Study of magnetization dynamics in magnetic nanoscale devices

NATIONAL UNIVERSITY OF SINGAPORE DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING STUDY OF MAGNETIZATION DYNAMICS IN MAGNETIC NANOSCALE DEVICES MAHDI JAMALI A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSPHY 2012 ACKNOWLEDGMENTS I am indebted to many people to support and encourage me during the completion of this dissertation. Foremost, I am heartily thankful to my supervisor, Hyunsoo Yang, whose encouragement, guidance and support from the initial to the final level enabled me to develop an understanding of the subject. His guidance helped me in all the time of research and writing of the dissertation. I could not have imagined having a better advisor and mentor for my PhD study. Besides my advisor, I would like to thank my co-advisor Prof. Thomas Liew Yun Fook and Prof. Charanjit Singh Bhatia their insightful comments. Over and above I would like to thank the academic and research staff of the Spin & Energy, ISML, and NUSNI-NANOCORE laboratories for their support in providing of the experimental facilities. The last but not the least, I am grateful to my parents. Their love for education, knowledge and learning has truly been an inspiration to me. Furthermore, I owe my deepest gratitude to my wife, Mahdieh. I would like to dedicate my dissertation to my wife for her love, patience, encouragement not only in my study journey but also in my life. Lastly, I offer my regards and blessings to all of those who supported me in any respect during the completion of the PhD degree. Abstract Abstract Spintronics (also known as magneto-electronics) is an emerging technology that exploits the intrinsic spin of electrons and its associated magnetic moments, in addition to its fundamental electronic charges. Utilization of the electron’s spins has advantages such as low power consumption, and non-volatility over the conventional electronic devices. Magnetization dynamics in magnetic nanoscale devices has been intensively studied recently due to its potential in memory and logic devices. Two aspects of magnetization dynamics have been investigated in this study such as magnetic domain walls (particle-like objects) and spin waves (wave-like objects). Furthermore, we have explored the effect of current-induced spin transfer torque on the magnetization dynamics where spin angular momentum from conduction electrons transfers to local magnetic moments. The main purpose of this study is in the utilization of the magnetization dynamics for device applications and each chapter of the thesis explores various characteristics of the magnetization dynamics as described below. We discuss the characterization of the domain wall resonant frequency. A resonant frequency is the eigenfrequency of the magnetic domain wall that determines the dynamical behavior of the domain wall. Obtaining information of the domain wall eigenfrequency is useful not only for better understanding of the domain wall dynamics, but also for assisting the domain wall depinning (resonant depinning) and improving the efficiency of the vortex/antivortex wall core switching. We first present our micromagnetic simulations of domain wall resonance frequency and calculate the I Abstract Doring mass of a transverse and vortex wall. The effect of nonadiabatic spin transfer torque on the domain wall resonance frequency and mass has been discussed. Furthermore, we have studied the dynamics of the domain wall in an L-shaped nanowires which is a direct result of the domain wall inertia. We have also discussed our experimental investigation of the domain wall eigenfrequency in an infinity-shaped ferromagnetic nanostructures. The domain wall eigenfrequency has been characterized in both frequency and time domains. Detection of the domain wall nucleation and annihilation has been shown in frequency domain. Furthermore, the effect of different parameters including bias magnetic field, dimension, and excitation amplitude on the resonance frequency has been discussed. We present our experimental characterization of spin waves in both frequency and time