Domain Wall Oscillations Research Articles

Experimental Study and Numerical Modelling of Magnetic Domain Walls Drift in Ferrite Garnet Crystals

The results of study of domain walls oscillations in harmonic magnetic field H = H0sin (2πft) oriented perpendicular to ferrite garnet (TbErGd)3(FeAl)5O12 (111) sample plate for amplitudes that include the drift of domain walls are reported. Numerical modelling of domain walls motion was performed for frequencies f~102 Hz, where the drift is observed experimentally. Comparison of results of numerical modelling with experimental results shows their qualitative agreement. It was established that domain walls oscillations amplitude is a linear function of amplitude of oscillating magnetic field.

Correlation between spin structure oscillations and domain wall velocities

Magnetic sensing and logic devices based on the motion of magnetic domain walls rely on the precise and deterministic control of the position and the velocity of individual magnetic domain walls in curved nanowires. Varying domain wall velocities have been predicted to result from intrinsic effects such as oscillating domain wall spin structure transformations and extrinsic pinning due to imperfections. Here we use direct dynamic imaging of the nanoscale spin structure that allows us for the first time to directly check these predictions. We find a new regime of oscillating domain wall motion even below the Walker breakdown correlated with periodic spin structure changes. We show that the extrinsic pinning from imperfections in the nanowire only affects slow domain walls and we identify the magnetostatic energy, which scales with the domain wall velocity, as the energy reservoir for the domain wall to overcome the local pinning potential landscape.

Observation of current-driven oscillatory domain wall motion in Ni80Fe20/Co bilayer nanowire

Direct observation of current-driven oscillatory domain wall motion above the Walker breakdown by x-ray magnetic circular dichroism in photoemission electron microscopy is reported in Ni80Fe20/Co nanowire, showing micrometer-scale displacement at ∼13 MHz. We identify two key factors that enhance the oscillatory motion: (i) increase of the hard-axis magnetic anisotropy field value |H⊥| and (ii) increase of the ratio between non-adiabatic spin-transfer parameter to the Gilbert damping coefficient, β/α, which is required to be larger than 1. These findings point to an important route to tune the long-scale oscillatory domain wall motion using appropriate geometry and materials.

Dynamic Oscillations of Coupled Domain Walls

In domain wall (DW) excitation experiments, nonlinearity (NL) intrinsic to the DW dynamics is often hard to distinguish from perturbation due to the confining potential or DW distortion. Here we numerically investigate the dynamic oscillations of magnetostatically coupled DWs: a system well understood in the quasistatic limit. NL is observed, even for a harmonic potential, due to the intrinsic DW motion. This behavior is principally dependent on terms normally associated with the DW canonical momentum and is in contrast with a NL restoring potential. This NL is not observable in quasistatic measurements, relatively insensitive to the confining potential, and may be tuned by the nanowire parameters. The shown NLs are present in any DW restoring potential and must be accounted for when probing DW potential landscapes.

Towards precise measurement of oscillatory domain wall by ferromagnetic Josephson junction

We theoretically propose a principle for precise measurement of oscillatory domain wall (DW) by a ferromagnetic Josephson junction, which is composed of a ferromagnetic wire with DW and two superconducting electrodes. The current-voltage curve exhibits stepwise structures, only when DW oscillates in the ferromagnetic wire. The voltage step appears at V=n(ℏ/2e)ωDW with the fundamental constant ℏ/e, integer number n, and the DW frequency ωDW. Since V can be determined in the order of 10−9 accuracy, the oscillatory DW will be measured more precisely than present status by conventional method.

Effect of Ni concentration on electromagnetic wave absorption of (Ni,Mn,Zn)Fe2O4/resin particulate composites

