Recent studies on magnetization dynamics induced by spin-orbit torque have revealed a weak dependence of the critical current for magnetization switching on the damping constant of a ferromagnetic free layer. This study, however, reveals that the damping constant nevertheless plays a key role in magnetization switching induced by spin-orbit torque. An undesirable switching, returning to an initial state, named as back switching, occurs in a ferromagnet with an easy axis parallel to the current direction. Numerical and theoretical analyses reveal that back switching is strongly suppressed when the damping constant of the ferromagnet is large.
In ferromagnetic trilayers, a spin-orbit-induced spin current can have a spin polarization of which direction is deviated from that for the spin Hall effect. Recently, magnetization switching in ferromagnetic trilayers has been proposed and confirmed by the experiments. In this work, we theoretically and numerically investigate the switching current required for perpendicular magnetization switching in ferromagnetic trilayers. We confirm that the tilted spin polarization enables field-free deterministic switching at a lower current than conventional spin-orbit torque or spin-transfer torque sw…
We use spin torque ferromagnetic resonance to measure the spectral properties of dipole-exchange spin waves in permalloy nanowires. Our measurements reveal that geometric confinement has a profound effect on the damping of spin waves in the nanowire geometry. The damping parameter of the lowest-energy quantized spin wave mode depends on applied magnetic field in a resonant way and exhibits a maximum at a field that increases with decreasing nanowire width. This enhancement of damping originates from a nonlinear resonant three-magnon confluence process allowed at a particular bias field value d…
We report time-resolved measurements of current-induced reversal of a free magnetic layer in Py/Cu/Py elliptical nanopillars at temperatures T = 4.2 K to 160 K. Comparison of the data to Landau-Lifshitz-Gilbert macrospin simulations of the free layer switching yields numerical values for the spin torque and the Gilbert damping parameters as functions of T. The damping is strongly T-dependent, which we attribute to the antiferromagnetic pinning behavior of a thin permalloy oxide layer around the perimeter of the free layer. This adventitious antiferromagnetic pinning layer can have a major impa…
We measure the magnetic damping parameter a in thin film CoFeB and permalloy (Py) nanomagnets at room temperature using ferromagnetic resonance driven by microwave frequency spin-transfer torque. We obtain $α_{CoFeB} = 0.014 \pm 0.003$ and $α_{Py}=0.010 \pm 0.002$, values comparable to measurements for extended thin films, but significantly less than the effective damping determined previously for similar nanomagnets by fits to time-domain studies of large-angle magnetic excitations and magnetic reversal. The greater damping found for the large amplitude nanomagnet dynamics is attributed to th…
Spin-transfer is a typical spintronics effect that allows a ferromagnetic layer to be switched by spin-injection. Most of the experimental results about spin transfer are described on the basis of the Landau-Lifshitz-Gilbert equation of the magnetization, in which additional current-dependent damping factors are added, and can be positive or negative. The origin of the damping can be investigated further by performing stochastic experiments, like one shot relaxation experiments under spin-injection in the activation regime of the magnetization. In this regime, the Néel-Brown activation law is …
In this paper, we investigate theoretically the spin-orbit torque as well as the Gilbert damping for a two band model of a 2D helical surface state with a Ferromagnetic (FM) exchange coupling. We decompose the density matrix into the Fermi sea and Fermi surface components and obtain their contributions to the electronic transport as well as the spin-orbit torque (SOT). Furthermore, we obtain the expression for the Gilbert damping due to the surface state of a 3D Topological Insulator (TI) and predicted its dependence on the direction of the magnetization precession axis.
