Session Q32: Magnetic Domains and Domain Walls

Effect of Wall Width on Spin Torque in Ferromagnetic Domain Walls

The amount of spin torque exerted on a domain wall in a ferromagnetic semiconductor depends on the amount of spin flip that occurs during the transport process. Starting with a model Hamiltonian[1], we calculate the total amount of spin torque exerted on a $\pi$ wall and a 2$\pi$ wall for ballistic transport across the domain wall, and calculate the dependence of the torque on the width of the domain wall. In very thin 2$\pi$ walls, transport occurs with almost no spin flip. As the wall width increases, spins precess more inside the domain wall, increasing the spin torque. In a $\pi$ wall, where most spins will flip during transport through a thick wall, we find that the spin torque increases monotonically with wall width. In contrast, spins in a thick 2$\pi$ wall will continue to precess back towards their original configuration, and there will be much less net spin flip. Thus there is very little spin torque in both very thin and very thick 2$\pi$ walls, but significant spin torque is possible in a range of intermediate widths. This non-trivial dependence on the width of the domain wall leads to an optimal wall width for achieving a maximum amount of spin torque. For a 2$\pi$ wall with an exchange-induced spin splitting of 100 meV, and an effective carrier mass equal to the electron mass, we calculate this optimal width to be $\sim$ 5nm. This work was supported by an ONR MURI. [1] G. Vignale and M.E. Flatt\'e, PRL 89, 098302 (2002).   

Transport across a pinned domain wall across a GaMnAs constriction: from AMR to spin-dependent tunneling.

We report on the different magnetotransport mechanism across a pinned domain wall in a GaMnAs nanowire dependent on constriction size. Nanometer-sized constrictions are realized in LT-MBE epifilm GaMnAs by standard e-beam lithography and wet-etch chemistries, as well as a ``break-junction method'' to further decrease constriction size. Four-point probe DC \textit{IV} measurements- with applied fields at varying angles to wire axis- are utilized to study the transport mechanism- as well as magnetic properties. As constriction size approaches epifilm thickness, nonlinear \textit{IV }response is observed with a differing field dependence on temperature. As constrictions become smaller, we observe a tunneling AMR-like behavior. This effect is more evident after series of high current pulses are applied to decrease the constriction width. ``Break-junction'' method results in higher constriction resistances and increases in resulting MR values.   

Mechanisms for low-field, and multiple domain wall injection into magnetic nanowires.

The motion of a domain wall within a magnetic nanowire is important for the development of future recording, sensing and logic devices.~ The speed of a field driven domain wall is quickest when the applied magnetic field is below the so-called Walker Field which depends on the size and material properties of the wire.~ However, the field needed to inject a domain wall into a wire is much greater than the Walker Field which leads to slow wall motion because of the nucleation of vortices and anti-vortices, or fast motion with complicated domain wall structures. We present Landau-Lifshitz simulation results showing a significant decrease in the field needed to inject a domain wall into the wire for a variety of injection designs including: pads, rings, straight ends, and tapered ends.~ We also find that by applying a transverse field the required driving field to inject the wall decreases, and that the domain wall motion in the wire is faster.~ The magnetization of the pad and ring injection designs can be easily manipulated so that multiple walls with a known magnetization structure are injected allowing for faster, more reliable domain wall motion.   

The influences of transverse magnetic anisotropy on field-induced domain wall propagation in magnetic nanowires

Domain wall (DW) propagation in magnetic nanowires is an important subject in nanomagnetism because of its fundamental interest and potential applications in spintronic devices. It is well known that a head-to-head (or tail-to-tail) domain wall in a nanowire will propagate along the wire under an axial magnetic field. In this talk, we shall show that a new velocity-field formula can fit well with numerical results obtained from the open-source micromagnetic simulation package OOMMF. The fitting parameters have clear physical meanings that relate to the transverse magnetic anisotropy. How the transverse magnetic anisotropy, which can be modified by both transverse magnetic field and the aspect ratio of wire cross section, affects the DW structure and hence the DW propagation velocity will be discussed systematically.   