This research aimed to investigate the effect of the Ni-concentration on the modulated crystallographic structure, constitutive electromagnetic properties, and microwave-absorbing behaviors of the MnZn ferrites. Substitution of Ni for Mn induced compressive strains in cubic spinel due to the smaller Ni than Mn. The activation energy of hopping carriers was determined from the plot of resistivity vs temperature. The conduction was considered to be small-polaron hopping among the spinel lattice which was distorted by Ni substitution. The ferrimagnetic properties of Ni0.5xMn0.5−0.5xZn0.5Fe2O4 ferrites were improved with the increasing Ni concentration. The ferrite with x=1 had the lowest intrinsic coercivity (Hc=7.4Oe) and the highest saturation magnetization (Ms=68.9emu/g). The increase of the saturation magnetization with the Ni substitution (x>0.24) is ascribed to the dense microstructure with less pores and the decrease of Fe2+/Fe3+ ratio. Additionally, a multilayer design of microwave-absorbing structure containing Ni0.5xMn0.5−0.5xZn0.5Fe2O4 granules distributing in a contiguous polymeric matrix was also investigated. The constitutive electromagnetic properties of the composite such as relative permeability and relative permittivity within the whole frequency range were characterized by a combined transmission/reflection method using a coaxial airline fixture. The frequency responses to the electromagnetic field of the ferrite–polymer composites are ascribed to macroscopic magnetic loss and dielectric loss in association with domain-wall oscillation, spin relaxation, and dipolar polarizations. In additions, the microwave-absorbing behaviors of the ferrite–polymer composites were determined using the constitutive electromagnetic properties. The maximum return loss was estimated as −32dB occurring at 2.3GHz for 6mm-thick composite for the composite with x=0.24. For composites with ferrites containing high Ni concentration, the broadening of absorption bandwidth reduced the products of matching thickness and frequency which consequently reduced the required thickness of the microwave absorber. The substitution of Ni for Mn in MnZn ferrites is beneficial in fabricating thin microwave absorbers in GHz frequency range due to the improved electromagnetic lossy characteristics.

Domain structure and magnetic pinning in ferromagnetic/superconducting hybrids

Magnetic patterns in three iron-garnet films with different magnetic properties covered with 100-nm superconducting Nb film are studied using a magneto-optical imaging technique. In all samples the strong coupling between ferromagnetic domains and vortices noticeably modifies the magnetization process. However, depending on the type and width of the magnetic domains, we observe different flux dynamics in the Nb film. Wide domains give rise to a combined domain structure and type I-like superconducting response resulting in enhanced attenuation of the flux motion due to cooperative pinning of vortices and magnetic domain walls. These combined domains strongly shrink in the ac fields due to a dynamic instability triggered by oscillating domain walls. Combined domains formed on narrow magnetic domains do not shrink but they guide the motion of vortices and, in turn, align in the vortex motion direction. This introduces superconducting current anisotropy due to strong pinning on the magnetic domain walls. Irregular magnetic domain structures with immobilized domain walls stochastically modify the vortex entry patterns. The presence of magnetic domains essentially arrests thermomagnetic avalanches in the superconducting layer. The studied magnetic pinning has a good potential for slowing down vortices in high-Tc superconductors.

Magnetization reversal in magnetic nanostripes via Bloch wall formation

We present results of micromagnetic simulations of the magnetization reversal in permalloy nanostripes with 5–10 nm thickness and 200–500 nm width under a longitudinal field of 0.4–16 kA m−1. The data show four distinct field regions: the well-known regions of uniform and oscillating domain wall movement as well as a process with multiple vortices, and finally a new process including Bloch walls and the generation of vortex–antivortex pairs in the inner part of the stripe rather than at the edges. We investigate this process in detail and derive a criterion for the formation of Bloch walls.

Magnetic Domain Wall Oscillator With Current-Perpendicular-to-Plane Geometry

By means of analytical 1-D model and full micromagnetic simulation, we investigated the magnetic domain wall (DW) oscillator with current-perpendicular-to-plane geometry. We found that the DW oscillation frequency linearly increases with the applying current density, but drops above a certain threshold. This frequency drop is caused by the deformation of DW due to spin-transfer torque. We found that by applying an external perpendicular magnetic field in addition to the current, this deformation and the frequency drop can be suppressed, which allows obtaining a reliable frequency range for the device application.

Oscillator based on pinned domain walls driven by direct current

The dynamics of a pinned domain wall in a thin ferromagnetic strip with high perpendicular magnetocrystalline anisotropy was examined by means of micromagnetic simulations. A preliminary analysis was carried out to describe both the cross-section dependence of the equilibrium states and the field-driven motion of a domain wall along perfect strips. Next, localized domain wall oscillations under application of direct currents in a strip with a notch were studied. This dynamical regime, and both the direct and the alternating contributions to the voltage signal induced by the pinned domain wall oscillations, were micromagnetically analyzed. Finally, a strip with several pinned domain walls was considered. Our analysis reveals that the direct contribution to the voltage signal can be linearly enhanced with the number of walls, an observation which could be useful to develop domain-wall-based nano-oscillators.

Critical current density of domain wall oscillation due to spin-transfer torque

The domain wall oscillation due to spin-transfer torque was studied by numerically solving the Landau-Lifshitz-Gilbert (LLG) equation. For a domain wall whose rotation angle θmax is less than 180°, we found the existence of the critical current density above which the magnetization dynamics are induced. We studied the dependence of the critical current density on the rotation angle θmax and found that the critical current density is proportional to 180° – θmax.

