Session V19: Magnetic Nanoparticles: Spin Waves and Strain

Fresnel diffraction of spin waves

Spin waves, which have long been investigated for their potential in microwave electronics, found a renewed interest in the emerging field of magnonics, with promising functionalities for computation applications. In this context, several concepts of optics are applied to spin-waves, which includes recent works on the generation of spin-wave beams in continuous thin films from constricted coplanar waveguides (CPW) [1,2]. In this work, we explore experimentally the nature of the emission for the isotropic magnetostatic forward volume wave mode via spin-wave spectroscopy [3]. We found that the spin wave propagation remains focused in a beam of width comparable to that of the constriction, and that the spin-wave amplitude displays oscillations in the direction transverse to the propagation. Both of these features are understood in the framework of the Fresnel theory of near-field diffraction. These findings are of particular importance for future exploration of spin-wave interferometry.   

Dipole exchange spin wave modes in multilayered ferromagnetic films

Dipole exchange spin wave modes are studied theoretically in multilayered ferromagnetic films under different and general configurations using a method that allows to calculate them with ease. The studied geometries correspond to a couple or several ferromagnetic films separated by non magnetic layers, or to periodically repeated configurations. In general there is a magnetic field applied obliquely with respect to the planar directions, boundary conditions of different origin are considered.
We determine the frequency dispersion relations as well as the shape of the modes using an application of the Green-Extinction theorem. This method allows to write eigenvalue integral equations for the modes, written on the edges of the samples. In these multilayered geometries there is translation invariance in the planar directions, meaning that these integral equations are local in wave vector space. Thus, for example, for a couple of films there is an algebraic eigenvalue problem that involves just a 12x12 matrix.
Results for different geometries and boundary conditions are discussed, with emphasis on the effect of coupling between films that may be of dipolar or exchange origin.   

Berry curvature of magnons coupled with elastic and electromagnetic waves in ferromagnets

The Berry curvature is a differential-geometric quantity defined in terms of the Bloch wavefunctions, and it manifests itself in Hall effects, in the shift of wavepackets, and even in various topological phases. Recently we calculated the Berry curvature of magnons in ferromagnetic films with dipole-exchange interactions. The Berry curvature of magnons is enhanced at the crossings of the eigenmodes due to the hybridizations between them.
In this presentation, we calculate the Berry curvature in the systems of magnons coupled with elastic waves and with electromagnetic waves. First, we reformulate the eigenmode problem in order to calculate the Berry curvature, and present the result of the Berry curvature of coupled waves. The Berry curvature also has a peak at the crossing point of the dispersions of the constituent waves, and it depends on the direction of the magnetization and the wavevector, similarly to the previous work. In particular, for the magnons coupled with the elastic waves, the behavior of the Berry curvature around k=0 is largely modified by the coupling.
We also discuss behaviors of the Berry curvature around k=0 for the waves for the magnons coupled with electromagnetic waves, and discuss its difference from the magnetoelastic waves.   

Direct imaging of delayed magneto dynamic modes induced by surface acoustic waves

Changes in strain can be used to modify electronic and magnetic properties in crystal structures, to manipulate nanoparticles and cells, or to control chemical reactions. The magneto-elastic effect--the change of magnetic properties caused by the elastic deformation (strain) of a magnetic material--has been proposed as an alternative approach to magnetic fields for the low-power control of magnetization states of nanoelements since it avoids charge currents, which entail ohmic losses. Multiferroic heterostructures and nanocomposites have exploited this effect in search of electric control of magnetic states, mostly in static regimes. We have studied the effect of dynamic strain accompanying a surface acoustic wave on magnetic nanostructures in thermal equilibrium. We have developed a new experimental technique based on stroboscopic X-ray microscopy that provides a pathway to the quantitative study of strain waves and magnetization at the nanoscale. We have simultaneously imaged the temporal evolution of both strain waves and magnetization dynamics of nanostructures at the picosecond timescale and found that magnetization modes have a delayed response to the strain modes, adjustable by the magnetic domain configuration. The results I will present in this talk provide fundamental insight into magnetoelastic coupling in nanostructures having implications in the design of strain-controlled magnetostrictivenano-devices.

