We have studied thermally driven magnon spin transport (spin Seebeck effect, SSE) in heterostructures of antiferromagnetic $α$-$\mathrm{Cr_2O_3}$ and Pt at low temperatures. Monitoring the amplitude of the local and nonlocal SSE signals as a function of temperature, we found that both decrease with increasing temperature and disappear above 100 K and 20 K, respectively. Additionally, both SSE signals show a tendency to saturate at low temperatures. The nonlocal SSE signal decays exponentially for intermediate injector-detector separation, consistent with magnon spin current transport in the relaxation regime. We estimate the magnon relaxation length of our $α$-$\mathrm{Cr_2O_3}$ films to be around 500 nm at 3 K. This short magnon relaxation length along with the strong temperature dependence of the SSE signal indicates that temperature-dependent inelastic magnon scattering processes play an important role in the intermediate range magnon transport. Our observation is relevant to low-dissipation antiferromagnetic magnon memory and logic devices involving thermal magnon generation and transport.
We have experimentally studied the role of thermoelectric effects in nanoscale nonlocal spin valve devices. A finite element thermoelectric model is developed to calculate the generated Seebeck voltages due to Peltier and Joule heating in the devices. By measuring the first, second and third harmonic voltage response non locally, the model is experimentally examined. The results indicate that the combination of Peltier and Seebeck effects contributes significantly to the nonlocal baseline resistance. Moreover, we found that the second and third harmonic response signals can be attributed to Jo…
We report a theoretical study on the spin and electron transport in the nonlocal lateral spin valve with non-collinear magnetic configuration. The nonlocal magnetoresistance, defined as the voltage difference on the detection lead over the injected current, is derived analytically. The spin transfer torques on the detection lead are calculated. It is found that spin transfer torques are symmetrical for parallel and antiparallel magnetic configurations, which is different from that in conventional sandwiched spin valve.
We investigate hot carrier propagation across graphene using an electrical nonlocal injection/detection method. The device consists of a monolayer graphene flake contacted by multiple metal leads. Using two remote leads for electrical heating, we generate a carrier temperature gradient that results in a measurable thermoelectric voltage VNL across the remaining (detector) leads. Due to the nonlocal character of the measurement, VNL is exclusively due to the Seebeck effect. Remarkably, a departure from the ordinary relationship between Joule power P and VNL, VNL ~ P, becomes readily apparent at…
The nonlocal transport of thermally generated magnons not only unveils the underlying mechanism of the spin Seebeck effect, but also allows for the extraction of the magnon relaxation length ($λ_m$) in a magnetic material, the average distance over which thermal magnons can propagate. In this study, we experimentally explore in yttrium iron garnet (YIG)/platinum systems much further ranges compared with previous investigations. We observe that the nonlocal SSE signals at long distances ($d$) clearly deviate from a typical exponential decay. Instead, they can be dominated by the nonlocal genera…
We report the nonlocal spin Seebeck effect (nlSSE) in a lateral configuration of Pt/Y$_3$Fe$_5$O$_{12}$(YIG)/Pt systems as a function of the magnetic field $B$ (up to 10 T) at various temperatures $T$ (3 K < $T$ < 300 K). The nlSSE voltage decreases with increasing $B$ in a linear regime with respect to the input power (the applied charge-current squared $I^2$). The reduction of the nlSSE becomes substantial when the Zeeman energy exceeds thermal energy at low temperatures, which can be interpreted as freeze-out of magnons relevant for the nlSSE. Furthermore, we found the non-linear power depe…
We performed measurements of Py/Cu and Py/Ag lateral spin valves as function of injection current direction and magnitude. Above a 'critical' current, there is an unexpected dependence of spin injection on current direction. Positive currents show higher polarization of spin injection than negative. This implies that in addition to current-induced spin injection, there is a thermally induced injection from a spin-dependent Seebeck effect. A temperature gradient in the Py electrode, caused by Joule heating, is responsible for injecting excess spins into the non-magnetic channel. This effect has…
We studied the nonlocal transport behavior of both electrically and thermally excited magnons in yttrium iron garnet (YIG) as a function of its thickness. For electrically injected magnons, the nonlocal signals decrease monotonically as the YIG thickness increases. For the nonlocal behavior of the thermally generated magnons, or the nonlocal spin Seebeck effect (SSE), we observed a sign reversal which occurs at a certain heater-detector distance, and it is influenced by both the opacity of the YIG/heater interface and the YIG thickness. Our nonlocal SSE results can be qualitatively explained b…
We study the nonlocal spin transport in a lateral spin valve with multiple ferromagnetic (FM) electrodes. When two current-injecting and two spin current-detecting electrodes are all ferromagnetic, the number of possible nonlocal spin signal states is four at maximum. In reality, this number is reduced, depending on the inter-probe distance and the relative magnitudes of the spin resistances. Our theoretical results are in agreement with recent experiments of spin injection into an Al island, a carbon nanotube, and graphene.