Tunable magnetic domain wall oscillator at an anisotropy boundary

We propose a magnetic domain wall (DW) oscillator scheme, in which a low dc current excites gigahertz angular precession of a DW at a fixed position. The scheme consists of a DW pinned at a magnetic anisotropy step in a perpendicularly magnetized nanostrip. The frequency is tuned by the current flowing through the strip. A perpendicular external field tunes the critical current density needed for precession, providing great experimental flexibility. We investigate this system using a simple one-dimensional model and full micromagnetic calculations. This oscillating nanomagnet is relatively easy to fabricate and could find application in future nanoscale microwave sources.

Autoresonance Excitation of Nonlinear Oscillations of Magnetization and Domain Walls in Ferromagnets

We investigate the conditions of capturing into resonance and exciting nonlinear ferromagnetic resonance in a ferromagnetic film with the anisotropic easy plane, as well as autoresonance excitation of nonlinear oscillations of the domain wall in uniaxial ferromagnets. The investigations demonstrate that in easy-plane ferromagnets with a narrow resonance line nonlinear oscillations of magnetization in the autoresonance mode can be generated. This autoresonance takes place if the resonance field grows slowly and pumping frequency is the constant which is equal to the frequency of linear resonance. It has been established that effectively exciting nonlinear oscillations of the domain wall in uniaxial ferromagnets and controlling the wall dynamics by low-amplitude alternating fields with the slow variation of the planar field in the autophasing mode are possible in the case of weak dissipation.

Domain walls riding the wave

Recent years have witnessed a rapid proliferation of electronic gadgets around the world. These devices are used for both communication and entertainment, and it is a fact that they account for a growing portion of household energy consumption and overall world consumption of electricity. Increasing the energy efficiency of these devices could have a far greater and immediate impact than a gradual switch to renewable energy sources. The advances in the area of spintronics are therefore very important, as gadgets are mostly comprised of memory and logic elements. Recent developments in controlled manipulation of magnetic domains in ferromagnet nanostructures have opened opportunities for novel device architectures. This new class of memories and logic gates could soon power millions of consumer electronic devices. The attractiveness of using domain-wall motion in electronics is due to its inherent reliability (no mechanical moving parts), scalability (3D scalable architectures such as in racetrack memory), and nonvolatility (retains information in the absence of power). The remaining obstacles in widespread use of 'racetrack-type' elements are the speed and the energy dissipation during the manipulation of domain walls. In their recent contribution to Physical Review Letters, Oleg Tretiakov, Yang Liu, and Artem Abanov from Texas AM i.e., one can read the stored information. The interaction of the spin-polarized electrons with the domain wall in the ferromagnetic nanowire is not very efficient. Even for materials achieving high polarization of the free electrons, it is very difficult to move the magnetic domain wall. Several factors contribute to this problem, with imperfections of the ferromagnetic nanowire that cause domain-wall pinning being the dominant one. Permalloy nanowires, one of the best candidates for domain-wall-based memory and logic devices, require current densities of the order of 10{sup 8} A/cm{sup 2} in order to move a domain wall from a pinning well. Considering that this current has to pass through a relatively long wire, it is not very difficult to imagine that most of the energy will go to Joule heating. The efficiency of the process - the ratio of the energy converted to domain-wall motion to the total energy consumed - is comparable to that of an incandescent light bulb converting electricity to light. A step towards more efficient domain-wall-based memory devices is the advance of using alternating currents or current pulses to drive the domain walls. Injection of a spin-polarized current below the threshold value necessary to move the domain wall only causes oscillation of the domain wall inside the pinning potential. Exploiting the effect of resonance, one can apply a specific current waveform to drive the oscillations of the domain wall into resonance. Resonant amplification of domain-wall oscillations will free the domain wall from the pinning well at current levels that are a fraction of the dc threshold. Currents of an order of magnitude lower than before were shown to be sufficient to manipulate domain walls, thus reducing Joule heating 100 times. In their current paper, Tretiakov et al. provide a theoretical basis for the mechanism of resonant domain-wall motion in ferromagnetic nanowires.« less

Controlling quasi-relativistic dynamics of domain walls in the regime of self-phasing

Quasi-relativistic nonlinear dynamics of domain walls in a plate of an orthorhombic magnet with a plane-parallel periodic domain structure in an external field with a slowly changing frequency has been investigated. It has been found that, in the regime of self-phasing, large-amplitude oscillations of a domain wall with a quasi-relativistic effective mass can be generated. It is shown that by modulating field frequency it is possible to transfer a system of domain walls from an equilibrium (or close to equilibrium) state into a stationary nonlinear regime of oscillations and to control the quasi-relativistic nonlinear dynamics of the walls under the conditions of self-phasing.