Near-field interaction between domain walls in adjacent permalloy nanowires

Proposed data storage schemes based on ferromagnetic nanowires rely on the controlled propagation of domain walls (DWs) along nanoscale shift registers [Allwood \textit{et al. }Science 309, 1688 (2005)]. To make technologically relevant devices, these nanowires must be fabricated to within a wire width of one another. However, the effect of magnetostatic interactions between DWs on their propagation through closely spaced nanowires has not been well studied. Using MOKE magnetometry we have experimentally observed the interaction between two DWs of opposite charge travelling in adjacent permalloy nanowires (8nm thick, 100 nm wide), with inter-wire separation between 125 and 13nm. For the smallest separations, depinning fields (H$_{D})$ as high as 93 Oe were measured. Considering the energy landscape experienced by the two DWs under the approximation they are isolated and rigid and accounting for finite temperature we can completely reproduce the experimental dependence of H$_{D}$ on the inter-wire spacing. Our results suggest that the interaction causes little perturbation to the DW shape. Pinning resulting from localised stray fields is of interest for studying the fundamental properties of DWs as it occurs without modification of the DW or nanowire shape. Our results suggest propagation could be compromised by DW-DW interactions unless careful DW control is used.   

Control of Domain Wall Structure and Pinning In Spin-Valve Nanowires

Domain walls (\textbf{DWs}) in magnetic nanowires are the basis for several proposed data storage devices [D Allwood et al. Science 309, 1688 (2005), SS Parkin, US Patent 6,834,005 (2004)]. Most schemes use artificial defects (\textbf{ADs}) to modify the potential landscape seen by the DW, and thereby control its propagation. This potential modification depends on the DW structure. Integrating the nanowire in a Spin-Valve (\textbf{SV}) stack allows the electrical probing of the magnetization as well as electronic integration in future devices. However, using SV systems introduces strong stray fields from the reference layer, especially on the ADs. These can significantly alter the internal structure and propagation of DWs. The study of their influence has been hindered so far by the difficulty of creating DWs of known internal structure and to propagate them at low fields. Here we demonstrate low field (20Oe) propagation of DWs and their pinning by ADs in L-shaped SV nanowires with dimensions for which only transverse DWs are stable (200nm width, free layer 8nm Ni$_{19}$Fe$_{81}$, pinned layer 2nm CoFe).This was verified with micromagnetic simulations. Moreover we show DW depinning at protrusions along the wire with fields lower than that required to nucleation (80/140Oe). These results contribute to furthering the electrical integration of DW based data storage devices.   

Detection of EMF induced by domain wall motion

It is now well established that an electric current can drive magnetic domain wall (DW) motion via coupling between conduction electrons and local magnetic moments. The reverse of this effect, i.e., an emf induced by a DW moving through a stationary electron gas, has also been predicted [1]. DW-induced emf has been explored in more detail in recent theoretical work [2,3], but has yet to be observed. In this talk, we describe the experimental detection of an emf induced by a field-driven DW in a Permalloy nanowire [4]. This DW-driven emf is discussed in terms of a generalized two-dimensional theoretical framework [4] capable of treating vortex DWs. Supported by NSF DMR-0404252, NSF DMR-0606485, DOE DE-FG03-02ER45958, and the Welch Foundation. [1] L. Berger, Phys. Rev. B 33, 1572 (1986). [2] S. E. Barnes et al., arXiv:cond-mat/0410021 (2004); Appl. Phys. Lett. 89, 122507 (2006) [3] R. A. Duine, Phys. Rev. B 77, 014409 (2008). [4] S. Yang, et al., submitted (2008).   

Domain Properties of a Single Magnetic Nanorod Investigated by Cantilever Magnetometry

Single Ni nanorods having 50 to 100 nm diameter were integrated as the tip of ultra-sensitive cantilevers, having a force sensitivity of 8 aN/Hz$^{1/2}$ at 4.2 K, designed for use in scanned-probe magnetic resonace force microscopy. We measured cantilever frequency, dissipation, and frequency fluctuations as a function of magnetic field, applied along both the easy axis and the hard axis of the nanorods while the cantilevers were self-oscillated. The nanorods exhibit bulk magnetization. Hard-axis magnetometry experiments show the nanorods have B$_{switch} \quad \sim $ 300 mT, in which the magnetization switches from being orthogonal to being parallel to the applied field, and the three observables each show multiple sharp peaks. We find the cantilever frequency shift is well described by modeling the tip as a single-domain of uniformly-magnetized spins interacting with the applied field (the Stoner-Wohlfarth model).   

