Magnetostrictive Nanomagnets Research Articles

Formation of binary magnon polaron in a two-dimensional artificial magneto-elastic crystal

We observed strong tripartite magnon-phonon-magnon coupling in a two-dimensional periodic array of magnetostrictive nanomagnets deposited on a piezoelectric substrate, forming a 2D magnetoelastic “crystal”; the coupling occurred between two Kittel-type spin wave (magnon) modes and a (non-Kittel) magnetoelastic spin wave mode caused by a surface acoustic wave (SAW) (phonons). The strongest coupling occurred when the frequencies and wavevectors of the three modes matched, leading to perfect phase matching. We achieved this condition by carefully engineering the frequency of the SAW, the nanomagnet dimensions and the bias magnetic field that determined the frequencies of the two Kittel-type modes. The strong coupling (cooperativity factor exceeding unity) led to the formation of a new quasi-particle, called a binary magnon-polaron, accompanied by nearly complete (~100%) transfer of energy from the magnetoelastic mode to the two Kittel-type modes. This coupling phenomenon exhibited significant anisotropy since the array did not have rotational symmetry in space. The experimental observations were in good agreement with the theoretical simulations.

Acousto‐Plasmo‐Magnonics: Coupling Spin Waves with Hybridized Phonon‐Plasmon Waves in a 2D Artificial Magnonic Crystal Deposited on a Plasmonic Material

AbstractCoupling between spin waves (SWs) and other waves in nanostructured media has emerged as an important topic of research because of the rich physics and the potential for disruptive technologies. Herein, a new phenomenon is reported in this family involving coupling between SWs and hybridized phonon‐plasmon waves in a 2D periodic array of magnetostrictive nanomagnets deposited on a silicon substrate with an intervening thin film of aluminium that acts as a source of surface plasmons. Hybridized phonon‐plasmon waves naturally form in this composite material when exposed to ultrashort laser pulses and they non‐linearly couple with SWs to produce a new breed of waves – acousto‐plasmo‐spin waves that can exhibit a “frequency comb” spanning more than one octave. This phenomenon, that we call acousto‐plasmo‐magnonics resulting from tripartite coupling of magnons, phonons and plasmons, is studied with time‐resolved magneto‐optical‐Kerr‐effect microscopy. The findings also reveal the presence of parametric amplification in this system; energy is transferred from the hybridized phonon‐plasmon modes to the acousto‐plasmo‐spin wave modes to amplify the latter. This opens a path to design novel active metamaterials with tailored and enhanced response. It may enable high‐efficiency magneto‐mechanical‐plasmonic frequency mixing in the GHz−THz frequency regime and provide a unique avenue to study non‐linear coupling, parametric amplification, and frequency comb physics.

Spin Wave Electromagnetic Nano-Antenna Enabled by Tripartite Phonon-Magnon-Photon Coupling.

Tripartite coupling between phonons, magnons, and photons in a periodic array of elliptical magnetostrictive nanomagnets delineated on a piezoelectric substrate to form a 2D two‐phase multiferroic crystal is investigated. Surface acoustic waves (SAW) (phonons) of 5–35 GHz frequency launched into the substrate cause the magnetizations of the nanomagnets to precess at the frequency of the wave, giving rise to confined spin‐wave modes (magnons) within the nanomagnets. The spin waves, in turn, radiate electromagnetic waves (photons) into the surrounding space at the SAW frequency. Here, the phonons couple into magnons, which then couple into photons. This tripartite phonon‐magnon‐photon coupling is thus exploited to implement an extreme sub‐wavelength electromagnetic antenna whose measured radiation efficiency and antenna gain exceed the approximate theoretical limits for traditional antennas of the same dimensions by more than two orders of magnitude at some frequencies. Micro‐magnetic simulations are in excellent agreement with experimental observations and provide insight into the spin‐wave modes that couple into radiating electromagnetic modes to implement the antenna.

Magnetic straintronics: Manipulating the magnetization of magnetostrictive nanomagnets with strain for energy-efficient applications