We study spin-orbit-torque-driven ferromagnetic resonance (FMR) in ferromagnetic (FM) bilayers, consisting of Co and permalloy (Py), sandwiched between Pt and MgO layers. We find that the FM layer in contact with the Pt layers dominantly determines that spin Hall angle, which is consistent with the spin-transparency model. By contrast, the FMR linewidths are considerably influenced not only by the spin-pumping effect across the Pt|FM in terface but also by the spin relaxation such as two-magnon scattering at the FMMgO interface.The CoMgO interface leads to notably increased FMR linewidths, whi…
The magnetic properties of annealed, epitaxial Ga0.93Mn0.07As layers under tensile and compressive stress have been investigated by X-band (9GHz) and Q-band (35GHz) ferromagnetic resonance (FMR) spectroscopy. From the analysis of the linewidths of the uniform mode spectra the FMR Gilbert damping factor "alpha" has been determined. At T=4K we obtain a minimum damping factor of "alpha" = 0.003 for the compressively stressed layer. Its value is not isotropic. It has a minimum value for the easy axes orientations of the magnetic field and increases with the measuring temperature. Its average value…
The switching of magnetic layers is studied under the action of a spin current in a ferromagnetic metal/non-magnetic metal/ferromagnetic metal spin valve. We find that the main contribution to the switching comes from the non-equilibrium exchange interaction between the ferromagnetic layers. This interaction defines the magnetic configuration of the layers with minimum energy and establishes the threshold for a critical switching current. Depending on the direction of the critical current, the interaction changes sign and a given magnetic configuration becomes unstable. To model the time depen…
We propose a magnetization reversal model to explain the perpendicular switching of a single ferromagnetic layer induced by an in-plane current. Contrary to previously proposed reversal mechanisms that such magnetic switching is directly from the Rashba or spin Hall effects, we suggest that this type of switching arises from the current-induced chirality dependent domain wall motion. By measuring the field dependent switching behaviors, we show that such switching can also be achieved between any two multidomain states, and all of these switching behaviors can be well explained by this model. …
We study the spin dynamics of a ferromagnetic insulator on which graphene is placed. We show that the Gilbert damping is enhanced by the proximity exchange coupling at the interface. The modulation of the Gilbert damping constant is proportional to the product of the spin-up and spin-down densities of states of graphene. Consequently, the Gilbert damping constant in a strong magnetic field oscillates as a function of the external magnetic field that originates from the Landau level structure of graphene. We find that a measurement of the oscillation period enables the strength of the exchange …
We investigate the spin dynamics including Gilbert damping in the ferromagnetic nanowire arrays. We have measured the ferromagnetic resonance of ferromagnetic nanowire arrays using vector-network analyzer ferromagnetic resonance (VNA-FMR) and analyzed the results with the micromagnetic simulations. We find excellent agreement between the experimental VNA-FMR spectra and micromagnetic simulations result for various applied magnetic fields. We find that the demagnetization factor for longitudinal conditions, Nz (Ny) increases (decreases) as decreasing the nanowire width in the micromagnetic simu…
Using a scattering matrix approach, the precession of the magnetization of a ferromagnet is shown to transfer spins into adjacent normal metal layers. This ``pumping'' of spins slows down the precession corresponding to an enhanced Gilbert damping factor in the Landau-Lifshitz equation. The damping is expressed in terms of the scattering matrix of the ferromagnet-normal metal interface, which is accessible to model and first-principles calculations. Our estimates for permalloy thin films explain the trends observed in recent experiments.
The controlled switching between two quasi-stable Neel states in adsorbed anti-ferromagnetic Fe chains has recently been achieved by Loth et al [Science 335, 196 (2012)]. In order to rationalize their data, we evaluate the rate of tunneling electron-induced switching between the Néel states. Good agreement is found with the experiment permitting us to identify three switching mechanisms: (i) low-bias direct electron-induced transitions, (ii) intermediate-bias switching via spin-wave-like excitation, and (iii) high-bias transitions mediated by domain wall formation. Spin correlations in the ant…
We obtain the exact one-spin intrinsic localized excitation in an anisotropic Heisenberg ferromagnetic spin chain in a constant/variable external magnetic field with Gilbert damping included. We also point out how an appropriate magnitude spin current term in a spin transfer nano-oscillator (STNO) can stabilize the tendency towards damping. Further, we show how this excitation can be sustained in a recently suggested PT-symmetric magnetic nanostructure. We also briefly consider more general spin excitations.
We introduce a highly sensitive and relatively simple technique to observe magnetization motion in single Ni nanoparticles, based on charge sensing by electron tunneling at millikelvin temperature. Sequential electron tunneling via the nanoparticle drives nonequilibrium magnetization dynamics, which induces an effective charge noise that we measure in real time. In the free spin diffusion regime, where the electrons and magnetization are in detailed balance, we observe that magnetic damping time exhibits a peak with the magnetic field, with a record long damping time of $\simeq 10$~ms.
