0018-9464 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. 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. Citation information: DOI 10.1109/TMAG.2017.2707127, IEEE Transactions on Magnetics FQ-12 0018-9464 © 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. (Inserted by IEEE.) 1 Micromagnetic Simulations of Magnetization Spatial Distribution in Ultra-Thin Cobalt Layers with Gradient Magnetic Anisotropy M. Kisielewski 1 , J. Kisielewski 1 , I. Sveklo 1 , A.Wawro 2 , and A. Maziewski 1 1 Faculty of Physics, University of Bialystok, K.Ciolkowskiego 1L, 15-245 Bialystok, Poland 2 Institute of Physics, Polish Academy of Sciences, Aleja Lotnikow 32/46, 02-668 Warsaw, Poland Spatial distribution of magnetization in an ultrathin ferromagnetic Co layer with a lateral gradient of magnetic anisotropy, while approaching spin reorientation transition (SRT) (from perpendicular to in-plane magnetization alignment), has been investigated by means of micromagnetic simulations in the two-dimensional mode, using OOMMF software. The geometry of the out-of-plane- magnetized domains (parallel stripes, labyrinth, and bubbles) has been found to be depended on both the initial distribution of magnetization and the direction of the applied magnetic field. A fast decrease of the domain size has been observed, while moving towards SRT. In the experiment, Pt/Co/Pt layers with initial in-plane magnetization orientation have been irreversibly modified by femtosecond laser pulses. In the irradiated spot, rings with induced perpendicular magnetic anisotropy have been formed, resulting in an appearance of several local SRTs. Magnetic domain structure in the SRT regions has been visualized using magnetic force microscopy. The experimental observations are qualitatively explained by the results of the micromagnetic simulations. Index Terms— magnetic domains, micromagnetic simulation, spin reorientation, ultrathin cobalt layer I. INTRODUCTION Engineering of magnetic anisotropy in ultrathin magnetic films, very often associated with an occurrence of the spin reorientation transition (SRT) between in-plane and out-of- plane states, is a challenging task. The SRT depends on many parameters, such as magnetic layer thickness and the structure of both underlayer and overlayer [1]. Domain patterns, close to the SRT, have been observed by different techniques and a drastic change of the domain size has been found [2, 3, 4, 5, 6, 7, 8]. Recently, a large effort has been made to create novel magnetic materials, by e.g. patterning of magnetic layers by either ion bombardment [9, 10] or pulses of electromagnetic irradiation [11, 12, 13, 14], as well as applying an electric field [15, 16]. In the first two cases, an appearance of an irreversible lateral gradient of the magnetic anisotropy was a typical feature. A description of the magnetic ordering, while approaching the SRT, is a challenging task. Micromagnetic simulation is a powerful tool for investigation of magnetic nanostructures and it has been successfully applied for e.g. an explanation of a variety of domain patterns in an ultrathin ferromagnetic layer close to the SRT, in a case when the variable magnetic anisotropy is driven by the variable thickness of the magnetic layer. To describe an equilibrium domain configuration, a quality factor Q is defined as the ratio of uniaxial anisotropy to demagnetization energy. We have found, combining both 1D- numerical simulation and analytical method [17], that the existence of domains and their magnetostatic contribution affects the SRT. The transition between the perpendicular and in-plane magnetization orientations goes through the sinusoidal-like domain structure, which extends below Q=1, down to Q*=0.981, with gradually decreasing amplitude and critical domain period p*150 nm. The aim of the present work is to find a spatial distribution of magnetization in an ultrathin ferromagnetic layer with a lateral gradient of magnetic anisotropy by simulations in the two-dimensional mode. II. MICROMAGNETIC SIMULATIONS Simulations have been performed with the OOMMF software [18]. The simulated sample consisted of a net of cube cells, each of 2×2×2 nm 3 in size (i.e. smaller than the exchange length of cobalt equal to 3.2 nm). A single layer of 2 700 000 cells extended in the xy-plane, forming a cuboid structure 3600×3000×2 nm 3 . A variable magnetic anisotropy, represented by Q, has been attributed to this structure by means of a linearly decreasing function along the x-axis, starting from one of the following four different values of Q at the left side of the sample: Q1=1.020, Q2=1.042, Q3=1.074, and Q4=1.107, and ending with the same value Qe=0.977, at the right side of the sample. Thus, the four cases of the lateral gradient of Q, have been analyzed: 1=0.012µm -1 , 2=0.018 µm -1 ,3=0.027µm -1 , and 4=0.036 µm -1 . The periodic boundary conditions have been switched on merely along the y-direction, avoiding boundary effects. Similarly to our previous simulations for cobalt [1, 17], we took saturation magnetization equal to 1420 kA/m and exchange constant to 1.3×10 −11 J/m. The damping coefficient has been set to 0.2. The calculations were terminated when the maximal absolute magnitude of the time derivative of magnetization across all spins dropped below one degree per nanosecond. The final results are strongly dependent on the assumed initial spatial distribution of magnetization. Two examples are shown in Figs 1 and 2. The initial magnetic domain configuration was stripe-like with a variable periodicity. The periodicity of stripes and the magnitude of the normal