Design and performance of domain wall displacing-type field sensors using a magnetic tunnel junction and a giant magnetoresistive device

We report a new type of field sensor, which utilizes the oscillatory domain wall displacement in the ferromagnetic free layer to detect an external field. The sensor consists of a 1200 × 100 µm2 Al conducting wire placed on a spin-valve giant magnetoresistive (GMR) or magnetic tunnel junction. By transmitting an alternating current through the Al conducting wire, an ac field can be generated to oscillate the domain wall in the free layer. The oscillatory domain wall displacement reduces the influence of wall coercivity and Barkhausen effect, and enables the sensor to detect the magnetic field which is much smaller than the wall coercivity. The field sensitivities of the domain wall displacing-type GMR and tunnel magnetoresistive (TMR) sensors are 2.73 mV V−1 Oe−1 and 5.81 mV V−1 Oe−1, respectively.

Coupled domain structures in superconductor/ferromagnet Nb-Fe/garnet bilayers

We investigate the magnetic structure in a superconducting Nb and ferromagnetic garnet hybrid film. Direct magneto-optical observations reveal a strong interaction between the superconducting vortices in Nb and the magnetic domains in the garnet, resulting in a unique coupled domain structure. The cooperative motion of vortices and domain walls results in an enhanced pinning and a modified electromagnetic response of the hybrid similar to that in type I superconductors. Application of ac field, routinely used for equilibration of domains, leads to their significant contraction. Our calculations explain this effect by a domain shrinkage instability induced by the vortex annihilation around oscillating domain walls.

Current-induced oscillation of a magnetic domain wall: Effect of damping enhanced by magnetization dynamics

Based on the Thiele’s approach, we investigate current-induced oscillation of a magnetic domain wall. A special attention is paid to effect of damping enhancement due to magnetization dynamics in the limit of no spin diffusion. Unlike for a translation motion, the enhanced damping due to magnetization dynamics has an important role for a rotational motion of a magnetic domain wall and can significantly reduce its oscillation frequency. The frequency reduction becomes more substantial for a narrower domain wall. This result provides a design strategy of high-frequency devices utilizing domain wall oscillation.

Domain Wall Dynamics Driven by a Localized Injection of a Spin-Polarized Current

This paper introduces an oscillator scheme based on the oscillations of magnetic domain walls due to spin-polarized currents, where the current is injected perpendicular to the sample plane in a localized part of a nanowire. Depending on the geometrical and physical characteristic of the system, we identify two different dynamical regimes (auto-oscillations) when an out-of-plane external field is applied. The first regime is characterized by nucleation of domain walls (DWs) below the current injection site and the propagation of those up to the end of the nanowire, we also found an oscillation frequency larger than 5GHz with a linear dependence on the applied current density. This simple system can be used as a tuneable steady-state domain wall oscillator. In the second dynamical regime, we observe the nucleation of two DWs which propagate back and forth in the nanowire with a sub-GHz oscillation frequency. The micromagnetic spectral mapping technique shows the spatial distribution of the output power is localized symmetrically in the nanowire. We suggest that this configuration can be used as micromagnetic transformer to decouple electrically two different circuits.

High sensitivity giant magnetoresistance magnetic sensor using oscillatory domain wall displacement

A high sensitivity giant magnetoresistance (GMR) magnetic sensor has been demonstrated using the oscillatory domain wall displacing method. This sensor consists of a 30-μm-wide GMR element, CoFeB (10 nm)/Cu (2.2 nm)/CoFe (3 nm)/MnIr (10 nm), and a 100-μm-wide aluminum conducting wire placed onto the GMR element with an insulation layer between them. Domain walls in the free layer, whose easy axis is perpendicular to the length direction of GMR element, are oscillation-driven by a 140 kHz alternating magnetic field produced by an ac flowing through the aluminum conducting wire. The oscillatory wall displacement reduces the influence of wall coercivity and enables an output proportional to the external field. By applying a 1-kHz external field and separating the 1-kHz component from the amplified bridge signal using a band-pass filter, we successfully detected a magnetic field as small as 0.21 mOe (21 nT), which is much smaller than the wall coercivity of the free layer.