Thin Film Nanomagnets Research Articles

Parametric resonance of spin waves in ferromagnetic nanowires tuned by spin Hall torque

We present a joint experimental and theoretical study of parametric resonance of spin wave eigenmodes in Ni$_{80}$Fe$_{20}$/Pt bilayer nanowires. Using electrically detected magnetic resonance, we measure the spectrum of spin wave eigenmodes in transversely magnetized nanowires and study parametric excitation of these eigenmodes by a microwave magnetic field. We also develop an analytical theory of spin wave eigenmodes and their parametric excitation in the nanowire geometry that takes into account magnetic dilution at the nanowire edges. We measure tuning of the parametric resonance threshold by antidamping spin Hall torque from a direct current for the edge and bulk eigenmodes, which allows us to independently evaluate frequency, damping and ellipticity of the modes. We find good agreement between theory and experiment for parametric resonance of the bulk eigenmodes but significant discrepancies arise for the edge modes. The data reveals that ellipticity of the edge modes is significantly lower than expected, which can be attributed to strong modification of magnetism at the nanowire edges. Our work demonstrates that parametric resonance of spin wave eigenmodes is a sensitive probe of magnetic properties at edges of thin-film nanomagnets.

Spin-transport Mediated Single-shot All-optical Magnetization Switching of Metallic Films

Ultrafast control of thin film nanomagnets using femtosecond laser pulses has attracted considerable attention for future ultrafast and energy-efficient photo-spintronics storage/memory devices. Si...

Interface-induced field-like optical spin torque in a ferromagnet/heavy metal heterostructure

Abstract The manipulation of magnetization in a metallic ferromagnet by using optical helicity has been much attracted attention for future opto-spintronic devices. The optical helicity–induced torques on the magnetization, optical spin torque, have been observed in ferromagnetic thin films recently. However, the interfacial effect of the optical spin torque in ferromagnet/nonmagnetic heavy metal heterostructures have not been addressed so far, which are widely utilized to efficiently control magnetization via electrical means. Here, we studied optical spin torque vectors in the ferromagnet/nonmagnetic heavy metal heterostructures and observed that in-plane field-like optical spin torque was significantly increased with decreasing ferromagnetic layer thicknesses. The interfacial field-like optical spin torque was explained by the optical Rashba–Edelstein effect caused by the structural inversion symmetry breaking. This work will aid in the efficient optical manipulation of thin film nanomagnets using optical helicity.

Electrical Tuning of Ferromagnetic Resonance in Thin-Film Nanomagnets Coupled to Piezoelectrically Active Substrates

In spintronics, electrical control of a ferromagnet could be achieved by integrating it onto a piezoelectrically active substrate. The authors describe theoretically such strain-mediated electric-field control of ferromagnetic resonance (FMR) in ultrathin-film nanomagnets. By calculating maps of FMR frequency and its electrical tunability, they show that the latter increases drastically at most spin-reorientation transitions driven by substrate-induced lattice strains. This feature provides efficient electrical control of FMR, which is necessary for developing signal-processing microwave devices with high tuning speed and low energy consumption.

Strain-Mediated Magnetization Reversal Through Spin-Transfer Torque

Recent experiments have shown the ability to introduce an anisotropy energy to the energy landscape of a thin-film nanomagnet through the use of mechanical strain. Assuming this strain-induced anisotropy is large enough, the low-energy state of the nanomagnet is altered and can be used to initialize the magnetization along a given axis. Utilizing this effect, we propose a more energy efficient method of nanomagnet reversal through spin-transfer torque (STT). This is accomplished by first initializing the magnetization to a high-energy state and then applying a short current pulse to nudge the magnetization in the appropriate energy basin. Using extensive numerical simulations, we qualitatively analyze this type of reversal and find the optimal parameters for reliable functionality while in the presence of thermal noise. We demonstrate that despite negating the initial portion of nominal STT reversal, where the STT must fight against the damping torque of the initial energy-basin, the magnitude of spin current required for our proposed strain-mediated reversal is equivalent to the nominal case. However, the strain-meditated reversal is beneficial by minimizing the spin-current pulsewidth necessary for reliable operation allowing for large energy savings. Assuming the strain-anisotropy is significantly larger than the nanomagnet’s internal free-axis anisotropy, strain-mediated reversals offer a ${10 \times }$ energy reduction over nominal STT reversals.