The desire to perform information processing, computation, communication, signal generation, and related tasks, while dissipating as little energy as possible, has inspired many ideas and paradigms. One of the most powerful among them is the notion of using magnetostrictive nanomagnets as the primitive units of the hardware platforms and manipulating their magnetizations (which are the state variables encoding information) with electrically generated static or time-varying mechanical strain to elicit myriad functionalities. This approach has two advantages. First, information can be retained in the devices after powering off since the nanomagnets are nonvolatile unlike charge-based devices, such as transistors. Second, the energy expended to perform a given task is exceptionally low since it takes very little energy to alter magnetization states with strain. This field is now known as “straintronics,” in analogy with electronics, spintronics, valleytronics, etc., although it pertains specifically to “magnetic” straintronics and excludes phenomena involving non-magnetic systems. We review the recent advances and trends in straintronics, including digital information processing (logic), information storage (memory), domain wall devices operated with strain, control of skyrmions with strain, non-Boolean computing and machine learning with straintronics, signal generation (microwave sources) and communication (ultra-miniaturized acoustic and electromagnetic antennas) implemented with strained nanomagnets, hybrid straintronics–magnonics, and interaction between phonons and magnons in straintronic systems. We identify key challenges and opportunities, and lay out pathways to advance this field to the point where it might become a mainstream technology for energy-efficient systems.

High-frequency spin wave modes excited by strain pulse in vortex state magnetostrictive nanomagnets

Using micromagnetic simulations, we find that the high frequency spin wave modes of vortexes in circular magnetostrictive nanomagnets can be excited by in-plane strain pulses, which are quite distinct from the spin wave modes excited by magnetic field pulses. The spectrum and spatial distribution of spin wave modes are obtained as a function of the diameter (D) and thickness (L) of nanomagnets. Our results show that the increase in diameter leads to a redshift of the frequencies of spin wave modes. Furthermore, we investigate the impact of ring shape impurities on the high frequency spin wave modes, and it is found that both the type and position of impurities can be used to tailor the strain induced spin wave spectroscopy of magnetic vortexes. Our findings provide meaningful guidelines for the further study of strain-mediated sub-nanosecond magnetization dynamics, which may obviously improve the operating frequency of straintronic devices.

Simulated annealing with surface acoustic wave in a dipole-coupled array of magnetostrictive nanomagnets for collective ground state computing

There is significant current interest in using arrays of interacting nanomagnets as efficient hardware platforms to solve difficult computational problems such as image processing, computer vision or combinatorial optimization. Problem variables are encoded in the magnetization states of the nanomagnets and the array is allowed to relax to the ground state, wherein the magnetic order represents the solution to the problem. This strategy is energy-frugal and ultrafast, since it does not involve software (executing instruction sets), but unfortunately it fails if the system gets stuck in a metastable state from which it cannot escape to the ground state. Here, we demonstrate, in a small system of dipole-coupled 3 × 3 array of magnetostrictive nanomagnets fabricated on a piezoelectric substrate, how the system can be driven out of the metastable state into the ground state with a surface acoustic wave. This process emulates ‘simulated annealing’, which is a well-known algorithm of finding the optimal solution of a function (representing the ground state) by driving the function out of a sub-optimal solution (representing a metastable state) by following a sequence of steps.

Extreme Subwavelength Magnetoelastic Electromagnetic Antenna Implemented with Multiferroic Nanomagnets

AbstractAntennas typically have emission/radiation efficiencies bounded by A/λ2(A < λ2) where A is the emitting area and λ is the emitted wavelength. That makes it challenging to miniaturize antennas to extreme subwavelength dimensions without severely compromising their efficiencies. To overcome this challenge, an electromagnetic (EM) antenna is actuated with a surface acoustic wave (SAW) whose wavelength is about five orders of magnitude smaller than the EM wavelength at the same frequency. This allows to implement an extreme subwavelength EM antenna, radiating an EM wave of wavelength λ = 2 m, whose emitting area is ≈10−8 m2 (A/λ2 = 2.5 × 10−9), and whose measured radiation efficiency exceeds the A/λ2 limit by over 105. The antenna consists of magnetostrictive nanomagnets deposited on a piezoelectric substrate. A SAW launched in the substrate with an alternating electrical voltage periodically strains the nanomagnets and rotates their magnetizations owing to the Villari effect. The oscillating magnetizations emit EM waves at the frequency of the SAW. These extreme subwavelength antennas that radiate with efficiencies a few orders of magnitude larger than the A/λ2 limit allow drastic miniaturization of communication systems.

Experimental Demonstration of an Extreme Subwavelength Nanomagnetic Acoustic Antenna Actuated by Spin–Orbit Torque from a Heavy Metal Nanostrip

AbstractA novel on‐chip extreme subwavelength “acoustic antenna” whose radiation efficiency is ≈50 times larger than the theoretical limit for a resonantly driven antenna is demonstrated. The antenna is composed of magnetostrictive nanomagnets deposited on a piezoelectric substrate. The nanomagnets are partially in contact with a heavy metal (Pt) nanostrip. Passage of alternating current through the nanostrip exerts alternating spin–orbit torque on the nanomagnets and periodically rotates their magnetizations. During the rotation, the magnetostrictive nanomagnets expand and contract, thereby setting up alternating tensile and compressive strain in the piezoelectric substrate underneath. This leads to the generation of a surface acoustic wave in the substrate and makes the nanomagnet assembly act as an acoustic antenna. The measured radiation efficiency of this acoustic antenna at the detected frequency is ≈1%, while the wavelength to antenna dimension ratio is ≈67:1. For a standard antenna driven at acoustic resonance, the efficiency would have been limited to ≈(1/67)2 = 0.02%. It became possible to beat that limit (by ≈50 times) via actuating the antenna not at acoustic resonance, but by using a completely different mechanism involving spin–orbit torque originating from the giant spin Hall effect in Pt.