We study terahertz radiation induced ratchet currents in low dimensional semiconductor structures with a superimposed one-dimensional lateral periodic potential. The periodic potential is produced by etching a grating into the sample surface or depositing metal stripes periodically on the sample top. Microscopically, the photocurrent generation is based on the combined action of the lateral periodic potential, verified by transport measurements, and the in-plane modulated pumping caused by the lateral superlattice. We show that a substantial part of the total current is caused by the polarizat…
We discuss the phase dependent nonlocal thermoelectric effect in a topological Josephson junction in contact with a normal-metal probe. We show that, due to the helical nature of topological edge states, nonlocal thermoelectricity is generated by a purely Andreev interferometric mechanism. This response can be tuned by imposing a Josephson phase difference, through the application of a dissipationless current between the two superconductors, even without the need of applying an external magnetic field. We discuss in detail the origin of this effect and we provide also a realistic estimation of…
The abilities to inject and detect spin carriers are fundamental for research on transport and manipulation of spin information. Pure electronic spin currents have been recently studied in nanoscale electronic devices using a non-local lateral geometry, both in metallic systems and in semiconductors. To unlock the full potential of spintronics we must understand the interactions of spin with other degrees of freedom, going beyond the prototypical electrical spin injection and detection using magnetic contacts. Such interactions have been explored recently, for example, by using spin Hall or sp…
We study the effect of the ferromagnetic (FM) contacts on the spin accumulation in the lateral spin valve system for the collinear magnetization configurations. When an additional FM electrode is introduced in the all-metallic lateral spin-valve system, we find that the transresistance can be fractionally suppressed or very weakly influenced depending on the position of the additional FM electrode, and relative magnitudes of contact resistance and the bulk resistance defined over the spin diffusion length. Nonlocal spin signals such as nonlocal voltage drop and leakage spin currents are indepe…
Experimental and theoretical studies on ratchet effects in graphene with a lateral superlattice excited by alternating electric fields of terahertz frequency range are presented. A lateral superlatice deposited on top of monolayer graphene is formed either by periodically repeated metal stripes having different widths and spacings or by inter-digitated comb-like dual-grating-gate (DGG) structures. We show that the ratchet photocurrent excited by terahertz radiation and sensitive to the radiation polarization state can be efficiently controlled by the back gate driving the system through the Di…
Recently, several groups have reported spin-dependent thermoelectric effects in magnetic tunnel junctions. In this paper, we present a setup for time-resolved measurements of thermovoltages and thermocurrents of a single micro- to nanometer-scaled tunnel junction. An electrically modulated diode laser is used to create a temperature gradient across the tunnel junction layer stack. This laser modulation technique enables the recording of time-dependent thermovoltage signals with a temporal resolution only limited by the preamplifier for the thermovoltage. So far, time-dependent thermovoltage co…
The spin diffusion length for thermally excited magnon spins is measured by utilizing a non-local spin-Seebeck effect measurement. In a bulk single crystal of yttrium iron garnet (YIG) a focused laser thermally excites magnon spins. The spins diffuse laterally and are sampled using a Pt inverse spin Hall effect detector. Thermal transport modeling and temperature dependent measurements demonstrate the absence of spurious temperature gradients beneath the Pt detector and confirm the non-local nature of the experimental geometry. Remarkably, we find that thermally excited magnon spins in YIG tra…
The possibility of electrically exciting and detecting magnon currents in magnetic insulators has opened exciting perspectives for transporting spin information in electronic devices. However, the role of the magnetic field and the nonlocal thermal gradients on the magnon transport remain unclear. Here, by performing nonlocal harmonic voltage measurements, we investigate magnon transport in perpendicularly magnetized ultrathin Tm3Fe5O12 (TmIG) films coupled to Pt electrodes. We show that the first harmonic nonlocal voltage captures spin-driven magnon transport in TmIG, as expected, and the sec…
