Static Properties and Current-Driven Dynamics of Domain Walls in Perpendicular Magnetocrystalline Anisotropy Nanostrips with Rectangular Cross-Section

The current-induced domain wall motion along thin ferromagnetic strips with high perpendicular magnetocrystalline anisotropy is studied by means of full micromagnetic simulations and the extended one-dimensional model, taking into account thermal effects and edge roughness. A slow creep regime, where the motion is controlled by wall pinning and thermal activation, and a flow regime with linear variation of the DW velocity, are observed. In asymmetric stacks, where the Rashba spin-orbit field stabilizes the domain wall against turbulent transformations, the steady linear regime is extended to higher currents, leading to higher velocities than in single-layer or symmetric stacks. The pinning and depinning at and from a local constriction were also studied. The results indicate that engineering pinning sites in these strips provide an efficient pathway to achieve both high stability against thermal fluctuations and low-current depinning avoiding Joule heating. Finally, the current-driven dynamics of a pinned domain wall is examined, and both the direct and the alternating contributions to the induced voltage signal induced are characterized. It was confirmed that the direct contribution to the voltage signal can be linearly enhanced with the number of pinned walls, an observation which could be useful to develop domain-wall-based nano-oscillators.

[1]  A. Hubert,et al.  Magnetic Domains: The Analysis of Magnetic Microstructures , 2014 .

[2]  Guido Meier,et al.  Direct imaging of stochastic domain-wall motion driven by nanosecond current pulses. , 2007, Physical review letters.

[3]  The effect of dry friction on domain wall dynamics: A micromagnetic study , 2012 .

[4]  D. Lacour,et al.  Nanometer scale observation of high efficiency thermally assisted current-driven domain wall depinning. , 2005, Physical review letters.

[5]  Russell P. Cowburn,et al.  Domain wall propagation in magnetic nanowires by spin-polarized current injection , 2003 .

[6]  Oscar Alejos,et al.  Thermal effects in domain wall motion: Micromagnetic simulations and analytical model , 2007 .

[7]  S. Fukami,et al.  Domain Wall Motion Induced by Electric Current in a Perpendicularly Magnetized Co/Ni Nano-Wire , 2009 .

[8]  C. Marrows,et al.  Spin-transfer-torque-assisted domain-wall creep in a Co/Pt multilayer wire. , 2010, Physical review letters.

[9]  B. Diény,et al.  Creep and flow regimes of magnetic domain-wall motion in ultrathin Pt/Co/Pt films with perpendicular anisotropy. , 2007, Physical review letters.

[10]  L. Torres,et al.  Thermal effects on domain wall depinning from a single notch. , 2007, Physical review letters.

[11]  Y Suzuki,et al.  Micromagnetic understanding of current-driven domain wall motion in patterned nanowires , 2005 .

[12]  K. Xia,et al.  An all-metallic logic gate based on current-driven domain wall motion. , 2008, Nature nanotechnology.

[13]  Hyun-Woo Lee,et al.  Current-induced domain wall motion in a nanowire width perpendicular magnetic anisotropy , 2008, 0804.3864.

[14]  L. Berger,et al.  Low‐field magnetoresistance and domain drag in ferromagnets , 1978 .

[15]  L. Torres,et al.  Thermally activated domain wall depinning in thin strips with high perpendicular magnetocrystalline anisotropy , 2009 .

[16]  J. Katine,et al.  Role of pinning in current driven domain wall motion in wires with perpendicular anisotropy , 2008 .

[17]  R. Duine.  Effects of nonadiabaticity on the voltage generated by a moving domain wall , 2009 .

[18]  C. Marrows,et al.  Citation for Published Item , 2022 .

[19]  G. Faini,et al.  Detection of current-induced resonance of geometrically confined domain walls. , 2007, Physical review letters.

[20]  A. Lemaître,et al.  Nonadiabatic spin-transfer torque in (Ga,Mn)As with perpendicular anisotropy , 2009 .

[21]  Luc Thomas,et al.  Dependence of current and field driven depinning of domain walls on their structure and chirality in permalloy nanowires. , 2006, Physical review letters.

[22]  Lars Bocklage,et al.  Direct observation of stochastic domain-wall depinning in magnetic nanowires. , 2009, Physical review letters.