domains. The nonreciprocity of the magnetostatic surface wave has been explored and the experimental results have been compared with the micromagnetic simulation results. The origin of the spin waves nonreciprocity and effects of the excitation stripline width as well as the bias field on the nonreciprocity have been discussed. Finally, a new type of the spin logic devices utilizing the nonreciprocity of the spin waves has been proposed. The operation and performance of the device such as speed, power consumption, and non-volatility has been explored. We have explored the interaction between magnetic domain wall, spin waves, and current-induced spin transfer torque. Adiabatic STT modifies spin waves frequency or wavelength, and generates Doppler effect on spin waves, while nonadiabatic spin transfer torque could amplify/attenuate the spin waves amplitude depending on the relative direction between the spin waves wavevector and electron flow. We also study the effect of propagating spin waves on a domain wall. It is found that spin waves can enhance the current induced domain wall velocity in the low current regime where the II Abstract domain wall velocity due to current induced STT is comparable to that of spin waves. We can manipulate this enhancement by changing the excitation amplitude and frequency of spin waves in the same regime. In a magnetic nanowire, usually one type of domain wall is in the minimum energy state, while other walls form metastable walls depending on the width and thickness of the nanowire. The dynamics of the metastable walls have been explained based on the domain wall automotion. In the case of current-induced domain wall motion, the direction of the metastable wall displacement is strongly related to the nonadiabaticity of spin-transfer torque. In a rough nanowire, it is found that the metastable wall could have a finite displacement in a magnetic field or current much below the critical field or current density required to displace a stable wall which make metastable walls very attractive for low power applications. III Table of contents Table of contents Abstract I Table of contents .A Table of figures . C Chapter : Introduction . 1.1 Motivations and objectives 1.2 Magnetic properties of materials 1.3 Magnetization dynamics 1.4 Spin transfer torque dynamics 1.5 Magnetic domain wall 11 1.5.1 Magnetic domain wall equation of motion . 15 1.6 Spin waves . 18 1.7 Micromagnetic behavior of ferromagnetic materials . 22 1.7.1 Micromagnetic simulation 23 1.7.2 Finite difference versus finite element method . 24 1.7.3 Simulation cell size and exchange length . 25 Chapter : Magnetic domain wall resonance frequency and mass . 27 2.1 Introduction 27 2.2 Micromagnetic study of a magnetic domain wall resonance frequency 28 2.2.1 Domain wall equation of motion in semi-ring 30 2.2.2 Domain wall damped oscillation and nonlinear behavior 33 2.2.3 Effect of magnetic field, exchange stiffness, and semi-ring radius 35 2.2.4 Domain wall dynamics in L-shaped nanowire . 39 2.2.5 Effect of nonadiabatic spin transfer torque on the domain wall eigenfrequency 41 2.3 Detection of domain wall eigenfrequency in infinity-shaped magnetic nanostructures . 44 2.3.1 Device fabrication and measurement setup 45 2.3.2 Magnetic domain wall nucleation and MFM imaging . 47 2.3.3 Excitation amplitude effect . 50 2.3.4 Size effect . 52 2.3.5 Effect of magnetic field 52 2.3.6 Time-resolved measurements . 55 2.3.7 Theoretical analysis 57 Chapter : Spin wave nonreciprocal behavior for spin logic devices 61 3.1 Introduction 61 3.2 Electrical characterization of the spin waves . 62 A Table of contents 3.3 Spin wave device fabrication . 64 3.4 Spin wave measurements . 67 3.4.1 Frequency-domain measurements 67 3.4.2 Time-domain measurements . 74 3.5 Surface spin wave nonreciprocal behavior 76 3.6 Spin wave logic based on the surface spin wave nonreciprocal behavior . 79 Chapter 4.1 : Spin wave, spin transfer torque, and domain wall interactions 87 Spin wave and spin transfer torque interactions 87 4.1.1 Current induced spin wave amplification . 88 4.1.2 Current induced spin wave Doppler effect . 