We present a theoretical study of the the effects of off-resonant polarized optical fields on a ferromagnetic model system. We determine the light-induced dynamics of itinerant carriers in a system that includes magnetism at the mean-field level and spin-orbit coupling. We investigate an all-optical switching process for ferromagnets, which is close to the one proposed by Qaiumzadeh et al. [Phys. Rev. B 88, 064416] for the inverse Faraday effect. By computing the optically driven coherent dynamics together with incoherent scattering mechanisms we go beyond a perturbation expansion in powers of…
The field dependence of the thermal switching rate of a ferromagnetic material with uniaxial anisotropy was studied by solving the Fokker-Planck equation. We derived the analytical expression of the thermal switching rate using the mean first-passage time approach, and found that Brown's formula [Phys. Rev. 130, 1677 (1963)] is applicable even in the low barrier limit by replacing the attempt frequency with the proper factor which is expressed by the error function.
Spin-orbit torques (SOT) allow the electrical control of magnetic states. Current-induced SOT switching of the perpendicular magnetization is of particular technological importance. The SOT consists of damping-like and field-like torques so that the efficient SOT switching requires to understand combined effects of the two torque-components. Previous quasi-static measurements have reported an increased switching probability with the width of current pulses, as predicted with considering the damping-like torque only. Here we report a decreased switching probability at longer pulse-widths, based…
We compute the Gilbert damping in (Ga,Mn)As based on the scattering theory of magnetization relaxation. The disorder scattering is included non-perturbatively. In the clean limit, the spin-pumping from the localized d-electrons to the itinerant holes dominates the relaxation processes. In the diffusive regime, the breathing Fermi-surface effect is balanced by the effects of interband scattering, which cause the Gilbert damping constant to saturate at around 0.005. In small samples, the system shape induces a large anisotropy in the Gilbert damping.
We have measured the size effect in nonlocal Gilbert relaxation rate in FM(t$_{FM}$) / Cu (5nm) [/ Pt (2nm)] / Al(2nm) heterostructures, FM = \{ Ni$_{81}$Fe$_{19}$, Co$_{60}$Fe$_{20}$B$_{20}$, pure Co\}. Common behavior is observed for three FM layers, where the additional relaxation obeys both a strict inverse power law dependence $ΔG =K \:t^{n}$, $n=-\textrm{1.04}\pm\textrm{0.06}$ and a similar magnitude $K=\textrm{224}\pm\textrm{40 Mhz}\cdot\textrm{nm}$. As the tested FM layers span an order of magnitude in spin diffusion length $λ_{SDL}$, the results are in support of spin diffusion, rathe…
As an alternative to conventional magnetic field, the effective spin-orbit field in transition metals, derived from the Rashba field experienced by itinerant electrons confined in a spatial inversion asymmetric plane through the s-d exchange interaction, is proposed for the manipulation of magnetization. Magnetization switching in ferromagnetic thin films with perpendicular magnetocrystalline anisotropy can be achieved by current induced spin-orbit field, with small in-plane applied magnetic field. Spin-orbit field induced by current pulses as short as 10 ps can initiate ultrafast magnetizatio…
Spin dynamics of a metallic ferromagnetic film imbedded between normal metal layers is studied using the spin-pumping theory of Tserkovnyak et al. [Phys. Rev. Lett. 88, 117601 (2002)]. The scattering matrix for this structure is obtained using a spin-dependent potential with quantum well in the ferromagnetic region. Owing to multiple reflections in the well, the excess Gilbert damping and the gyromagnetic ratio exhibit quantum oscillations as a function of the thickness of the ferromagnetic film. The wavelength of the oscillations is given by the depth of the quantum well. For iron film imbedd…
We investigate the Gilbert damping and the magnetization switching of perpendicularly magnetized FeCoB-based free layers embedded in tunnel junctions adequate for spin-torque operated memories. We study the influence of the boron content in MgO / FeCoB /Ta systems alloys on their Gilbert damping after crystallization annealing. Increasing the boron content from 20 to 30\% increases the crystallization temperature, thereby postponing the onset of elemental diffusion within the free layer. This reduction of the interdiffusion of the Ta atoms helps maintaining the Gilbert damping at a low level o…
Ferromagnetic resonance (FMR) was used to investigate the static and dynamic magnetic properties of carbon-doped Mn5Ge3 (C$_{0.1}$ and C$_{0.2}$) thin films grown on Ge(111). The temperature dependence of magnetic anisotropy shows an increased perpendicular magneto-crystalline contribution at 80K with an in-plane easy axis due to the large shape contribution. We find that our samples show a small FMR linewidth (corresponding to an intrinsic magnetic damping parameter $α$=0.005), which is a measure of the spin relaxation and directly related with the magnetic and structural quality of the mater…