Resonant acoustic wave assisted spin-transfer-torque switching of nanomagnets

We report the possibility of achieving an order of magnitude reduction in the energy dissipation needed to write bits in perpendicular magnetic tunnel junctions by simulating the magnetization dynamics under a combination of resonant surface acoustic waves (r-SAWs) and spin-transfer-torque (STT). The magnetization dynamics were simulated using the Landau-Lifshitz-Gilbert equation under macrospin assumption with the inclusion of thermal noise. The resonant magnetization dynamics in the magnetostrictive nanomagnet builds over few tens of cycles of SAW application that drives the magnetization to precess in a cone with a deflection of ∼45° from the perpendicular direction. This reduces the STT current density required to switch the magnetization direction without increasing the STT application time or degrading the switching probability in the presence of room temperature thermal noise. This could lead to a pathway to achieve energy efficient switching of spin-transfer-torque random access memory whose lateral dimensions can be scaled aggressively despite using materials with low magnetostriction by employing SAW excitation to drive ferromagnetic resonance.

Electric field driven multi-state magnetization switching in triangular nanomagnets on piezoelectric substrate

Electric field control of magnetic state switching mediated by magneto-elastic coupling in multiferroic heterostructures consisting of shape anisotropic magnetostrictive nanomagnets elastically coupled with a piezoelectric substrate has a promising potential for next generation magneto-elastic memory and logic devices. In this work, by using micromagnetic simulation, we showed that localized strain-induced magnetic anisotropy caused by the electric field-induced piezostrain combined with strong multifold shape anisotropy effect can be used for achieving a multistate switching of magnetization in a triangular soft magnetic nano-island on a piezoelectric substrate. A piezostrain-induced uniaxial magnetic anisotropy pulse applied in specific directions switches the magnetization within the triangular nanomagnet by an angle of 60° from the initial state. The relation between critical magnitude of the strain pulse for the switching of the magnetization states and geometric parameters (thickness and lateral size) within the triangular nanomagnets has been worked out. Complete cycles of clockwise as well as counter-clockwise switching of the magnetization states of the triangular nanomagnet have been achieved by a series of sequential switching with different directions of applied strain-induced magnetic anisotropy. This local gating scheme-based multistate switching can be used for electric field-induced ultra-fast, deterministic and reversible magnetization switching which are the key challenges in designing of the magnetoelastic and/or magnetoelectric memory and logic devices.

Hybrid Magnetodynamical Modes in a Single Magnetostrictive Nanomagnet on a Piezoelectric Substrate Arising from Magnetoelastic Modulation of Precessional Dynamics.

Magnetoelastic (or "straintronic") switching has emerged as an extremely energy-efficient mechanism for switching the magnetization of magnetostrictive nanomagnets in magnetic memory and logic, and non-Boolean circuits. Here, we investigate the ultrafast magnetodynamics associated with straintronic switching in a single quasielliptical magnetostrictive Co nanomagnet deposited on a piezoelectric Pb(Mg1/3Nb2/3)O3-PbTiO3 substrate using time-resolved magneto-optical Kerr effect (TR-MOKE) measurements. The pulsed laser pump beam in the TR-MOKE plays a dual role: it causes precession of the nanomagnet's magnetization about an applied bias magnetic field and it also generates surface acoustic waves in the piezoelectric substrate that produce periodic strains in the magnetostrictive nanomagnet and modulate the precessional dynamics. This modulation gives rise to intriguing hybrid magnetodynamical modes in the nanomagnet, with a rich spin-wave texture. The characteristic frequencies of these modes are 5-15 GHz, indicating that strain can affect magnetization in a magnetostrictive nanomagnet in time scales much smaller than 1 ns (∼100 ps). This can enable ∼10 GHz range magnetoelastic nano-oscillators that are actuated by strain instead of a spin-polarized current, as well as ultrafast magnetoelectric generation of spin waves for magnonic logic circuits, holograms, etc.