The spin Seebeck effect (SSE) is observed in magnetic insulator|heavy metal bilayers as an inverse spin Hall effect voltage under a temperature gradient. The SSE can be detected nonlocally as well, viz. in terms of the voltage in a second metallic contact (detector) on the magnetic film, spatially separated from the first contact that is used to apply the temperature bias (injector). Magnon-polarons are hybridized lattice and spin waves in magnetic materials, generated by the magnetoelastic interaction. Kikkawa et al. [Phys. Rev. Lett. \textbf{117}, 207203 (2016)] interpreted a resonant enhanc…
The nonlocal spin injection in lateral spin valves is highly expected to be an effective method to generate a pure spin current for potential spintronic application. However, the spin valve voltage, which decides the magnitude of the spin current flowing into an additional ferromagnetic wire, is typically of the order of 1 μV. Here we show that lateral spin valves with low resistive NiFe/MgO/Ag junctions enable the efficient spin injection with high applied current density, which leads to the spin valve voltage increased hundredfold. Hanle effect measurements demonstrate a long-distance collec…
We report on the observation and systematic study of polarization sensitive magnetic quantum ratchet effects induced by alternating electric fields in the terahertz frequency range. The effects are detected in (Cd,Mn)Te-based quantum well (QW) structures with inter-digitated dual-grating-gate (DGG) lateral superlattices. A dc electric current excited by cw terahertz laser radiation shows 1/B-periodic oscillations with an amplitude much larger than the photocurrent at zero magnetic field. Variation of gate voltages applied to individual grating gates of the DGG enables us to change the degree a…
Crossed Andreev reflection in a lateral spin valve geometry device is an aspect of considerable recent interest, particularly with regards to Cooper pair splitting experiments to realize solid state quantum entanglement. In this work, devices are fabricated consisting of two ferromagnetic permalloy (Py) electrodes contacted by a overlaid perpendicular superconducting Ta electrode, of variable lateral in-plane offset within the expected BCS superconducting coherence length $ξ_0$. Experimental electrical transport measurements are presented of local and nonlocal conduction, showing characteristi…
Thermally-driven spin-transfer torques have recently been reported in electrically insulating ferromagnet$|$normal-metal heterostructures. In this paper, we propose two physically distinct mechanisms for such torques. The first is a local effect: out-of-equilibrium, thermally-activated magnons in the ferromagnet, driven by a spin Seebeck effect, exert a torque on the magnetization via magnon-magnon scattering with coherent dynamics. The second is a nonlocal effect which requires an additional magnetic layer to provide the symmetry breaking necessary to realize a thermal torque. The simplest st…
Creating, manipulating and detecting spin polarized carriers are the key elements of spin based electronics. Most practical devices use a perpendicular geometry in which the spin currents, describing the transport of spin angular momentum, are accompanied by charge currents. In recent years, new sources of pure spin currents, i.e., without charge currents, have been demonstrated and applied. In this paper, we demonstrate a conceptually new source of pure spin current driven by the flow of heat across a ferromagnetic/non-magnetic metal (FM/NM) interface. This spin current is generated because t…
We present a numerical model of local and nonlocal transport properties in a lateral spin valve structure consisting of two magnetic electrodes in contact with a third perpendicular superconducting electrode. By considering the transport paths for a single electron incident at the local F/S interface - in terms of probabilities of crossed or local Andreev reflection, elastic cotunneling or quasiparticle transport - we show that this leads to nonlocal charge imbalance. We compare this model with experimental data from an aluminum-permalloy (Al/Py) lateral spin valve geometry device and demonstr…
Thermoelectric effect generating electricity from thermal gradient and vice versa appears in numerous generic applications. Recently, an original prospect of thermoelectricity arising from the nonlocal Cooper pair splitting (CPS) and the elastic co-tunneling (EC) in hybrid normal metal-superconductor-normal metal (NSN) structures was foreseen. Here we demonstrate experimentally the existence of non-local Seebeck effect in a graphene-based CPS device comprising two quantum dots connected to an aluminum superconductor and theoretically validate the observations. This non-local Seebeck effect off…
We present the detection of the spin-flop transition in the antiferromagnetic van der Waals material MnPS3 via thermally generated nonlocal magnon transport using permalloy detector strips. The inverse anomalous spin Hall effect has the unique power to detect an out-of-plane spin accumulation which enables us to detect magnons with an out-of-plane spin polarization; in contrast to strips of high spin-orbit material such as Pt which only possess the spin Hall effect and are only sensitive to an in-plane spin polarization of the spin accumulation. We show that nonlocal magnon transport is able t…
