Session W15: Focus Session: Spins in Metals - Domain Wall, Vortex, Magnonic Based Devices

High speed domain wall motion in MgO-based magnetic tunnel junctions driven by perpendicular current injection

The ability to efficiently drive fast domain wall (DW) motion will pave the way for revolutionary new electronic devices ranging from DW-MRAMs to spintronic memristors. The majority of domain wall devices use a lateral, current-in-plane configuration in which critical current densities for domain wall motion remain quite high, typically being on the order of 100 MA/cm$^{2}$ with velocities generally limited to about 100 m/s. In this contribution we show that critical current densities can be decreased by up to two orders of magnitude using the current-perpendicular-to-plane geometry. Indeed, we demonstrate that a DW can be propagated back and forth along the free layer of a MgO-based magnetic tunnel junction (MTJ) in the absence of an external magnetic field using current densities that are on the order of 5 MA/cm$^{2}$. More notably however, we obtain high domain wall velocities for these low current densities: the MTJ's large resistance variations allow us to carry out time-resolved measurements of the wall motion from which we evidence DW velocities exceeding 500m/s.   

Thermal activation energy for domain wall motion in out-of-plane magnetized submicron strips

We have experimentally studied micrometer-scale domain wall (DW) motion driven by magnetic field and electric current in 500-nm wide out-of-plane magnetized Co/Pt multilayer strips with Co layer thicknesses 0.5-0.7 nm. The scaling of thermal activation energy for DW motion with driving field and current has been extracted directly from the temperature dependence of the DW velocity. For DWs driven by field, the activation energy follows creep and depinning dynamics below a critical field and collapses to zero above the critical field. DW motion assisted by current shows velocity enhancement independent of current polarity, but causes no measurable change in the activation energy barrier. Through this analysis, the observed current-induced DW velocity enhancement in these Co/Pt multilayer strips can be entirely and unambiguously attributed to Joule heating.   

Intrinsic domain wall flexing from current-induced spin torque

Spin torque generated by coherent carrier transport in domain walls [1] is a major component in the development of spintronic devices [2]. We model spin torque in N\'eel walls [3] using a piecewise linear transfer-matrix method [4] to calculate spin torque on interior wall segments. For a $\pi$ wall with a total positive torque (current left-to-right), we find the largest positive and negative spin torques left of the central region, 4-5 orders of magnitude larger than the center. The wall's rightward push comes from the back of the wall; all other significant regions pull to the left. Adding a second wall (both walls with positive total torque) changes the first wall little, but produces spin torques in the second wall with large canceling torques on the left, and the push rightward from a smaller torque on the right. The gradient of torque across the wall generates an intrinsic domain wall flexing (distinct from extrinsic wall flexing from pinning centers [5]). Work supported by an ARO MURI.\\[4pt] [1] M. Yamanouchi et al., Nature 428, 539 (2004).\\[0pt] [2] S. Parkin et al., Science 320, 190 (2008)\\[0pt] [3] G. Vignale and M. Flatt\'e, Phys. Rev. Lett. 89, 098302 (2002)\\[0pt] [4] E. Golovatski and M. Flatt\'e, Phys. Rev. B, 84, 115210 (2011)\\[0pt] [5] A. Balk et al., Phys. Rev. Lett. 107, 077205 (2011).   

Spinmotive force due to domain wall motion in high field regime

Spinmotive force associated with a moving vortex domain wall is investigated numerically. Dynamics of magnetization textures such as a domain wall exerts a non-conservative spin-force on conduction electrons [1], offering a new concept of magnetic devices [2]. This spinmotive force in permalloy nanowires has been detected by voltage measurement [3] where magnitude of the signal is limited less than 500 nV. Theoretically it is suggested that the spinmotive force signal increases as a function of external magnetic fields. At higher magnetic fields, however, the wall propagation mode becomes rather chaotic involving transformations of the wall structure and it remains to be seen how the spinmotive force appears. Numerical simulations show that the spinmotive force scales with the field even in a field range where the wall motion is no longer associated coherent precession. This feature has been tested in a recent experiment [4]. Further enhancement of the spinmotive force is explored by designing ferromagnetic nanostructures [5] and materials. [1] S. Barnes and S. Maekawa, PRL (2007). [2] S. Barnes, J. Ieda, and S. Maekawa, APL (2006). [3] S. A. Yang et al., PRL (2009). [4] M. Hayashi, J. Ieda et al., submitted. [5] Y. Yamane, J. Ieda et al., APEX (2011).   

