Thermal skyrmion diffusion used in a reshuffler device

Magnetic skyrmions in thin films can be efficiently displaced with high speed by using spin-transfer torques1,2 and spin–orbit torques3–5 at low current densities. Although this favourable combination of properties has raised expectations for using skyrmions in devices6,7, only a few publications have studied the thermal effects on the skyrmion dynamics8–10. However, thermally induced skyrmion dynamics can be used for applications11 such as unconventional computing approaches12, as they have been predicted to be useful for probabilistic computing devices13. In our work, we uncover thermal diffusive skyrmion dynamics by a combined experimental and numerical study. We probed the dynamics of magnetic skyrmions in a specially tailored low-pinning multilayer material. The observed thermally excited skyrmion motion dominates the dynamics. Analysing the diffusion as a function of temperature, we found an exponential dependence, which we confirmed by means of numerical simulations. The diffusion of skyrmions was further used in a signal reshuffling device as part of a skyrmion-based probabilistic computing architecture. Owing to its inherent two-dimensional texture, the observation of a diffusive motion of skyrmions in thin-film systems may also yield insights in soft-matter-like characteristics (for example, studies of fluctuation theorems, thermally induced roughening and so on), which thus makes it highly desirable to realize and study thermal effects in experimentally accessible skyrmion systems.Thermal diffusion of skyrmions in a non-flat energy landscape shows exponential temperature dependence and can be used for a reshuffler device with potential application in probabilistic computing.

[1]  A. Rosch,et al.  Capturing of a magnetic skyrmion with a hole , 2014, 1411.2857.

[2]  K. Jaqaman,et al.  Robust single particle tracking in live cell time-lapse sequences , 2008, Nature Methods.

[3]  J. Sinova,et al.  Current-driven periodic domain wall creation in ferromagnetic nanowires , 2016, 1607.03336.

[4]  Johannes Schindelin,et al.  TrackMate: An open and extensible platform for single-particle tracking. , 2017, Methods.

[5]  C. Reichhardt,et al.  Thermal creep and the skyrmion Hall angle in driven skyrmion crystals , 2018, Journal of physics. Condensed matter : an Institute of Physics journal.

[6]  R. Wiesendanger,et al.  Scattering States of Ionized Dopants Probed by Low Temperature Scanning Tunneling Spectroscopy , 1998 .

[7]  A. Saxena,et al.  Fluctuations and noise signatures of driven magnetic skyrmions , 2017, 1704.04272.

[8]  P. Böni,et al.  Spin Transfer Torques in MnSi at Ultralow Current Densities , 2010, Science.

[9]  C. Pfleiderer,et al.  Spontaneous skyrmion ground states in magnetic metals , 2006, Nature.

[10]  Yan Zhou,et al.  Magnetic skyrmion logic gates: conversion, duplication and merging of skyrmions , 2014, Scientific Reports.

[11]  Kang L. Wang,et al.  Direct observation of the skyrmion Hall effect , 2016, Nature Physics.

[12]  Kang L. Wang,et al.  Blowing magnetic skyrmion bubbles , 2015, Science.

[13]  T. Moriya Anisotropic Superexchange Interaction and Weak Ferromagnetism , 1960 .

[14]  H. Mehrer Diffusion in solids : fundamentals, methods, materials, diffusion-controlled processes , 2007 .

[15]  F. Buttner,et al.  Investigation of the Dzyaloshinskii-Moriya interaction and room temperature skyrmions in W/CoFeB/MgO thin films and microwires , 2017, 1706.05987.

[16]  U. Nowak Classical Spin Models , 2007 .

[17]  Jacques Droulez,et al.  Skyrmion Gas Manipulation for Probabilistic Computing , 2017, Physical Review Applied.

[18]  P. Böni,et al.  Skyrmion Lattice in a Chiral Magnet , 2009, Science.

[19]  R. Wiesendanger,et al.  Imaging of domain-inverted gratings in LiNbO3 by electrostatic force microscopy , 1997 .

[20]  K. Khoo,et al.  Tunable room-temperature magnetic skyrmions in Ir/Fe/Co/Pt multilayers. , 2016, Nature materials.

[21]  A. Fert,et al.  Skyrmions on the track. , 2013, Nature nanotechnology.

[22]  Yan Zhou,et al.  Magnetic skyrmion-based synaptic devices , 2016, Nanotechnology.

[23]  U. Nowak,et al.  Skyrmions with Attractive Interactions in an Ultrathin Magnetic Film. , 2016, Physical review letters.

[24]  J. Miltat,et al.  Brownian motion of magnetic domain walls and skyrmions, and their diffusion constants , 2018, Physical Review B.

[25]  N. Nagaosa,et al.  Inertia, diffusion, and dynamics of a driven skyrmion , 2014, 1501.00444.

[26]  S. Eisebitt,et al.  Field-free deterministic ultrafast creation of magnetic skyrmions by spin-orbit torques. , 2017, Nature nanotechnology.