Detailed understanding of spin dynamics in magnetic nanomaterials is necessary for developing ultrafast, low-energy and high-density spintronic logic and memory. Here, we develop micromagnetic models and analytical solutions to elucidate the effect of increasing damping and uniaxial anisotropy on magnetic field pulse-assisted switching time, energy and field requirements of nanowires with perpendicular magnetic anisotropy and yttrium iron garnet-like spin transport properties. A nanowire is initially magnetized using an external magnetic field pulse (write) and self-relaxation. Next, magnetic …
In a number of recent experiments, it has been shown that femtosecond laser pulses can control magnetization on picosecond timescales, which is at least an order of magnitude faster compared to conventional magnetization dynamics. Among these demonstrations, one material system (GdFeCo ferromagnetic films) is particularly interesting, as deterministic toggle-switching of the magnetic order has been achieved without the need of any symmetry breaking magnetic field. This phenomenon is often referred to as all optical switching (AOS). However, so far, GdFeCo remains the only material system where…
We determined the spin-transport properties of Pd and Pt thin films by measuring the increase in ferromagnetic resonance damping due to spin-pumping in ferromagnetic (FM)-nonferromagnetic metal (NM) multilayers with varying NM thicknesses. The increase in damping with NM thickness depends strongly on both the spin- and charge-transport properties of the NM, as modeled by diffusion equations that include both momentum- and spin-scattering parameters. We use the analytical solution to the spin-diffusion equations to obtain spin-diffusion lengths for Pt and Pd. By measuring the dependence of cond…
Flexible control of magnetization switching by electrical manners is crucial for applications of spin-orbitronics. Besides of a switching current that is parallel to an applied field, a bias current that is normal to the switching current is introduced to tune the magnitude of effective damping-like and field-like torques and further to electrically control magnetization switching. Symmetrical and asymmetrical control over the critical switching current by the bias current with opposite polarities is both realized in Pt/Co/MgO and $α$-Ta/CoFeB/MgO systems, respectively. This research not only …
The Gilbert damping of ferromagnetic materials is arguably the most important but least understood phenomenological parameter that dictates real-time magnetization dynamics. Understanding the physical origin of the Gilbert damping is highly relevant to developing future fast switching spintronics devices such as magnetic sensors and magnetic random access memory. Here, we report an experimental study of temperature-dependent Gilbert damping in permalloy (Py) thin films of varying thicknesses by ferromagnetic resonance. From the thickness dependence, two independent contributions to the Gilbert…
We theoretically investigate the switching of a perpendicular magnetic layer by in-plane charge current due to the spin Hall effect. We find that, in the high damping regime, the threshold switching current is independent of the damping constant, and is almost linearly proportional to both effective perpendicular magnetic anisotropy field and external in-plane field applied along the current direction. We obtain an analytic expression of the threshold current, in excellent agreement with numerical results. This expression can be used to determine the physical quantities associated with spin Ha…
Ferromagnetic resonance in thin films is analyzed under the influence of spatiotemporal feedback effects. The equation of motion for the magnetization dynamics is nonlocal in both space and time and includes isotropic, anisotropic and dipolar energy contributions as well as the conserved Gilbert- and the non-conserved Bloch-damping. We derive an analytical expression for the peak-to-peak linewidth. It consists of four separate parts originated by Gilbert damping, Bloch-damping, a mixed Gilbert-Bloch component and a contribution arising from retardation. In an intermediate frequency regime the …
Levitated nanoparticles and microparticles are excellent candidates for the realization of extremely isolated mechanical systems, with a huge potential impact in sensing applications and in quantum physics. Magnetic levitation based on static fields is a particularly interesting approach, due to the unique property of being completely passive and compatible with low temperatures. Here, we show experimentally that micromagnets levitated above type-I superconductors feature very low damping at low frequency and low temperature. In our experiment, we detect 5 out of 6 rigid-body mechanical modes …
We show that Co spins in Co/FeRh epitaxial bilayers grown on W(110) switch reversibly between the two orthogonal in-plane directions as the FeRh layer undergoes temperature driven antiferromagnetic-ferromagnetic (AFM-FM) phase transition. Switching of Co magnetization is characterized by a hysteretic behavior owing to a temperature hysteresis of the AFM-FM transition in FeRh. The spin reorientation of Co is driven by the evolution interfacial exchange coupling to FeRh system across the AFM-FM process. Our results provide a new method of writing information purely by a local temperature change.