Magneto-elastic switching of magnetostrictive nanomagnets with in-plane anisotropy: the effect of material defects

We theoretically study the effect of a material defect (material void) on switching errors associated with magneto-elastic switching of magnetization in elliptical magnetostrictive nanomagnets having in-plane magnetic anisotropy. We find that the error probability increases significantly in the presence of the defect, indicating that magneto-elastic switching is particularly vulnerable to material imperfections. Curiously, there is a critical stress value that gives the lowest error probability in both defect-free and defective nanomagnets. The critical stress is much higher in defective nanomagnets than in defect-free ones. Since it is more difficult to generate the critical stress in small nanomagnets than in large nanomagnets (having the same energy barrier for thermal stability), it would be a challenge to downscale magneto-elastically switched nanomagnets in memory and other applications where reliable switching is required. This is likely to be further exacerbated by the presence of defects.

Experimental Demonstration of Complete 180° Reversal of Magnetization in Isolated Co Nanomagnets on a PMN-PT Substrate with Voltage Generated Strain.

Rotating the magnetization of a shape anisotropic magnetostrictive nanomagnet with voltage-generated stress/strain dissipates much less energy than most other magnetization rotation schemes, but its application to writing bits in nonvolatile magnetic memory has been hindered by the fundamental inability of stress/strain to rotate magnetization by full 180°. Normally, stress/strain can rotate the magnetization of a shape anisotropic elliptical nanomagnet by only up to 90°, resulting in incomplete magnetization reversal. Recently, we predicted that applying uniaxial stress sequentially along two different axes that are not collinear with the major or minor axis of the elliptical nanomagnet will rotate the magnetization by full 180°. Here, we demonstrate this complete 180° rotation in elliptical Co nanomagnets (fabricated on a piezoelectric substrate) at room temperature. The two stresses are generated by sequentially applying voltages to two pairs of shorted electrodes placed on the substrate such that the line joining the centers of the electrodes in one pair intersects the major axis of a nanomagnet at ∼ +30° and the line joining the centers of the electrodes in the other pair intersects at ∼ -30°. A finite element analysis has been performed to determine the stress distribution underneath the nanomagnets when one or both pairs of electrodes are activated, and this has been approximately incorporated into a micromagnetic simulation of magnetization dynamics to confirm that the generated stress can produce the observed magnetization rotations. This result portends an extremely energy-efficient nonvolatile "straintronic" memory technology predicated on writing bits in nanomagnets with electrically generated stress.

Ultralow Energy Analog Straintronics Using Multiferroic Composites

Electric field-induced magnetization switching in multiferroics holds profound promise for ultra-low-energy computing in beyond Moore's law era. Bistable nanomagnets in the multiferroics are usually deemed to be suitable for storing a binary bit of information and switching between the two stable states allows us to process digital information. However, it requires to process continuous analog signals too for seamless integration of nanomagnetic devices in our future information processing systems. Here, we show that it is possible to harness the analog nature in the magnetostrictive nanomagnets, contrary to writing a digital bit of information. By solving stochastic Landau-Lifshitz-Gilbert equation of magnetization dynamics at room-temperature, we demonstrate such possibility and show that there exists a transistor-like high-gain region in the input-output characteristics of the magnetostrictive nanomagnets in strain-mediated multiferroic composites. This can be the basis of ultra-low-energy analog and mixed signal precessing in our future information processing systems and it eliminates the requirement of using charge-based transistors.

Incoherent magnetization dynamics in strain mediated switching of magnetostrictive nanomagnets

Micromagnetic studies of the magnetization change in magnetostrictive nanomagnets subjected to stress are performed for nanomagnets of different sizes. The interplay between demagnetization, exchange and stress anisotropy energies is used to explain the rich physics of size-dependent magnetization dynamics induced by modulating stress anisotropy in planar nanomagnets. These studies have important implications for strain mediated ultralow energy magnetization control in nanomagnets and its application in energy-efficient nanomagnetic computing devices.

Experimental demonstration of acoustic wave induced magnetization switching in dipole coupled magnetostrictive nanomagnets for ultralow power computing

Dipole-coupled cobalt nanomagnet pairs of elliptical shape (with their major axes parallel) are delineated on 128° Y-cut lithium niobate. Each pair is initially magnetized along the major axis with a magnetic field forming the (↑↑) state. When an acoustic wave (AW) is launched in the substrate from interdigitated electrodes, the softer nanomagnet in the pair flips to produce the (↑↓) state since the AW modulates the stress anisotropy. This executes the logical NOT operation because the output bit encoded in the magnetization state of the softer nanomagnet becomes the logic complement of the input bit encoded in the magnetization of the harder one. The AW acts as a clock to trigger the NOT operation and the energy dissipated is a few tens of aJ. Such AW clocking can be utilized to flip nanomagnets in a chain sequentially to steer logic bits unidirectionally along a nanomagnetic logic wire with miniscule energy dissipation.