92 4.2 Spin wave and domain wall interactions 93 4.2.1 Spin wave and domain wall interaction in the absence of current 96 4.2.2 Spin wave and domain wall interaction in the presence of current 97 4.2.2.1 Spin wave excitation amplitude effect 98 4.2.2.2 Spin wave excitation frequency effect 101 Chapter : Metastable-magnetic domain wall dynamics 108 5.1. Introduction 108 5.2. Simulations . 110 5.3. Metastable wall dynamics in perfect nanowires 111 5.3.1. Spin wave excitation . 111 5.3.2. Domain wall automotion equation 114 5.3.3. Magnetic field excitation 115 5.3.4. Electric current excitation . 117 5.4. Metastable wall dynamics in rough nanowire 120 5.4.1. Periodic roughness 120 5.4.1.1. Magnetic field excitation . 120 5.4.1.2. Electric current excitation .123 5.4.2. Random roughness 128 Chapter : Summary and future work 130 Bibliography . 133 Appendix A . 141 Appendix B . 143 Appendix C . 145 Appendix D . 148 Publications . 150 B Table of figures Table of figures Figure 1.1: Categories of all materials based on their magnetic properties. . Figure 1.3: Directions of different torque terms in precessional motion. . Figure 1.4: STT torque direction relative to the other torque terms. 10 Figure 1.5: The schematics represent a Neel wall and Bloch wall [26]. 12 Figure 1.6: Different magnetic domain wall configurations in nanowires: a transverse wall (a) and a vortex wall (b). . 13 Figure 1.7: Transverse and vortex wall magnetization profiles [26]. . 16 Figure 1.8: The dispersion profiles of different magnetostatic spin waves [52]. . 21 Figure 2.1: (a) A magnetic domain wall generated by applying a magnetic field of Hy =10 kOe and relaxing the system. (b) Displacing the domain wall from the initial position by applying Hx. . 30 Figure 2.2: Time evolution of the domain wall dynamics for Hy =200 Oe . 31 Figure 2.3: Displacement angle () and decomposition of the applied field. A domain wall releasing with Hy is equivalent to that of a pendulum in a gravity field. 32 Figure 2.4: (a) A damped sinusoidal curve fitting of  for Hy =200 Oe simulation data. (b) Domian wall displacement () and tilting angle () profile for Hy = 200 Oe. 33 Figure 2.5: Domain wall transformations due to the Walker breakdown with Hy = 200 Oe. . 34 Figure 2.6: Magnetic domain wall displacement angle (θ) and tilting angle () profiles in the absence and presence of kOe out of the plane magnetic field. 35 Figure 2.7: (a) Displacement angle profile for three different magnetic fields of Hy = 150, 200, and 300 Oe. (b) Oscillation frequency of a domain wall in the different magnetic fields. . 37 Figure 2.8: Displacement angle profile for a vortex wall under a 200 Oe transverse magnetic field. 37 Figure 2.9: (a) Displacement angle profiles for the exchange stiffness constants of A = 10, 14, and 20 pJ/m. (b) Domain wall free oscillation frequency and mass for different exchange stiffness constants. . 38 Figure 2.10: Domain wall displacement angle profile for the different radii of r = 450, 550, and 650 nm 39 Figure 2.11: Time evolution of the domain wall dynamics in a rounded L shape structure. . 40 Figure 2.12: Domain wall real time position in L shape nanowire for an excitation of Hy = 200 Oe upto 1.3 ns. 41 Figure 2.13: Magnetic domain wall frequency response in the presence of an ac current, (a) displacement angle profile in semi-circular nanowire, (b) the tilting angle profile in semi-circular nanowire. . 42 Figure 2.14: The displacement angle profile in a straight nanowire with a notch. . 43 Figure 2.15: A SEM image of the ferromagnetic structure and a schematic representation of the electric circuit used for the measurements of the domain wall resonance frequency. 46 Figure 2.16: (a) Normalized two dimensional trajectories of the antivortex structure for the resonant excitation. (b) The frequency spectrum of the magnetic structure for different values of the perpendicular magnetic field with a μV voltage offset for each data set. . 49 C Table of figures Figure 2.17: (a) MFM image of the magnetic antivortex. (b) Micromagnetic simulations of the magnetization profile after nucleation of the magnetic antivortex. 