Magnetic Domain Structures in an In-plane Array of Cobalt Filaments with Periodic Structures

With a unique electrochemical deposition method we fabricated in-plane arrays of straight cobalt filaments with periodic corrugations over a silicon substrate without using templates. The periodic corrugations on the filaments are induced by spontaneous oscillation in electrodeposition, and the periodicity can be tuned from a few tens of nanometers to a few hundreds of nanometers by controlling the electric current in experiments. Magnetic force microscopy indicates that each corrugated structure on the filament may correspond to a local single magnetic domain. When the inter-filament separation is large, the magnetic domains are regularly aligned along the filament. The domains become random when the filaments are closely packed. We suggest that our results could be helpful in understanding the evolution of magnetic domain patterns on microscopic scale and may have potential application in spintronics.   

Direct evidence of imprinted vortices in exchange-biased patterned bilayer nanomagnets

We investigate the magnetic domain structure in lithographically patterned nanomagnet arrays using element-sensitive circularly polarized XPEEM imaging. ZFC Py/IrMn (FM/AFM) bilayer nanodot (0.5 um -- 4um dia.) arrays imaged across the Fe and Ni L edges clearly demonstrate spontaneous formation of vortex states. Magnetic contrast at the Mn L edge resonance indicates that the vortex state is transferred into the underlying AFM layer. The exchange-bias, measured through magneto-optical hysteresis measurements, verifies the AFM nature of the underlying IrMn, suggesting that the imprinted vortex state is confined to the interface by local interactions of the uncompensated interfacial Mn spins with the FM Py layer.   

Confinement distance of the closure structure around a single hole in a 2D magnetic thin film

One common feature in many magnetic nanostructures, such as nanorings or patterned thin films [1], is the existence of non magnetic holes within the magnetic material. However, up to now, the simple problem of a a single non magnetic hole in a 2D magnetic film has received little attention, even though it is qualitatively different from the blade domains that appear around holes in 3D magnetic material. In this work [2] this basic problem has been analyzed in detail by magnetic force microscopy, micromagnetic simulations and an analytical model. The closure magnetization configuration can be described by two -1/2 half vortices located at the hole edge along the easy anisotropy axis, and confined within a distance L that is determined by the minimization of magnetostatic and anisotropy energies constrained by the magnetic charge conservation within the system. [1] A. Perez-Junquera et al, J. Appl. Phys. 99 (2006) 033902 [2] G. Rodriguez-Rodriguez et al, Phys. Rev. B (2008) in press.   

A shape phase diagram for a ferromagnetic liquid drop

A ferromagnetic liquid phase has been predicted by mean field theory and computer simulations but conclusive experimental evidence is lacking. Liquids such as ferrofluids, that are suspensions of ferromagnetic particles in solvents, magnetize only in the presence of an applied magnetic field and thus are paramagnets, not ferromagnets. A ferromagnetic liquid, if it existed, would spontaneously magnetize even in the absence of a magnetic field. A droplet of such a liquid will likely not be a sphere due to the magnetostatic energies involved. These energies will induce a magnetization texture in the drop analogous to domain formation in solids. We examine possible shapes for the droplet by optimizing its shape and magnetization textures with respect to its overall energy.   

GGA+$U$ calculation of the magnetic ground state of GdB$_{4}$

We have studied eight collinear and non-collinear magnetic orientations of GdB$_{4}$ using the GGA + $U$ method, without and with spin-orbit coupling, for values of $U - J$ between 0 and 6. For $U $-- $J$ = 6, the value which had been found to yield the correct Gd lattice constants, we obtain GdB$_{4}$ lattice constants within 0.26{\%} of experiment. We find the magnetization lies in-plane but is collinear, in disagreement with the most recent experimental determination.