Ultra-Low-Energy Electric Field-Induced Magnetization Switching in Multiferroic Heterostructures

Electric field-induced magnetization switching in multiferroics is intriguing for both fundamental studies and potential technological applications. Here, we review the recent developments on electric field-induced magnetization switching in multiferroic heterostructures. Particularly, we study the dynamics of magnetization switching between the two stable states in a shape-anisotropic single-domain nanomagnet using stochastic Landau–Lifshitz–Gilbert (LLG) equation in the presence of thermal fluctuations. For magnetostrictive nanomagnets in strain-coupled multiferroic composites, such study of magnetization dynamics, contrary to steady-state scenario, revealed intriguing new phenomena on binary switching mechanism. While the traditional method of binary switching requires to tilt the potential profile to the desired state of switching, we show that no such tilting is necessary to switch successfully since the magnetization’s excursion out of magnet’s plane can generate a built-in asymmetry during switching. We also study the switching dynamics in multiferroic heterostructures having magnetoelectric coupling at the interface and magnetic exchange coupling that can facilitate to maintain the direction of switching with the polarity of the applied electric field. We calculate the performance metrics like switching delay and energy dissipation during switching while simulating LLG dynamics. The performance metrics turn out to be very encouraging for potential technological applications.

Acoustic-Wave-Induced Magnetization Switching of Magnetostrictive Nanomagnets from Single-Domain to Nonvolatile Vortex States.

We report experimental manipulation of the magnetic states of elliptical cobalt magnetostrictive nanomagnets (with nominal dimensions of ∼340 nm × 270 nm × 12 nm) delineated on bulk 128° Y-cut lithium niobate with acoustic waves (AWs) launched from interdigitated electrodes. Isolated nanomagnets (no dipole interaction with any other nanomagnet) that are initially magnetized with a magnetic field to a single-domain state with the magnetization aligned along the major axis of the ellipse are driven into a vortex state by acoustic waves that modulate the stress anisotropy of these nanomagnets. The nanomagnets remain in the vortex state until they are reset by a strong magnetic field to the initial single-domain state, making the vortex state nonvolatile. This phenomenon is modeled and explained using a micromagnetic framework and could lead to the development of extremely energy efficient magnetization switching methodologies for low-power computing applications.

Dynamic Error in Strain-Induced Magnetization Reversal of Nanomagnets Due to Incoherent Switching and Formation of Metastable States: A Size-Dependent Study

Modulation of stress anisotropy of magnetostrictive nanomagnets with strain offers an extremely energy-efficient method of magnetization reversal. The reversal process, however, is often incoherent and hence error-prone in the presence of thermal noise at room temperature. Occurrence of incoherent metastable states in the potential landscape of the nanomagnet can further exacerbate the error. Stochastic micromagnetic simulations at room temperature are used to understand and calculate energy dissipations and switching error probabilities in this important magnetization switching methodology. We find that these quantities have an intriguing dependence on nanomagnet size: small nanomagnets perform better owing to the fact that they are more resilient to the formation of metastable states and magnetization dynamics in them is more coherent. However, for a fixed stress anisotropy energy density, smaller nanomagnets will also have poorer resilience against thermal instability. Thus, the challenge in straintronics is to maximize the stress anisotropy energy density by developing materials and processes that yield the largest magnetostriction.

Experimental Clocking of Nanomagnets with Strain for Ultralow Power Boolean Logic.

Nanomagnetic implementations of Boolean logic have attracted attention because of their nonvolatility and the potential for unprecedented overall energy-efficiency. Unfortunately, the large dissipative losses that occur when nanomagnets are switched with a magnetic field or spin-transfer-torque severely compromise the energy-efficiency. Recently, there have been experimental reports of utilizing the Spin Hall effect for switching magnets, and theoretical proposals for strain induced switching of single-domain magnetostrictive nanomagnets, that might reduce the dissipative losses significantly. Here, we experimentally demonstrate, for the first time that strain-induced switching of single-domain magnetostrictive nanomagnets of lateral dimensions ∼200 nm fabricated on a piezoelectric substrate can implement a nanomagnetic Boolean NOT gate and steer bit information unidirectionally in dipole-coupled nanomagnet chains. On the basis of the experimental results with bulk PMN-PT substrates, we estimate that the energy dissipation for logic operations in a reasonably scaled system using thin films will be a mere ∼1 aJ/bit.