50 Figure 2.18: (a) Frequency spectrum of the antivortex for different lock-in amplifier output voltages normalized by m with a μV voltage offset for each data set. (b) The frequency spectrum of the antivortex for different values of the signal generator amplitudes on a logarithmic scale . 51 Figure 2.19: (a) The frequency spectrum of the antivortex structure for different device sizes. (b) The resonance frequency versus the device size, D, which is defined in the inset of (b). 52 Figure 2.20: (a) The effect of the in-plane magnetic field in the x-direction on the frequency spectrum with a 12 μV voltage offset for each data set. (b) The frequency response of the new magnetic structure at different magnetic fields in the x-direction. The micromagnetic simulation of the new magnetic structure is shown in the inset of (b). 53 Figure 2.21: Normalized two-dimensional trajectories of the antivortex wall for the impulse excitation. 55 Figure 2.22: The electric circuit configuration for the measurements of transient response. . 56 Figure 2.23: The measured output signal with the corresponding excitation pulse and the curve fitting data. 57 Figure 3.1: The schematic of the device that has been used for spin wave excitation and measurements 63 Figure 3.2: Schematic illustration of the device structure. . 64 Figure 3.3: (a) The optical image and (b) the scanning electron micrograph (SEM) of the device. . 65 Figure 3.4: The spin wave characterization device with 10 μm wide signal striplines. . 66 Figure 3.5: The spin wave characterization device with (a) μm and (b) μm wide ferromagnetic microwires. 67 Figure 3.6: The schematic of the measurement setup for the characterization of the spin waves in the frequency domain. . 68 Figure 3.7: The definition of port & in spin wave characterization. 69 Figure 3.8: The spin wave frequency spectrum of a µm width signal line measured using a vector network analyzer for different magnetic fields of ±135, ±225 and ±300 Oe . 69 Figure 3.9: (a) The time domain simulation of the surface spin waves for an excitation stripline of μm width and a bias field of 200 Oe. The inset shows the magnified view of the spin wave tail. (b) The FFT data of the simulated signal. . 71 Figure 3.10: The spin wave frequency measured for different magnetic fields for excitation amplitude of dBm and a gap of μm. . 72 Figure 3.11: The simulation results of the surface spin waves at different magnetic fields 72 Figure 3.12: The spin wave frequency versus magnetic field with the curve fitting. . 73 Figure 3.13: The schematic of the measurement setup for the characterization of the spin waves in the time-domain. 74 Figure 3.14: (a-c) The time resolved measurements of the surface spin waves for bias magnetic fields of ±60, ±135, and ±200 Oe. For spin wave excitation, an excitation impulse voltage of V and pulse width of about 80 ps has been used. (d-f) The micromagnetic simulation results of the surface spin waves for ±60, ±135, and ±200 Oe bias magnetic fields 75 D Table of figures Figure 3.15: The magnetic field profile generated by a current passing through a stripline. 77 Figure 3.16: The transmission parameters i.e. S12 and S21 measured at different magnetic fields for a stripline width of μm. 78 Figure 3.17: The nonreciprocity factors of surface spin waves measured at different magnetic fields in both frequency and time domains and the corresponding micromagnetic simulation results. 79 Figure 3.18: The schematic of the cross section view (a) and the top view (b) of logic device structure for one input (A) and two complementary outputs (Y and Y ). The device has an easy-axis in the y-direction with an effective field of Hb. The field generated by the input A should be strong enough to switch the magnetization in the reverse direction [H(I) > Hb]. 81 Figure 3.19: The truth table of the logic gate with the corresponding Boolean expression of each output that resembles a NOT gate for the Y output and a PASS gate for the Y port. . 82 Figure 3.20: The schematic of the cross section view (a) and the top view (b) of the device structure for two-input (A and B) logic gate. . 