Tailoring the magnetic order in a supermagnetic metamaterial

The emergent magnetism in close-packed assemblies of interacting superparamagnetic particles is commonly referred to as supermagnetism. The magnetic characteristics of such systems are determined by the dipolar coupling between the nanomagnets, rather than the exchange interaction responsible for ferro- and antiferromagnetism in continuous material. The dipolar coupling facilitates tuning of the magnetism, which renders supermagnetic ensembles suitable model systems for exploration of new physics. In this work, we discuss micromagnetic simulations of regular arrays of thin film nanomagnets, with magnetic material parameters typical of the ferromagnetic oxide La0.7Sr0.3MnO3. The ground state supermagnetic order in these systems is primarily determined by the lattice configuration, in that a square lattice results in antiferromagnetic order, whereas a triangular lattice shows ferromagnetic order. We found that a square lattice of circular nanomagnets may be switched from superferromagnetic to superantiferromagnetic order by a small external field applied in the appropriate direction.

Non-monotonic probability of thermal reversal in thin-film biaxial nanomagnets with small energy barriers

The goal of this paper is to investigate the short time-scale, thermally-induced probability of magnetization reversal for an biaxial nanomagnet that is characterized with a biaxial magnetic anisotropy. For the first time, we clearly show that for a given energy barrier of the nanomagnet, the magnetization reversal probability of an biaxial nanomagnet exhibits a non-monotonic dependence on its saturation magnetization. Specifically, there are two reasons for this non-monotonic behavior in rectangular thin-film nanomagnets that have a large perpendicular magnetic anisotropy. First, a large perpendicular anisotropy lowers the precessional period of the magnetization making it more likely to precess across the x^=0 plane if the magnetization energy exceeds the energy barrier. Second, the thermal-field torque at a particular energy increases as the magnitude of the perpendicular anisotropy increases during the magnetization precession. This non-monotonic behavior is most noticeable when analyzing the magnetization reversals on time-scales up to several tens of ns. In light of the several proposals of spintronic devices that require data retention on time-scales up to 10’s of ns, understanding the probability of magnetization reversal on the short time-scales is important. As such, the results presented in this paper will be helpful in quantifying the reliability and noise sensitivity of spintronic devices in which thermal noise is inevitably present.

Reduced model for precessional switching of thin-film nanomagnets under the influence of spin torque

We study the magnetization dynamics of thin-film magnetic elements with in-plane magnetization subject to a spin-current flowing perpendicular to the film plane. We derive a reduced partial differential equation for the in-plane magnetization angle in a weakly damped regime. We then apply this model to study the experimentally relevant problem of switching of an elliptical element when the spin-polarization has a component perpendicular to the film plane, restricting the reduced model to a macrospin approximation. The macrospin ordinary differential equation is treated analytically as a weakly damped Hamiltonian system, and an orbit-averaging method is used to understand transitions in solution behaviors in terms of a discrete dynamical system. The predictions of our reduced model are compared to those of the full Landau--Lifshitz--Gilbert--Slonczewski equation for a macrospin.

Reliable spin-transfer torque driven precessional magnetization reversal with an adiabatically decaying pulse

We show that a slowly decaying current pulse can lead to nearly deterministic precessional switching in the presence of noise. We consider a biaxial macrospin, with an easy axis in the plane and a hard axis out-of-the plane, typical of thin film nanomagnets patterned into asymmetric shapes. Out-of-plane precessional magnetization orbits are excited with a current pulse with a component of spin polarization normal to the film plane. By numerically integrating the stochastic Landau-Lifshitz-Gilbert-Slonczewski equation we show that thermal noise leads to strong dephasing of the magnetization orbits. However, an adiabatically decreasing pulse amplitude overwhelmingly leads to magnetization reversal, with a final state that {\em only} depends on the pulse polarity, not on the pulse amplitude. We develop an analytic model to explain this phenomena and to determine the pulse decay time necessary for adiabatic magnetization relaxation and thus precessional magnetization switching.