[23]  Y. Nakatani,et al.  Magnetic Domain Wall Oscillator , 2008 .

[24]  Shunsuke Fukami,et al.  Current-Induced Magnetic Domain Wall Motion in Co/Ni Nanowire at Low Temperature , 2011 .

[25]  W Wernsdorfer,et al.  Controlled and reproducible domain wall displacement by current pulses injected into ferromagnetic ring structures. , 2005, Physical review letters.

[26]  A. Fert,et al.  Reversible and irreversible current induced domain wall motion in CoFeB based spin valves stripes , 2007 .

[27]  Bernard Rodmacq,et al.  Current-driven spin torque induced by the Rashba effect in a ferromagnetic metal layer. , 2010, Nature materials.

[28]  L. Buda-Prejbeanu,et al.  Fast current-induced domain-wall motion controlled by the Rashba effect. , 2011, Nature materials.

[29]  Shunsuke Fukami,et al.  Analysis of current-driven domain wall motion from pinning sites in nanostrips with perpendicular magnetic anisotropy , 2008 .

[30]  L. Torres,et al.  Oscillator based on pinned domain walls driven by direct current , 2011 .

[31]  S. Parkin,et al.  Magnetic Domain-Wall Racetrack Memory , 2008, Science.

[32]  Margaret Evans Best,et al.  High K/sub u/ materials approach to 100 Gbits/in/sup 2/ , 2000 .

[33]  S. Zhang,et al.  Localized steady-state domain wall oscillators , 2007, cond-mat/0703105.

[34]  A. MacDonald,et al.  Thermally assisted current-driven domain-wall motion. , 2006, Physical review letters.

[35]  D Petit,et al.  Magnetic Domain-Wall Logic , 2005, Science.

[36]  J. Kwo,et al.  Demonstration of edge roughness effect on the magnetization reversal of spin valve submicron wires , 2010 .

[37]  Wayne M. Saslow,et al.  Spin pumping of current in non-uniform conducting magnets , 2007, NanoScience + Engineering.

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

[39]  Current-induced distortion of a magnetic domain wall , 2003, cond-mat/0301293.

[40]  R. Duine.  Spin pumping by a field-driven domain wall , 2007, 0706.3160.

[41]  Joo-Von Kim,et al.  Influence of magnetic viscosity on domain wall dynamics under spin-polarized currents , 2009, 0907.2867.

[42]  M. Klaui,et al.  Tunable steady-state domain wall oscillator with perpendicular magnetic anisotropy , 2009, 0909.4733.

[43]  E. Martínez,et al.  The stochastic nature of the domain wall motion along high perpendicular anisotropy strips with surface roughness , 2012, Journal of physics. Condensed matter : an Institute of Physics journal.

[44]  G. Tatara,et al.  Theory of current-driven domain wall motion: spin transfer versus momentum transfer. , 2004, Physical review letters.

[45]  H. Ohno,et al.  Domain wall creep in (Ga,Mn)As , 2010 .

[46]  Shunsuke Fukami,et al.  Micromagnetic analysis of current driven domain wall motion in nanostrips with perpendicular magnetic anisotropy , 2008 .

[47]  S. Zhang,et al.  Roles of nonequilibrium conduction electrons on the magnetization dynamics of ferromagnets. , 2004, Physical review letters.

[48]  V. Cros,et al.  Switching the magnetic configuration of a spin valve by current-induced domain wall motion , 2002, cond-mat/0206182.

[49]  M. Mecklenburg,et al.  Electron transport driven by nonequilibrium magnetic textures , 2007, 0710.5193.

[50]  S. Fukami,et al.  Current-Driven Domain Wall Motion in CoCrPt Wires with Perpendicular Magnetic Anisotropy , 2008 .

[51]  L. Berger,et al.  Exchange interaction between ferromagnetic domain wall and electric current in very thin metallic films , 1984 .

[52]  C. Chappert,et al.  Dynamics of magnetization reversal in a mesoscopic wire , 2002 .

[53]  G. Faini,et al.  Nonadiabatic spin transfer torque in high anisotropy magnetic nanowires with narrow domain walls. , 2008, Physical review letters.