82 Figure 3.21: The truth table of the logic gate and the Boolean expressions implemented by each of the device output port. . 83 Figure 3.22: Implementation of different standard gates using the spin wave logic gates. 83 Figure 3.23: The spin wave reshaping circuits. 84 Figure 4.1: Spin wave propagating along a ferromagnetic nanowire. 88 Figure 4.2: Real time variation of the magnetization at the detection area µm away from the source. 89 Figure 4.3: Real time variation of the magnetization at the detection area for different injection current densities. 90 Figure 4.4: Spin wave propagation profile in a 12 µm nanowire before and after injection of an electric current. . 92 Figure 4.5: Schematic illustration of a magnetic nanowire with a transverse domain wall at 1505 nm from the left edge of the nanowire. 95 Figure 4.6: (a) Domain wall displacements due to spin waves with different field amplitudes. 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Saitoh, Nature Commun. 3, 629 (2012). 140 Appendix A Appendix A set PI [expr {4*atan(1.)}] set MU0 [expr {4*$PI*1e-7}] set Ms 860e3 Specify Oxs_ImageAtlas:atlas1 [subst { xrange {0 2700e-9} yrange {0 700e-9} zrange {0 10e-9} image UL-2.7-0.7.bmp viewplane xy colormap { white nonmagnetic black magnetic } }] Specify Oxs_RectangularMesh:mesh { cellsize {4e-9 4e-9 10e-9} atlas :atlas1 } Specify Oxs_UniformExchange { A 13E-12 } Specify Oxs_ScriptUZeeman { script_args total_time script Pulse_Field } proc Pulse_Field { total_time } { set Hy 15915.9637 if { $total_time < 1.3e-9 } { return [list $Hy 0 0] } return [list 0 0 0] } Specify Oxs_Demag {} Specify Oxs_RungeKuttaEvolve { do_precess gamma_LL 2.21e5 alpha 0.01 method rkf54 } 141 Appendix A Specify Oxs_TimeDriver { stage_count_check evolver Oxs_RungeKuttaEvolve stopping_time {{5e-12 3000} :expand:} mesh :mesh basename data1/SW scalar_output_format "%#.8g" vector_field_output_format {binary 8} Ms {Oxs_AtlasScalarField { atlas :atlas1 values { nonmagnetic magnetic 860E3 } } } m0 { Oxs_FileVectorField { file SW-Oxs_TimeDriver-Magnetization-03-0002436.omf norm atlas :atlas1 } } } Destination archive mmArchive Schedule Oxs_TimeDriver::Magnetization archive stage 142 Appendix B Appendix B set PI [expr {4*atan(1.)}] set MU0 [expr {4*$PI*1e-7}] set Ms 860e3 Specify Oxs_ImageAtlas:atlas1 [subst { xrange {0 1000e-9} yrange {0 700e-9} zrange {0 10e-9} image u1.jpeg viewplane xy colormap { white nonmagnetic black magnetic } }] Specify Oxs_RectangularMesh:mesh { cellsize {4.0e-9 4.0e-9 10e-9} atlas :atlas1 } Specify Oxs_UniformExchange { A 13E-12 } Specify Oxs_Demag {} Specify Oxs_UZeeman:extfield0 [subst { comment {Field values in Tesla; scale to A/m} multiplier [expr {1/$MU0}] Hrange { {0.02 0.0 0.0 0.02 0.0 0.0 1} } }] Specify Oxs_RungeKuttaEvolve { do_precess gamma_LL 2.21e5 alpha 0.01 method rkf54 } Specify Oxs_TimeDriver { stage_count_check evolver Oxs_RungeKuttaEvolve stopping_time {{5e-12 1000} :expand:} mesh :mesh basename data2/SW scalar_output_format "%#.8g" 143 Appendix B vector_field_output_format {binary 8} Ms {Oxs_AtlasScalarField { atlas :atlas1 values { nonmagnetic magnetic 860E3 } } } m0 { Oxs_FileVectorField { file SW-Oxs_TimeDriver-Magnetization-15-0003956.omf norm atlas :atlas1 } } } Destination archive mmArchive Schedule Oxs_TimeDriver::Magnetization archive stage 144 Appendix C Appendix C set set set set set set set set PI [expr {4*atan(1.)}] MU0 [expr {4*$PI*1e-7}] wait 1e-9 risetime 40e-12 falltime 40e-12 pulsewidth 20e-12 W 10e-6 H0 5e-4 proc PulseField { totaltime } { global wait risetime falltime pulsewidth if { $totaltime [...]