Deterministic current-induced spin-orbit torque (SOT) switching of magnetization in a heavy transition metal/ferromagnetic metal/oxide magnetic heterostructure with the ferromagnetic layer being perpendicularly-magnetized typically requires an externally-applied in-plane field to break the switching symmetry. We show that by inserting an in-plane magnetized ferromagnetic layer CoFeB underneath the conventional W/CoFeB/MgO SOT heterostructure, deterministic SOT switching of the perpendicularly-magnetized top CoFeB layer can be realized without the need of in-plane bias field. Kerr imaging study…
Vortex core polarity switching in NiFe disks has been evidenced using an all-electrical rectification scheme. Both simulation and experiments yield a consistent loss of the rectified signal when driving the core at high powers near its gyrotropic resonant frequency. The frequency range over which the loss occurs grows and shifts with increasing signal power, consistent with non-linear core dynamics and periodic switching of the core polarity induced by the core attaining its critical velocity. We demonstrate that core polarity switching can be impeded by displacing the core towards the disk's …
We analytically determine the optimal microwave field that allows for the magnetization reversal of a nanomagnet modeled as a macrospin. This is done by minimizing the total injected energy. The results are in good agreement with the fields obtained numerically using the optimal control theory. For typical values of the damping parameter, a weak microwave field is sufficient to induce switching through a resonant process. The optimal field is orthogonal to the magnetization direction at any time and modulated both in amplitude and frequency. The dependence of the pulse shape on the applied fie…
Magnetization reversal of a perpendicular ferromagnetic free layer by spin-orbit torque (SOT) is an attractive alternative to spin-transfer torque (STT) switching in magnetic random-access memory (MRAM) where the write process involves passing a high current across an ultrathin tunnel barrier. A small symmetry-breaking bias field is usually needed for deterministic SOT switching but it is impractical to generate the field externally for spintronic applications. Here, we demonstrate robust zero-field SOT switching of a perpendicular Co90Fe10 (CoFe) free layer where the symmetry is broken by mag…
Using the Landau-Lifshitz-Bloch (LLB) equation for ferromagnetic materials, we derive analytic expressions for temperature dependent absorption spectra as probed by ferromagnetic resonance (FMR). By analysing the resulting expressions, we can predict the variation of the resonance frequency and damping with temperature and coupling to the thermal bath. We base our calculations on the technologically relevant L1$_0$ FePt, parameterised from atomistic spin dynamics simulations, with the Hamiltonian mapped from ab-initio parameters. By constructing a multi-macrospin model based on the LLB equatio…
Dynamics of magnetic vortex core switching in nanometer-scale permalloy disk, having a single vortex ground state, was investigated by micromagnetic modeling. When an in-plane magnetic field pulse with an appropriate strength and duration is applied to the vortex structure, additional two vortices, i.e., a circular- and an anti-vortex, are created near the original vortex core. Sequentially, the vortex-antivortex pair annihilates. A spin wave is created at the annihilation point and propagated through the entire element; the relaxed state for the system is the single vortex state with a switch…
Electrical current manipulation of magnetization switching through spin-orbital coupling in ferromagnetic semiconductor (Ga,Mn)As Hall bar devices has been investigated. The efficiency of the current-controlled magnetization switching is found to be sensitive to the orientation of the current with respect to the crystalline axes. The dependence of the spin-orbit effective magnetic field on the direction and magnitude of the current is determined from the shifts in the magnetization switching angle. We find that the strain induced effective magnetic field is about three times as large as the Ra…