All-magnonic spin-transfer torque and domain wall propagation

In this talk, we will discuss the spin-transfer torque (STT) between magnons and magnetic domain wall (DW). It is found that a spin wave passes through a transverse magnetic DW in a magnetic nanowire without reflection. A magnon, the quantum of the spin wave, carries opposite spins on the two sides of the DW. As a result, there is a spin angular momentum transfer from the propagating magnons to the DW. This magnonic STT can efficiently drive a DW to propagate in the opposite direction to that of the spin wave. In comparison with the electronic STT, the energy consumption is much lower when the magnonic STT is used to drive a DW propagating at a useful velocity. Since this STT does not require any itinerant electrons, it opens a door of using magnetic insulators like YIG in spintronics devices. One extra benefit of using magnetic insulators is the low damping coefficient so that it should further lower the energy consumption and increase operation efficiency.   

Disentangling the physical contributions to the anomalous Hall effect and domain wall resistance in isoelectronic L1$_{0}$-FePd and L1$_{0}$-FePt alloys

We analyze the origin of the electrical resistance arising in domain walls of perpendicularly magnetized materials by considering a superposition of anisotropic magnetoresistance and the resistance implied by the magnetization chirality. The domain wall profiles of L1$_{0}$-FePd and L1$_{0}$-FePt are determined by micromagnetic simulations based on which we perform first principles calculations to quantify electron transport through the core and closure region of the walls. The wall resistance, being twice as high in L1$_{0}$-FePd than in L1$_{0}$-FePt, is found to be clearly dominated in both cases by a high gradient of magnetization rotation, and not by the spin-orbit interaction driven anisotropic magnetoresistance effect. Concerning the anomalous Hall effect on the other hand, we show that difference in spin-orbit interaction strength of Pt and Pd atoms leads to a pronounced cross-over from an extrinsic side jump mechanism in L1$_{0}$-FePd to an intrinsic Berry-phase anomalous Hall effect in L1$_{0}$-FePt.   

Stochastic dynamics of vortex cores in a pinning potential observed via torsional magnetometry

Measurements of a single 1 micrometer diameter permalloy disk fabricated on a silicon nitride torsional resonator are presented. Sensitivity of this device is sufficiently high to allow study of the vortex core interaction with very weak pinning sites. Low speed stochastic dynamics are revealed and attributed to the vortex core hopping between bistable states around pinning sites. The temperature and field dependence of this noise around the pinning site was investigated. Analysis employing an analytical description of the vortex in a thin disk and an Arrhenius model allows determination of the pinning potential.   

Dimensionality crossover in magnetic vortex dynamics

The ground state of a micron diameter ferromagnetic disk is often a single magnetic vortex, in which the gyrotropic mode of the vortex core is the lowest frequency excitation. In thin disks (thickness $L\ll $ diameter $D$), the vortex can be treated two-dimensionally (2D), and the gyrotropic frequency $f_G$ is determined by $L/D$. We have observed a crossover from 2D to 3D dynamics as the thickness increases. Using time-resolved Kerr microscopy, we have investigated the gyrotropic mode in 1~$\mu$m diameter Ni$_{80}$Fe$_{20}$ disks as a function of $L$, which was varied from 20 nm to 200 nm. In thin disks ($L < $ 80~nm), $f_G$ is approximately proportional to $L$. For $L > 100$~nm, $f_G$ increases less rapidly than predicted by the 2D model, and an additional gyrotropic mode appears at higher frequencies. We have explored the thickness dependences of both modes. In the ordinary gyrotropic mode, which is magnetostatic in character, the core oscillates uniformly through the thickness of the disk. The second gyrotropic mode is exchange-dominated, and the core oscillates with larger amplitude at the surfaces and a node in the equatorial plane of the disk. In the thickest disks, the exchange-dominated mode is the lowest in frequency.   