Magnetic field induced modulation of heat transport in CrPS$_4$ probed by TaIrTe$_4$ transverse Seebeck thermometry
University of Groningen（格罗宁根大学）；Cavendish Laboratory, University of Cambridge（剑桥大学卡文迪许实验室）；School of Physics and Astronomy, University of Leeds（利兹大学物理与天文学院）
Using four-terminal nonlocal magnetoresistance measurements in lateral spin-valve devices with Si$_{\rm 0.1}$Ge$_{\rm 0.9}$, we study pure spin current transport in a degenerate SiGe alloy ($n \sim$ 5.0 $\times$ 10$^{18}$ cm$^{-3}$). Clear nonlocal spin-valve signals and Hanle-effect curves, indicating generation, manipulation, and detection of pure spin currents, are observed. The spin diffusion length and spin lifetime of the Si$_{\rm 0.1}$Ge$_{\rm 0.9}$ layer at low temperatures are reliably estimated to be $\sim$ 0.5 $μ$m and $\sim$ 0.2 ns, respectively. This study demonstrates the possibi…
We report on experiments allowing to set an upper limit on the magnitude of the spin Hall effect and the conductance by edge channels in quantum wells of PbTe embedded between PbEuTe barriers. We reexamine previous data obtained for epitaxial microstructures of n-type PbSe and PbTe, in which pronounced nonlocal effects and reproducible magnetoresistance oscillations were found. Here we show that these effects are brought about by a quasi-periodic network of threading dislocations adjacent to the BaF$_2$ substrate, which give rise to a p-type interfacial layer and an associated parasitic parall…
We study room-temperature generation and detection of pure spin currents using lateral spin-valve devices with Heusler-compound electrodes, Co$_{2}$FeSi (CFS) or Fe$_{3}$Si (FS). The magnitude of the nonlocal spin-valve (NLSV) signals is seriously affected by the dispersion of the resistivity peculiarly observed in the low-temperature grown Heusler compounds with ordered structures. From the analysis based on the one-dimensional spin diffusion model, we find that the spin polarization monotonically increases with decreasing the resistivity, which depends on the structural ordering, for both CF…
We demonsrtate electrical spin injection and detection in $n$-type Ge ($n$-Ge) at room temperature using four-terminal nonlocal spin-valve and Hanle-effect measurements in lateral spin-valve (LSV) devices with Heusler-alloy Schottky tunnel contacts. The spin diffusion length ($λ$$_{\rm Ge}$) of the Ge layer used ($n \sim$ 1 $\times$ 10$^{19}$ cm$^{-3}$) at 296 K is estimated to be $\sim$ 0.44 $\pm$ 0.02 $μ$m. Room-temperature spin signals can be observed reproducibly at the low bias voltage range ($\le$ 0.7 V) for LSVs with relatively low resistance-area product ($RA$) values ($\le$ 1 k$Ω$$μ$m…
Spin relaxation in mesoscopic Ag wires in the diffusive transport regime is studied via nonlocal spin valve and Hanle effect measurements performed on permalloy/Ag lateral spin valves. The ratio between momentum and spin relaxation times is not constant at low temperatures. This can be explained with the Elliott-Yafet spin relaxation mechanism by considering the momentum surface relaxation time as being temperature dependent. We present a model to separately determine spin flip probabilities for phonon, impurity and surface scattering and find that the spin flip probability is highest for surf…
Localized laser heating creates temperature gradients in all directions and thus leads to three-dimensional electron flux in metallic materials. Temperature gradients in combination with material magnetization generate thermomagnetic voltages. The interplay between these direction-dependent temperature gradients and the magnetization along with their control enable to manipulate the generated voltages, e.g. in magnetic nanodevices. We identify the anomalous Nernst effect (ANE) generated on a nanometer length scale by micrometer sized temperature gradients in magnetic tunnel junctions (MTJs). I…
Nonlinear charge transport in strongly coupled semiconductor superlattices is described by Wigner-Poisson kinetic equations involving one or two minibands. Electron-electron collisions are treated within the Hartree approximation whereas other inelastic collisions are described by a modified BGK (Bhatnaghar-Gross-Krook) model. The hyperbolic limit is such that the collision frequencies are of the same order as the Bloch frequencies due to the electric field and the corresponding terms in the kinetic equation are dominant. In this limit, spatially nonlocal drift-diffusion balance equations for …
We developed an easy, upscalable process to prepare lateral spin-valve devices on epitaxially grown monolayer graphene on SiC(0001) and perform nonlocal spin transport measurements. We observe the longest spin relaxation times tau_S in monolayer graphene, while the spin diffusion coefficient D_S is strongly reduced compared to typical results on exfoliated graphene. The increase of tau_S is probably related to the changed substrate, while the cause for the small value of D_S remains an open question.