Thermal Stability of Magnetic States in Circular Thin-Film Nanomagnets with Large Perpendicular Magnetic Anisotropy

The scaling of the energy barrier to magnetization reversal in thin-film nanomagnets with perpendicular magnetization as a function of their lateral size is of great interest and importance for high-density magnetic random access memory devices. Experimental studies of such elements show either a quadratic or linear dependence of the energy barrier 2 3 on element diameter. I will discuss a theoretical model we developed to determine the micromagnetic configurations that set the energy barrier for thermally activated reversal of a thin disk with perpendicular magnetic anisotropy as a function of disk diameter 4. We find a critical length in the problem that is set by the exchange and effective perpendicular magnetic anisotropy energies, with the latter including the size dependence of the demagnetization energy. For diameters smaller than this critical length, the reversal occurs by nearly coherent magnetization rotation and the energy barrier scales with the square of the diameter normalized to the critical length (for fixed film thickness), while for larger diameters, the transition state has a domain wall, and the energy barrier depends linearly on the normalized diameter. Simple analytic expressions are derived for these two limiting cases and verified using full micromagnetic simulations with the string method. Further, the effect of an applied field is considered and shown to lead to a plateau in the energy barrier versus diameter dependence at large diameters. Based on these finding I discuss the prospects and material challenges in the scaling of magnetic memory devices based on thin films with strong perpendicular magnetic anisotropy.

Micromagnetic study of spin transfer switching with a spin polarization tilted out of the free layer plane

We present the results of zero temperature macrospin and micromagnetic simulations of spin transfer switching of thin film nanomagnets in the shape of an ellipse with a spin-polarization tilted out of the layer plane. The perpendicular component of the spin-polarization is shown to increase the reversal speed, leading to a lower current for switching in a given time. However, for tilt angles larger than a critical angle, the layer magnetization starts to precess about an out-of-plane axis, which leads to a final magnetization state that is very sensitive to simulation conditions. As the ellipse lateral size increases, this out-of-plane precession is suppressed, due to the excitation of spatially non-uniform magnetization modes.

Energy barriers to magnetization reversal in perpendicularly magnetized thin film nanomagnets

Understanding the stability of thin film nanomagnets with perpendicular magnetic anisotropy (PMA) against thermally induced magnetization reversal is important when designing perpendicularly magnetized patterned media and magnetic random access memories. The magnetization reversal rate depends primarily on the energy barrier the system needs to surmount in order for reversal to proceed. In this paper, we study the reversal dynamics of these systems and compute the relevant barriers using the string method of E, Vanden-Eijnden, and Ren. We find the reversal to be often spatially incoherent; that is, rather than all parts of the element switching simultaneously, reversal proceeds instead through a soliton-like domain wall sweeping through the system. We show that for square nanomagnetic elements, the energy barrier increases with element size up to a critical length scale, beyond which the energy barrier is constant. For circular elements, the energy barrier continues to increase indefinitely, albeit more slowly beyond a critical size. In both cases, the energy barriers are smaller than those expected for coherent magnetization reversal.

Minimum action paths for spin-torque assisted thermally induced magnetization reversal

We calculate the most probable reaction paths for thermally induced magnetization reversal of a nanomagnet under the influence of spin transfer torque. The presence of the spin transfer torque implies that the standard reaction rate theory of Kramers cannot be used since the dynamics no longer shows detailed balance and so the magnetization reversals are nonequilibrium transitions. Thin film nanomagnets with a biaxial anisotropy, a shape anisotropy that leads to in-plane magnetization with a preferred axis in the plane, are considered. The reaction pathways and rates are computed using geometrical Minimum Action Method. Our results indicate that the transition state has an out-of-plane magnetization component, in contrast to the case without an applied spin transfer torque.