[54]  Di Xiao,et al.  Universal electromotive force induced by domain wall motion. , 2009, Physical review letters.

[55]  E. Martínez.  Micromagnetic analysis of the Rashba field on current-induced domain wall propagation , 2012 .

[56]  S. Auffret,et al.  Domain wall spin torquemeter. , 2008, Physical review letters.

[57]  Oscar Alejos,et al.  Resonant domain wall depinning induced by oscillating spin-polarized currents in thin ferromagnetic strips , 2008 .

[58]  Ryu.  Spin motive force and Faraday law for electrons in mesoscopic rings. , 1996, Physical review letters.

[60]  G. Beach,et al.  Enhanced current-induced domain wall motion by tuning perpendicular magnetic anisotropy , 2011 .

[61]  Mathias Kläui,et al.  Current-induced domain wall motion in nanoscale ferromagnetic elements , 2011 .

[62]  P. Levy,et al.  Mechanisms of spin-polarized current-driven magnetization switching. , 2002, Physical review letters.

[63]  W. Brown.  Thermal Fluctuations of a Single‐Domain Particle , 1963 .

[64]  Mario Carpentieri,et al.  Stochastic resonance of a domain wall in a stripe with two pinning sites , 2011 .

[65]  Eric E. Fullerton,et al.  Threshold currents to move domain walls in films with perpendicular anisotropy , 2007 .

[66]  C. Chappert,et al.  Non-adiabatic spin-torques in narrow magnetic domain walls , 2010 .

[67]  H. Ohno,et al.  Current-induced domain wall motion in perpendicularly magnetized CoFeB nanowire , 2011 .

[68]  Stern.  Berry's phase, motive forces, and mesoscopic conductivity. , 1992, Physical review letters.

[69]  S. Maekawa,et al.  Generalization of Faraday's Law to include nonconservative spin forces. , 2007, Physical review letters.

[70]  F. Lázaro,et al.  Langevin-dynamics study of the dynamical properties of small magnetic particles , 1998 .

[71]  G. Beach,et al.  Nonlinear domain-wall velocity enhancement by spin-polarized electric current. , 2006, Physical review letters.

[72]  Geoffrey S. D. Beach,et al.  Current-induced domain wall motion , 2008 .

[73]  Gang Xiong,et al.  Submicrometer Ferromagnetic NOT Gate and Shift Register , 2002, Science.

[74]  Mario Carpentieri,et al.  Domain-wall dynamics driven by short pulses along thin ferromagnetic strips : Micromagnetic simulations and analytical description , 2009 .

[75]  A. Schuhl,et al.  High domain wall velocities induced by current in ultrathin Pt/Co/AlOx wires with perpendicular magnetic anisotropy , 2008, 0812.1515.

[76]  D Bedau,et al.  Temperature dependence of the spin torque effect in current-induced domain wall motion. , 2006, Physical review letters.

[77]  J. Ferré,et al.  Domain wall mobility, stability and Walker breakdown in magnetic nanowires , 2007, cond-mat/0702492.

[78]  Luc Thomas,et al.  Resonant Amplification of Magnetic Domain-Wall Motion by a Train of Current Pulses , 2007, Science.

[79]  D. Eastwood,et al.  Controlling domain wall pinning in planar nanowires by selecting domain wall type and its application in a memory concept , 2008 .

[80]  E. Martínez.  The influence of the Rashba field on the current-induced domain wall dynamics: A full micromagnetic analysis, including surface roughness and thermal effects , 2012 .

[81]  Sam Palmer,et al.  Magnetic domains , 2012, Journal of High Energy Physics.

[82]  Berger.  Possible existence of a Josephson effect in ferromagnets. , 1986, Physical review. B, Condensed matter.

[83]  Aurelien Manchon,et al.  Nonequilibrium intrinsic spin torque in a single nanomagnet , 2008 .

[84]  Shunsuke Fukami,et al.  Control of Domain Wall Position by Electrical Current in Structured Co/Ni Wire with Perpendicular Magnetic Anisotropy , 2008, 0809.0047.

[85]  Luc Thomas,et al.  Current driven domain wall velocities exceeding the spin angular momentum transfer rate in permalloy nanowires. , 2007, Physical review letters.