In recent years, new spin-dependent thermal effects have been discovered in ferromagnets, stimulating a growing interest in spin caloritronics, a field that exploits the interaction between spin and heat currents. Amongst the most intriguing phenomena is the spin Seebeck effect, in which a thermal gradient gives rise to spin currents that are detected through the inverse spin Hall effect. Non-magnetic materials such as graphene are also relevant for spin caloritronics, thanks to efficient spin transport, energy-dependent carrier mobility and unique density of states. Here, we propose and demon…
We have investigated spin Hall effects in 4$d$ and 5$d$ transition metals, Nb, Ta, Mo, Pd and Pt, by incorporating the spin absorption method in the lateral spin valve structure; where large spin current preferably relaxes into the transition metals, exhibiting strong spin-orbit interactions. Thereby nonlocal spin valve measurements enable us to evaluate their spin Hall conductivities. The sign of the spin Hall conductivity changes systematically depending on the number of $d$ electrons. This tendency is in good agreement with the recent theoretical calculation based on the intrinsic spin Hall…
We investigate magnon spin transport in epitaxial nickel ferrite (NiFe$_2$O$_4$, NFO) films grown on magnesium gallate spinel (MgGa$_2$O$_4$, MGO) substrates, which have a lattice mismatch with NFO as small as 0.78%, resulting in the reduction of antiphase boundary defects and thus in improved magnetic properties in the NFO films. In the nonlocal transport experiments, enhanced signals are observed for both electrically and thermally excited magnons, and the magnon relaxation length ($λ_m$) of NFO is found to be around 2.5 $μ$m at room temperature. Moreover, at both room and low temperatures, …
Spin Hall effect and its inverse provide essential means to convert charge to spin currents and vice versa, which serve as a primary function for spintronic phenomena such as the spin-torque ferromagnetic resonance and the spin Seebeck effect. These effects can oscillate magnetization or detect a thermally generated spin splitting in the chemical potential. Importantly this conversion process occurs via the spin-orbit interaction, and requires neither magnetic materials nor external magnetic fields. However, the spin Hall angle, i.e., the conversion yield between the charge and spin currents, …
At the interface between a nonmagnetic metal (NM) and a ferromagnetic insulator (FI) spin current can interact with the magnetization, leading to a modulation of the spin current. The interfacial exchange field at these FI-NM interfaces can be probed by placing the interface in contact with the spin transport channel of a lateral spin valve (LSV) device and observing additional spin relaxation processes. We study interfacial exchange field in lateral spin valve devices where Cu spin transport channel is in proximity with ferromagnetic insulator EuS (EuS-LSV) and yttrium iron garnet Y$_3$Fe$_5$…
Spin-flip mechanism in Ag nanowires with MgO surface protection layers has been investigated by means of nonlocal spin valve measurements using Permalloy/Ag lateral spin valves. The spin flip events mediated by surface scattering are effectively suppressed by the MgO capping layer. The spin relaxation process was found to be well described in the framework of Elliott-Yafet mechanism and then the probabilities of spin-filp scattering for phonon or impurity mediated momentum scattering is precisely determined in the nanowires. The temperature dependent spin-lattice relaxation follows the Bloch-G…
We consider the two-dimensional electron gas confined laterally to a narrow channel by a harmonic potential. As the Zeeman splitting matches the intersubband separation the nonlocal spin polarization develops a minimum as reported by Frolov et al. [Nature (London) 458, 868 (2009)]. This phenomenon termed Ballistic Spin Resonance is due to the degeneracy between the nearest oppositely polarized subbands that is lifted by spin-orbit coupling. We showed that the resonance survives the weak and short-range interaction. The latter detunes it and as a result shifts the Zeeman splitting at which the …
We demonstrate the electrical injection and detection of spin-polarized electrons in the Co2FeSi/GaAs hybrid system using lateral transport structures. Spin valve signatures and characteristic Hanle curves are observed both in the nonlocal and the local configuration. The comparatively large magnitude of the local spin valve signal and the high signal-to-noise ratio are attributed to the large spin polarization at the Fermi energy of Co2FeSi in the well-ordered L21 phase.