Magnonic band gaps in films with periodically modified surfaces

It is of current interest to understand the electromagnetic response of different nano-structures. In this study we focus on the role of geometry in ferromagnetic modes and response. Specifically we consider a ferromagnetic thin film with periodically perturbed surfaces, in the magnetostatic limit. We focus on the changing behavior of surface modes of the unperturbed film. Our film shows a behavior of interest since magnons propagate in it with band gaps associated to the geometry, i.e. they may be controlled by design. A reduced Brillouin zone scheme is introduced to describe the modes, which are of the Bloch type. Different bands are identified, and they are calculated numerically. For small geometric perturbations we develop a perturbation theory that agrees with our numerical results, and we obtain analytic expressions for the band gaps at the edges of the Brillouin zone. The underlying theory used to calculate the modes was previously developed, and relies on solving integral equations along the edges of the sample for the magnetostatic potential. We also calculate the response to magnetic field waves of a given wavevector that travel along the modulation direction, finding effective line width increments at the edge of the Brillouin zone, where the bands strongly couple.   

Manipulation of propagating spin waves in straight and curved magnetic microstrips

The main challenges in realizing magnonics devices are the generation, manipulation and detection of spin waves, especially in metallic magnetic materials where the length scales are of interest for applications. We have studied the propagation of spin waves in transversely magnetized Permalloy (Py) microstrips of different shapes using micro-Brillouin light scattering. The Py stripe was 30-nm thick, several micrometers wide and $>$50 $\mu$m long. Spin waves were excited in the Py strip using a 2-$\mu$m wide antenna. We compare the spin wave propagation along a straight wire to the propagation along a magnetic microstrip with a smooth bend. We will also discuss the use of a current through a gold wire under the Permalloy to provide a local magnetic field to maintain a transverse magnetization around the bend.   

Dynamics of wavepacket of magnetostatic spin wave in magnet

A semiclassical equation of motion of a wave packet of the magnetostatic spin wave is theoretically constructed. There appears the Berry curvature as an anomalous velocity term in the equation of motion, which causes characteristic orbital motions of the wave packet such as a self-rotational motion and a motion along the edge of the system. Due to the symmetry, the Berry curvature in the case of a thin film of an insulating ferromagnet appears when the magnetization is perpendicular to the film. We show a numerical calculation of the Berry curvature for this mode, i.e., the magnetostatic forward volume wave mode. Around the degeneracy point, the Berry curvature from the highest energy band enhances and that from other bands decreases. We also propose experimental settings to observe this effect.   

Nonlinear Behavior for the Uniform Mode and Horizontal Standing Spin Wave Modes in Metallic Ferromagnetic Microstrips: Experiment and Theory

Micron sized rectangular ferromagnetic bars have a variety of spin excitations, including a quasi-uniform mode, horizontal and vertical standing spin wave modes, and edge and corner modes. When driven by a strong microwave field, these modes differ from those found in the linear regime. For example, the resonance field or frequency becomes amplitude dependent. We study the nonlinear spin dynamics in such microstrips both experimentally and theoretically for a geometry where the static magnetic field is perpendicular to the plane of the sample. Experimentally it is found that, at a fixed microwave frequency, the resonance field for the uniform mode is significantly reduced as the microwave power is increased. In contrast, the resonance fields for the standing horizontal spin wave modes are only slightly reduced. This behavior is confirmed theoretically using micromagnetic calculations, and an intuitive explanation for this behavior is developed.   

Efficient computation of Magnon dispersions within Time Dependent Density Functional Theory Using Maximally Localized Wannier Functions

An efficient scheme is presented to compute the transverse magnetic susceptibility within time dependent density functional theory from which magnon dispersions can be extracted. The scheme makes use of maximally localized Wannier functions in order to interpolate the band structure onto a fine k-mesh in order to converge sums on the first Brillouin zone. An optimal real space basis set containing few basis functions is shown to be sufficient to extract the magnon dispersion, making computations very efficient. The gap error in the magnon dispersion at $\Gamma$, numerically violating Goldstone's theorem, is analysed and a correction scheme is devised which can be generalized to systems where Goldstone's theorem does not apply. The method is applied to the computation of the magnon dispersion of bulk bcc iron and fcc nickel.   

Electron Paramagnetic Resonance of Transition Metal Ions: New Relativistic Effects at High Magnetic Fields

We calculate the shift in the Electron Spin Resonance (ESR) frequency due to an inhomogeneous term in the equation of motion describing the precession of the angular momenta of relativistic electrons coupled to a static magnetic field. It is proposed that the calculated frequency shift may be observed in transition metal complexes in which the contributions from the ligand field are completely and precisely known. Furthermore, it is shown that a measurable transient oscillation of the dipole moment occurs after the external magnetic field is suddenly switched off.