Stochastic formation of magnetic vortex structures in asymmetric disks triggered by chaotic dynamics

ARTICLE Received 2 Apr 2014 | Accepted 21 Oct 2014 | Published 17 Dec 2014 DOI: 10.1038/ncomms6620 Stochastic formation of magnetic vortex structures in asymmetric disks triggered by chaotic dynamics Mi-Young Im1,2, Ki-Suk Lee3, Andreas Vogel4, Jung-Il Hong2, Guido Meier4,5,6 & Peter Fischer1,7 The non-trivial spin configuration in a magnetic vortex is a prototype for fundamental studies of nanoscale spin behaviour with potential applications in magnetic information technologies. Arrays of magnetic vortices interfacing with perpendicular thin films have recently been proposed as enabler for skyrmionic structures at room temperature, which has opened exciting perspectives on practical applications of skyrmions. An important milestone for achieving not only such skyrmion materials but also general applications of magnetic vortices is a reliable control of vortex structures. However, controlling magnetic processes is hampered by stochastic behaviour, which is associated with thermal fluctuations in general. Here we show that the dynamics in the initial stages of vortex formation on an ultrafast timescale plays a dominating role for the stochastic behaviour observed at steady state. Our results show that the intrinsic stochastic nature of vortex creation can be controlled by adjusting the interdisk distance in asymmetric disk arrays. 1 Center for X-ray Optics, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA. 2 Department of Emerging Materials Science, Daegu Gyeongbuk Institute of Science and Technology, Daegu 711-873, Korea. 3 School of Materials Science and Engineering, KIST-UNIST Ulsan Center for Convergent Materials, Ulsan National Institute of Science and Technology, Ulsan 689-798, Korea. 4 Institut für Angewandte Physik und Zentrum für Mikrostrukturforschung, Universität Hamburg, 20355 Hamburg, Germany. 5 Hamburg Centre for Ultrafast Imaging, University of Hamburg, 22761 Hamburg, Germany. 6 Max-Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg, Germany. 7 Physics Department, University of California, Santa Cruz, California 94056, USA. Correspondence and requests for materials should be addressed to M.-Y.I. (email: ) or to K.-S.L. (email: ). NATURE COMMUNICATIONS | 5:5620 | DOI: 10.1038/ncomms6620 | www.nature.com/naturecommunications & 2014 Macmillan Publishers Limited. All rights reserved. 1 ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms6620 2R = 200 h = 40 nm l rna ld fie (+x r= 500 ) 800 1st 2nd +y +x CCW CW 1.0 0.8 0.6 Majority 0.4 500 Minority CCW 0.0 CW 0.2 CW b 200 Figure 1 | Arrays of asymmetric Py disks with different interdisk distances. Schematic diagram of two neighbouring disks together with raw MTXM images for the arrays consisting of asymmetric disks with a radius of R ¼ 500 nm, a height of h ¼ 40 nm, an asymmetry ratio of r ¼ 0.3R and interdisk distances of d ¼ 200, 500 and 800 nm are shown. 2 d (nm) = 200 800 200 500 800 Interdisk distance, d (nm) R 0.3 te Ex a CCW m 1µ Results Direct observation of magnetic VSs. Figure 1 shows schematically the geometrical parameters for the asymmetric disks as well as raw MTXM images for the set of arrays studied. With a radius of R ¼ 500 nm, a height h ¼ 40 nm and an asymmetry ratio r ¼ 0.3R, the interdisk distance was varied between d ¼ 200, 500 and 800 nm. An external magnetic field was applied parallel to the flat edges of the disks in þ x direction to magnetically saturate the disks. To generate a VS, the disks were fully saturated at a field of þ 1 kOe and then immediately released to zero field without applying any external field in between saturation and remanent states. In Fig. 2a, representative images of in-plane domain structures taken from two successive measurements in the arrays of d ¼ 200, 500 and 800 nm are displayed. Repeated images were recorded at the same area of each array under identical measurement conditions. To enhance magnetic contrast and eliminate non-magnetic background, each image was normalized to a reference image taken at saturation state. As a result CCW 500 d d (nm) 800 formation process, are used to interpret the observed steady-state configurations. Generation probability C ontrolling fluctuations such as Barkhausen noise in ferroand antiferro-magnetic materials require a fundamental understanding of non-deterministic phenomena1–8. As the length scales in nanomagnetism approach fundamental limits such as the exchange lengths, the question arises, whether there is an intrinsic stochastic nature, which ultimately would tremendously affect the performance of high-density magnetic storage devices aiming at faster processing speed. Understanding and controlling stochastic behaviour in nanoscale magnetic systems are thus a topic of paramount interest and numerous studies have been performed, for example, on magnetization reversal of nano-size domains in ultrathin magnetic films5,8,9 and domain wall motion in magnetic nanowires7,10,11. The magnetic vortex is characterized by an in-plane circulating domain structure, the circularity c, which rotates either clockwise (CW, c ¼ þ 1) or counter-clockwise (CCW, c ¼  1) and an out-of-plane magnetization, the polarity p pointing either up (p ¼ þ 1) or down (p ¼  1)12–18. In the context of skyrmions, the magnetic vortex structure (VS) can be described by a topological charge, the skyrmion number of np/2 ¼ ±1/2 with H the winding number of n ¼ [a (f)/2p]dS ¼ þ 1 (refs 19–21). Recently, magnetic VSs combined with perpendicular materials have been proposed to generate skyrmionic materials at room temperature22. This approach would open a route for practical uses of skyrmions23–29, which have so far been hampered by requirements such as specific crystal symmetries and low temperature24,28. A comprehensive investigation of stochasticity in the vortex formation and the clarification of its origin are essential particularly within closely packed arrays of nanodisks for achieving such skymionic structures and also for novel applications of VSs, but they have not been addressed so far. Here we report a systematic experimental and simulation study on the stochastic nature in the formation process of VSs in asymmetrically shaped permalloy (Ni80Fe20, Py) disks. A-priori, one would assume that only one type of circularity in asymmetrically shaped disks would be reliably selected as long as the direction of external fields for saturating and releasing the disks is fixed30–33. However, our results show that the final outcome of circularity depends on minute details of the dynamics in the initial stage of the formation process. We have used fullfield magnetic transmission soft X-ray microscopy (MTXM) at the Advanced Light Source in Berkeley, CA, providing a spatial resolution of better than 25 nm to image the magnetic structures in asymmetric Py disks in their steady state34. The experimental details are described in the Methods section. Mic (...truncated)