The energy efficiency of the spin Hall effects (SHE) can be enhanced if the electrical conductivity is decreased without sacrificing the spin Hall conductivity. The resistivity of Pt films can be increased to 150-300 μΩ*cm by mesoscopic lateral confinement, thereby decreasing the conductivity. The SHE and inverse spin Hall effects (ISHE) in these mesoscopic Pt films are explored at 10 K by using the nonlocal spin injection/detection method. All relevant physical quantities are determined in-situ on the same substrate, and a quantitative approach is developed to characterize all processes effec…
We have measured the spin injection efficiency and spin lifetime in Co$_2$FeSi/$n$-GaAs lateral nonlocal spin valves from 20 to 300 K. We observe large ($\sim$40 $μ$V) spin valve signals at room temperature and injector currents of $10^3~$A/cm$^2$, facilitated by fabricating spin valve separations smaller than the 1 $μ$m spin diffusion length and applying a forward bias to the detector contact. The spin transport parameters are measured by comparing the injector-detector contact separation dependence of the spin valve signal with a numerical model accounting for spin drift and diffusion. The a…
We study charge and spin transport along grain boundaries in single layer graphene in the presence of a quantizing magnetic field. Transport states in a grain boundary are produced by hybridization of Landau zero modes with interfacial states. In selected energy regimes quantum Hall edge states can be deflected either fully or partially into grain boundary states. The degree of edge state deflection is studied in the nonlocal conductance and in the shot noise. We also consider the possibility of grain boundaries as gate-switchable spin filters, a functionality enabled by counterpropagating tra…
We show nonlocal spin transport in n-Ge based lateral spin-valve devices with highly ordered Co_2FeSi/n^+-Ge Schottky tunnel contacts. Clear spin-valve signals and Hanle-effect curves are demonstrated at low temperatures, indicating generation, manipulation, and detection of pure spin currents in n-Ge. The obtained spin generation efficiency of ~ 0.12 is about two orders of magnitude larger than that for a device with Fe/MgO tunnel-barrier contacts reported previously. Taking the spin related behavior with temperature evolution into account, we infer that it is necessary to simultaneously demo…
Temperature gradient in a ferromagnetic conductor may generate a spontaneous transverse voltage drop in the direction perpendicular to both magnetization and heat current. This anomalous Nernst effect (ANE) has been considered to be proportional to the magnetization, and thus observed only in ferromagnets, while recent theories indicate that ANE provides a measure of the Berry curvature at the Fermi energy $E_{\rm F}$. Here we report the observation of a large ANE at zero field in the chiral antiferromagnet Mn$_3$Sn. Despite a very small magnetization $\sim 0.002$ $μ_{\rm B}/$Mn, the transvers…
Several spin-orbit effects allow performing spin to charge inter-conversion: the spin Hall effects, the Rashba effect, or the spin-momentum locking in topological insulators. Here we focus on how the detection of this inter-conversion can be made electrically, using three different cross-shaped nanostructures. We apply these measurement configurations to the case of the spin Hall effect in Pt, using CoFe electrodes to detect and inject spins. Both the direct and inverse spin Hall effect can be detected, with a spin Hall signal up to two order of magnitude higher than that of nonlocal measureme…
Giant spin Hall effect (GSHE) has been observed in heavy metal materials such as Ta, Pt, and W, where spins are polarized in the surface plane and perpendicular to the charge current direction. Spins generated in these materials have successfully switched magnets with in-plane magnetic anisotropy (IMA) and perpendicular magnetic anisotropy (PMA) through spin orbit torque (SOT) mechanism. It is generally accepted that PMA magnets are preferred over IMA magnets in data storage applications owing to their large thermal stability even at ultra scaled dimensions. However, SOT switching of PMA magne…