... them In both cases, two regions with the magnetization in the opposite directions are separated by a transition region (a domain wall) In a Bloch wall, a continuous 180-degree transition of the magnetic moment occurs where magnetizations of the domain wall are normal to the film plane in the middle of the transition In a Neel wall, magnetic moments remain in the plane of the 11 Introduction domain magnetizations... interaction energy, magnetic anisotropy energy and demagnetization energy In order to minimize the total energy of the magnetic structure, the magnetization splits into domains Inside each domain, the magnetizations are aligned in the same direction, whereas two neighboring domains may point into different directions Upon formation of domains, there are transition regions where the magnetization smoothly... spin waves in soft magnetic material like Permalloy using both experimental methods and micromagnetic simulations The surface spin waves have a large group velocity and could be easily excited and detected in ultrathin thin film of the magnetic materials Utilizing the nonreciprocal behavior of the surface spin wave, a new type of the spin wave logic devices have been proposed in chapter 3 employing... becomes spin polarized because of spin-dependent electron scattering processes in magnetic materials 15 Introduction The motion of a magnetic domain wall is connected to the magnetization reversal Figure ‎ 6: Transverse and vortex wall magnetization profiles [26] 1 The spin angular momentum from a polarized current results in the excitation of the dynamics inside a domain wall and the domain wall displacement... the dynamics of the domain wall, and influence of the external excitations on the resonance frequency We further addressed a novel method for displacing of the domain wall using a propagating spin wave which is a promising methods involving no charge carrier during the process in chapter 4 To address the power consumption in the domain wall based devices, a novel idea has been developed in this thesis... parameters of the magnetic domain wall are the width of domain wall and the energy of the domain wall that the system costs during the domain wall nucleation In the material with a large anisotropy energy, usually the energy cost of the domain wall formation is high and the thin film homogeneously tends to saturate into a single domain state Two important types of domain walls are demonstrated in figure... an increase in the angular momentum of the lattice Even if an electric current is not initially spin polarized, it can still exert torque via a spin-dependent scattering process such as spin orbit coupling in a ferromagnetic lattice [26] The current induced spin transfer torque is able to excite magnons and microwave [11], move magnetic domain walls, and reverses the magnetization of free layers in nanoscale. .. current induced spin transfer torque is considered one of the most exciting achievements in contemporary magnetism Depending on the direction of the current, current induced spin transfer torque can increase the effective damping of the magnetic material thereby stiffening the system, or can compensate the dissipative torque in the system, leading to current induced switching of the magnetization or... the direction of one domain to the other one This transition region is called the magnetic domain wall and its formation may increase some other energy term for the magnetic system The study of magnetic domain walls is an attractive topic in magnetic microcopies The domain wall structure is different in the thin film compared to the bulk material and can be changed by patterning of the magnetic materials... dynamics in both cases of the field-induced and current-induced domain wall motions However, the magnetization of the domain wall varies significantly across the width of a nanowire and the domain wall width is not well defined as shown in figure 1.6 The width of the magnetic domain wall (Δ) could be estimated by curve fitting of the domain wall magnetization profile over the one dimensional Bloch . NATIONAL UNIVERSITY OF SINGAPORE DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING STUDY OF MAGNETIZATION DYNAMICS IN MAGNETIC NANOSCALE DEVICES MAHDI JAMALI . displacing of the domain wall using a propagating spin wave which is a promising methods involving no charge carrier during the process in chapter 4. To address the power consumption in the domain. assisting the domain wall depinning (resonant depinning) and improving the efficiency of the vortex/antivortex wall core switching. We first present our micromagnetic simulations of domain wall