[1] Nat. Commun. 8, 407 (2017)

  

Manipulation of Magnetic Nano-Particles with Strain Mediated Multiferroics

Strain mediated multiferroic systems provide an energy-efficient path to the manipulation of magnetic nano-particles for small scale mechanical, electrical, and biological applications. In this system, there is a magnetoleastic disk, a piezoelectric substrate and soft magnetic nano particles near the disk. The simulation consists of 1) voltage generated piezo-strains; 2) disk magnetic spin reorientation; and 3) the dynamic nano-particle movement. The particle dynamic model includes both translation and rotation considering: magnetic force, fluid drag, frictional force. The particle movement is studied for three dynamic cases with different frictional and drag coefficients: underdamped, critically damped and over damped. When the frictional and drag forces are small, the particle follows the rotation with a lag angle at steady state. The lag angle highly depends on the rotating frequency and the frictional/drag coefficients. When the frictional and drag forces further increase, the particle detaches from the disk when a critical velocity is reached. This work provides guidance on how to implement magnetic particle manipulation for a wide range of applications.   

Multi-Particle Dynamics in Strain Mediated Multiferroics

Strain mediated multiferroics has opened the possibility of localized control of the magnetization vector which in turn allows for soft-magnetic nanoparticle manipulation with high precision. No dynamic model exists to simulate the full multi-particle dynamics in multiferroic systems. This work focuses on developing a 3D multi-body model of magnetic particle motion driven by magnetic forces, particle repulsive forces, frictional forces, fluid drag and adhesion forces considering asperities. Magnetic forces and particle repulsive force were evaluated directly from the finite difference model by post-processing the output nodal fields. Other forces were calculated using analytical expressions. The system studied in this work is a FeGa disk on a PZT substrate. First, we studied the particle distribution when the magnetization is static. The results show good agreement with previous experimental data. Next, the dynamic distribution of particles was studied with the magnetization rotating at constant angular velocity, comparing the distribution under different angular velocities. Particle distribution highly depends on the magnetic properties and particle number. We believe that this is the first model to predict multi-particle dynamics in multiferroic systems with full 3D dynamics.   

Broadband Electrically Small Antennas with Strain Powered Multiferroics

Antennae built from magnetic materials offer a promising concept for reducing antennae’s size to below free space wavelengths (i.e. < λ/50). However, recent studies on strain mediated multiferroic antenna heterostructures show only narrow band operation. To overcome this issue, we studied a system consisting of a magnetoelastic single domain disk placed atop a piezoelectric substrate. The spinning magnetization radiates electromagnetic energy into free space over broadband frequencies, i.e. from very-high frequency to ultra-high frequency. The magnetization is driven with patterned electrodes with periodic input voltages, which produce strain that couples to the magnetoelastic media. Two magnetoelastodynamic modeling approaches were used; one within a micromagnetic finite element formulation and the other in a macro spin framework. The free space radiation is modeled by considering two orthogonal magnetic dipoles rotating out of phase.
We studied magnetic materials with frequencies ranging from 10 MHz to 2 GHZ, which show similar results for the dynamics. These results are used in an analytical formulation to predict radiation power densities of ~mW/m². Arraying these elements produces larger radiation magnitudes, suggesting a new path for creating small broadband antennae.   

Chaotic magnetization dynamics excited by spin transfer torque in elliptical nanodots

Recent theoretical work has shown that ac-driven magnetization dynamics near saddle equilibria in magnetic elliptical nanodots exhibits chaotic behavior. The tools of nonlinear dynamical systems allow the definition of the concept of erosion of the stability region of magnetic equilibria in absence of the ac drive. From an energy perspective, the effect of the erosion is similar to a reduction of the magnetic potential barrier separating two stable equilibrium states of the nanodot, as exploited in energy assisted magnetic reversal schemes. In this framework, we study experimentally this phenomenon by measuring thermal telegraph noise of the free magnetic layer in nanoscale elliptical magnetic tunnel junctions (MTJs) in the presence of AC drive provided by the spin transfer torque arising from radio-frequency (RF) current applied to the MTJ. We follow the switching rate of the free layer, which serves as an indicator for the occurrence of chaotic dynamics as a function of both the frequency and power of the applied microwave excitation. The experimental results are compared to analytical solutions and micromagnetic simulations.   