[27]  I. Dzyaloshinsky A thermodynamic theory of “weak” ferromagnetism of antiferromagnetics , 1958 .

[28]  Chemical-specific imaging of multicomponent metal surfaces on the nanometer scale by scanning tunneling spectroscopy , 1996 .

[29]  U. Nowak,et al.  Formation and stability of metastable skyrmionic spin structures with various topologies in an ultrathin film , 2016, 1609.07012.

[30]  R. Wiesendanger,et al.  Simultaneous imaging of the In and As sublattice on InAs(110)-(1×1) with dynamic scanning force microscopy , 1999 .

[31]  J. Zang,et al.  Skyrmions in magnetic multilayers , 2017, 1706.08295.

[32]  M. Stier,et al.  Skyrmion-Anti-Skyrmion Pair Creation by in-Plane Currents. , 2017, Physical Review Letters.

[33]  G. Beach,et al.  Accurate model of the stripe domain phase of perpendicularly magnetized multilayers , 2017 .

[34]  J. Sinova,et al.  Skyrmion production on demand by homogeneous DC currents , 2016, 1610.08313.

[35]  A. Thiele Steady-State Motion of Magnetic Domains , 1973 .

[36]  Y. Tokura,et al.  Skyrmion flow near room temperature in an ultralow current density , 2012, Nature Communications.

[37]  Kang L. Wang,et al.  Room-Temperature Creation and Spin-Orbit Torque Manipulation of Skyrmions in Thin Films with Engineered Asymmetry. , 2016, Nano letters.

[38]  R. Wiesendanger Nanoscale magnetic skyrmions in metallic films and multilayers: a new twist for spintronics , 2016 .

[39]  Time-reversal-breaking topological phases in antiferromagnetic Sr2FeOsO6 films , 2016, 1606.07343.

[40]  C. Marrows,et al.  Role of B diffusion in the interfacial Dzyaloshinskii-Moriya interaction in Ta / Co 20 F e 60 B 20 / MgO nanowires , 2015 .

[41]  Y. Tokura,et al.  Near room-temperature formation of a skyrmion crystal in thin-films of the helimagnet FeGe. , 2011, Nature materials.

[42]  A. Saxena,et al.  Particle model for skyrmions in metallic chiral magnets: Dynamics, pinning, and creep , 2013, 1302.6205.

[43]  Ramdas Kumaresan,et al.  Binary multiplication with PN sequences , 1988, IEEE Trans. Acoust. Speech Signal Process..

[44]  Hans Fangohr,et al.  Skyrmion-skyrmion and skyrmion-edge repulsions in skyrmion-based racetrack memory , 2014, Scientific Reports.

[45]  R. Wiesendanger,et al.  Recent Advances in Spin-Polarized Scanning Tunneling Spectroscopy for Imaging of Magnetic Domains , 1999 .

[46]  Benjamin Krueger,et al.  Observation of room-temperature magnetic skyrmions and their current-driven dynamics in ultrathin metallic ferromagnets. , 2015, Nature materials.

[47]  Roberto E. Troncoso,et al.  Brownian motion of massive skyrmions in magnetic thin films , 2014 .

[48]  R. Wiesendanger,et al.  Micromagnetic properties and magnetization switching of single domain Co dots studied by magnetic force microscopy , 1996 .

[49]  R. Wiesendanger,et al.  Atomic and local electronic structure of Gd thin films studied by STM and STS , 1997 .

[50]  H. Mehrer Diffusion in solids : fundamentals, methods, materials, diffusion-controlled processes , 2007 .

[51]  A. Fert,et al.  Magnetic skyrmions: advances in physics and potential applications , 2017 .

[52]  Hjm Henk Swagten,et al.  Magnetic states in low-pinning high-anisotropy material nanostructures suitable for dynamic imaging , 2013 .

[53]  Yan Zhou,et al.  Skyrmion Domain Wall Collision and Domain Wall-Gated Skyrmion Logic , 2016, 1604.01310.

[54]  Edward L Cussler,et al.  Diffusion: Mass Transfer in Fluid Systems , 1984 .

[55]  T. Nozaki,et al.  Brownian motion of skyrmion bubbles and its control by voltage applications , 2019, Applied Physics Letters.

[56]  A. S. Nunez,et al.  Brownian motion of massive skyrmions in magnetic thin films , 2014, 1408.4861.

[57]  F. Buttner,et al.  Skyrmion Hall effect revealed by direct time-resolved X-ray microscopy , 2016, Nature Physics.

[58]  Ralf Jungmann,et al.  Quantitative analysis of single particle trajectories: mean maximal excursion method. , 2010, Biophysical journal.

[59]  Johannes E. Schindelin,et al.  Fiji: an open-source platform for biological-image analysis , 2012, Nature Methods.

[60]  C. Chien,et al.  Extended Skyrmion phase in epitaxial FeGe(111) thin films. , 2012, Physical review letters.