Spin-transfer pulse switching: From the dynamic to the thermally activated regime

The effect of thermal fluctuations on spin-transfer switching has been studied for a broad range of time scales (subnanoseconds to seconds) in a model system, a uniaxial thin film nanomagnet. The nanomagnet is incorporated into a spin-valve nanopillar, which is subject to spin-polarized current pulses of variable amplitude and duration. Two physical regimes are clearly distinguished: a long pulse duration regime, in which reversal occurs by spin-transfer assisted thermal activation over an energy barrier, and a short-time large pulse amplitude regime, in which the switching probability is determined by the spin-angular momentum in the current pulse.

Sidewall oxide effects on spin-torque- and magnetic-field-induced reversal characteristics of thin-film nanomagnets

The successful operation of spin-based data storage devices depends on thermally stable magnetic bits. At the same time, the data-processing speeds required by today's technology necessitate ultrafast switching in storage devices. Achieving both thermal stability and fast switching requires controlling the effective damping in magnetic nanoparticles. By carrying out a surface chemical analysis, we show that through exposure to ambient oxygen during processing, a nanomagnet can develop an antiferromagnetic sidewall oxide layer that has detrimental effects, which include a reduction in the thermal stability at room temperature and anomalously high magnetic damping at low temperatures. The in situ deposition of a thin Al metal layer, oxidized to completion in air, greatly reduces or eliminates these problems. This implies that the effective damping and the thermal stability of a nanomagnet can be tuned, leading to a variety of potential applications in spintronic devices such as spin-torque oscillators and patterned media.

Spin transfer by nonuniform current injection into a nanomagnet

We have used nanofabrication techniques to incorporate an ∼20–30nm diameter nanoaperture within a 150×250nm2 elliptical magnetic multilayer to enable the localized injection of spin-polarized currents into a thin film nanomagnet. This results in very low spin transfer currents being required for at least partial nanomagnet reversal as well as for onset of dynamic precession. Micromagnetic simulations using Landau-Liftshitz-Gilbert equation with a spin-torque term indicate that reversal occurs via domain nucleation at the injection site followed by domain wall propagation away from the aperture, with the nanomagnet ending in one of several different states depending upon the current amplitude.

Spin-transfer-induced precessional magnetization reversal

A magnetoelectronic device is proposed in which a spin-current pulse produces a rapid reversal of the magnetization of a thin film nanomagnet. A spin-transfer torque induces the reversal and the switching speed is determined by the precession frequency of the magnetization in a thin film element’s demagnetization field. Micromagnetic simulations show that this switching occurs above a threshold pulse current and can be faster than 50 ps. In contrast to present spin-transfer devices, the switching does not require an initial fluctuation or deviation of magnetic layers from collinear alignment and is far more energy efficient. This device operates at room temperature and can be realized with present-day magnetic nanostructure technology.

Angular dependence of spin-transfer switching in a magnetic nanostructure

We measured switching of a thin film nanomagnet driven by spin-polarized current in giant magnetoresistance spin valves as small as 50 nm×100 nm. Spin-transfer reversal is observed in both dc current and magnetic field sweeps, with a switching current of ∼5 mA, for example, for a bit with ∼900 Oe switching field in zero current. We studied the dependence of spin-transfer switching on the relative angle φ between the layer magnetizations by using a magnetic field to orient the magnetization of a bulk magnetic layer at an angle to a patterned layer held in place by shape anisotropy. The critical current is a minimum for collinear magnetizations and diverges as 1/|cos φ| as φ increases to 90°, consistent with switching current calculations using the Slonczewski spin-transfer torque model.

Spin-polarized current switching of a Co thin film nanomagnet

A thin film Co nanomagnet in the shape of an elongated hexagon has been incorporated in a vertical device structure consisting of the nanomagnet and a thin Cu spacer layer formed on top of a thick Co film. The spin-polarized current flowing between the nanomagnet and the Co film is used to abruptly switch the magnetic alignment of the nanomagnet relative to that of the thick Co layer by the transfer of spin angular momentum from the conduction electrons to the nanomagnet moment. The shape anisotropy in the nanomagnet promotes the single domain behavior required for nonvolatile memory applications.