A hybrid magnetic random-access memory using spin-orbit torque and multiferroics

Spin-orbit torque (SOT) is an energy efficient method to control magnetization with magnetic memory applications. However, using SOT to switch memory bits with perpendicular magnetic anisotropy (PMA) is still a challenge. Here we present a new strain-mediated SOT switching mechanism. The strain induced magnetoelastic anisotropy in the multiferroic heterostructure breaks lateral symmetry of SOT device thus produces field-free deterministic perpendicular switching. A finite element model and a macrospin model are used to numerically simulate the switching mechanism. Space inversion transformation is performed to show the symmetry breaking of strain-mediated SOT system. A relatively small voltage (±0.5V) combined with a modest current (3.5×10⁷ A/cm²) produces 180° perpendicular magnetization reversal. The switching direction (‘up’ or ‘down’) is dictated by the voltage polarity (positive or negative) applied to piezoelectric layer in the multiferroic heterostructure. The switching is fast (up to 10GHz) and does not require precisely timed voltage or current pulses. Based on the strain-mediated SOT control mechanism, a new random-access memory system is designed with high storage density and high scalability.   

Spin superfluid junction oscillator

A spin oscillator is proposed based on a spin superfluid junction composed of two exchange coupled easy-plane ferromagnets. A spin chemical potential across the junction, with its spin polarization perpendicular to the easy-plane, can be established by driving electrical currents through two heavy metal contacts. When the spin chemical potential exceeds the threshold, it drives steady-state spin oscillation with a 2π precession angle, which can be electrically measured by the giant magnetoresistance, the anisotropic magnetoresistance, and the inverse spin Hall effect. The oscillation amplitude and frequency can be tuned via the applied D.C. current. An A.C. current applied to the heavy metal contacts, the spin oscillation also exhibits Shapiro steps, whose time-averaged component is fixed by the mode-locking. These features provide signatures for the experimental verification of spin superfluidity in easy-plane ferromagnets. This new type of spin nano-oscillator could serve as a device in a spintronic based neuromoprhic computing scheme.   

All-magnonic switching and spin-valve using antiferromagnetic magnons

In a collinear antiferromagnet (AF) with uniaxial anisotropy, symmetry guarantees that magnon excitations are doubly degenerate. The two degenerate modes carry opposite spin angular momentum and can play a similar role as spin-1/2 electrons. At an exchange coupled interface with a ferromagnet (F), thermal populations of the two modes are imbalanced, which can form a pure spin current that propagates under a thermal gradient. Here we present a theoretical framework of magnon transport in an insulating F/AF/F heterostructure. We find that a sufficiently large temperature gradient can switch the downstream F via magnon spin current in the AF if the system is initially prepared in an antiparallel configuration. This thermomagnetic switching opens the possibility of all-magnonic spin valve.   

High Frequency Spin Dynamics of Magnetic Tunneling Junctions Consisting of Two Perpendicular Free Layers

Magnetic Tunnel Junctions (MTJ) with one fixed layer and one free layer have been extensively studied as a memory element, a microwave oscillator and a microwave detector. With the advent of harvesting interfacial perpendicular magnetic anisotropy (IPMA), perpendicular MTJs have drawn much recent attention over the prior sate of the art in-plane structures. We report our experimental investigation of MTJ structures with two perpendicular free-layers, with different strengths of IPMA. We find high frequency microwave emission can be produced at zero bias field when a small DC current is applied. We will show our understanding on mutual roles played by each IPMA layer. Micromagnetic simulations will be presented demonstrating the spin dynamics of the two free layers. The role of electron heating in these nanoscale structures, on the microwave emission spectrum, will be discussed. The work was supported by Center for Function Accelerated nano-Materials (FAME).   

Spin Wave Field Effect Transistor

Spin waves (SWs) have been proposed as information carriers in novel logic devices. Voltage-controlled magnetic anisotropy (VCMA) is a promising approach to generation and control of spin waves due to its high energy efficiency. We developed a spin wave field effect transistor (SW-FET), which can turn on and turn off SW propagation in a ferromagnetic nanowire with a gate voltage via VCMA effect. We experimentally demonstrate a functioning nanoscale SW-FET based on a Ta/CoFeB/MgO multilayer nanowire. The device consists of a ferromagnetic nanowire channel magnetized out of the sample plane for SW propagation and a voltage gate on top of the wire. Propagating SWs are excited on one side of the gate via application of a localized ac spin Hall torque at the SW resonance frequency. SW propagation to the other side of the gate is detected via anomalous Hall effect (AHE). Utilizing VCMA, a dc voltage applied to the gate adjusts perpendicular magnetic anisotropy under the gate and transforms the spatially uniform magnetic energy landscape into a potential well or barrier for SW propagation depending on the gate voltage polarity. Our data demonstrate that VCMA-induced magnetic barrier can efficiently suppress SW propagation under the top gate.