We report ultra-low intrinsic magnetic damping in Co$_{\text{25}}$Fe$_{\text{75}}$ heterostructures, reaching the low $10^{-4}$ regime at room temperature. By using a broadband ferromagnetic resonance technique, we extracted the dynamic magnetic properties of several Co$_{\text{25}}$Fe$_{\text{75}}$-based heterostructures with varying ferromagnetic layer thickness. By estimating the eddy current contribution to damping, measuring radiative damping and spin pumping effects, we found the intrinsic damping of a 26\,nm thick sample to be $$α_{\mathrm{0}} \lesssim 3.18\times10^{-4}$. Furthermore, u…
Current induced magnetization dynamics in asymmetric Cu/Co/Cu single magnetic layer nanopillars has been studied experimentally at room temperature and in low magnetic fields applied perpendicular to the thin film plane. In sub-100 nm junctions produced using a nanostencil process a bistable state with two distinct resistance values is observed. Current sweeps at fixed applied fields reveal hysteretic and abrupt transitions between these two resistance states. The current induced resistance change is 0.5%, a factor of 5 greater than the anisotropic magnetoresistance (AMR) effect. We present an…
We develop a theory of the reversible switching of the magnetic state of the ferromagnet-insulator-normal metalferromagnet (FINF) nanostructure. The switching is controlled by tuning the Coulomb blockade strength via the gate voltage on the normal metal granule. The proposed mechanism allows for realizing the switching without passing a dissipative current through the structure.
All-optical magnetic switching promises ultrafast, high-resolution magnetisation control with the technological attraction of requiring no magnetic field. Existing all-optical switching schemes are driven by ultrafast transient effects, typically requiring power-hungry femtosecond-pulsed lasers and complex magnetic materials. Here, we demonstrate deterministic, all-optical magnetic switching in simple ferromagnetic nanomagnets (Ni$_{81}$Fe$_{19}$, Ni$_{50}$Fe$_{50}$) with sub-diffraction limit dimensions using a focused low-power, linearly-polarised continuous-wave laser. Isolated nanomagnets …
We discuss the effects of thermal noise on the magnetic response of a lateral ferromagnetic Josephson junction with spin-orbit coupling and out-of-plane magnetization. The direction of the magnetic moment in the ferromagnetic layer can be inverted by using controlled current pulses. This phenomenon is due to the magnetoelectric effect that couples the flowing charge current and the magnetization of the ferromagnet. We investigate the magnetization reversal effect versus intrinsic parameters of the ferromagnet, such as the Gilbert damping and strength of the spin-orbit coupling. We estimate the…
We study the switching-process of the magnetization in a ferromagnetic-normal-metal multilayer system by a spin polarized electrical current via the spin transfer torque. We use a spin drift-diffusion equation (SDDE) and the Landau-Lifshitz-Gilbert equation (LLGE) to capture the coupled dynamics of the spin density and the magnetization dynamic of the heterostructure. Deriving a fully analytic solution of the stationary SDDE we obtain an accurate, robust, and fast self-consistent model for the spin-distribution and spin transfer torque inside general ferromagnetic/normal metal heterostructures…
We present magnetoresistance (MR) experiments on an InAs nanowire quantum dot device with two ferromagnetic sidegates (FSGs) in a split-gate geometry. The wire segment can be electrically tuned to a single dot or to a double dot regime using the FSGs and a backgate. In both regimes we find a strong MR and a sharp MR switching of up to 25\% at the field at which the magnetizations of the FSGs are inverted by the external field. The sign and amplitude of the MR and the MR switching can both be tuned electrically by the FSGs. In a double dot regime close to pinch-off we find {\it two} sharp trans…
Power dissipation in switching devices is believed to be the single most important roadblock to the continued down scaling of electronic circuits. There is a lot of experimental effort at this time to implement switching circuits based on magnets and it is important to establish power requirements for such circuits and their dependence on various parameters. This paper analyzes switching energy which is dissipated in the switching process of single domain Ferromagnets used as cascadable logic bits. We obtain generic results that can be used for comparison with alternative technologies or guide…
