Co/Pt)8/Co/RuBran1, Butenko2, Kiselev3 et al. 2009Phys. Rev. B392190View full textAdd to dashboardCite

“…Stray field calculations in combination with magnetic force microscopy ͑MFM͒ contrast simulations, however, suggest that such domains should be resolvable by high-resolution MFM when they are present. 10 Consequently, the detailed study of domain structure and magnetization processes, and their description by domain theory is an important contribution to quantitatively describe the complex interactions present in these multilayers. In this paper, we study the domain structure and the magnetization processes in a rather thick ͓Co/Pt͔/Ru multilayer, which zero-field state is characterized by the above described FM stripe domains also common for simple single layer films with perpendicular anisotropy.…”

Dependence of domain wall structures on repetition n in [Pt(0.5 nm)/Co(0.4 nm)] n /NiO(1.1 nm)/[Co(0.4 nm)/Pt(0.5 nm)] n multilayers

“…These hypotheses have stimulated the increasing interest in magnetic multilayers with perpendicular anisotropy [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22].…”