The dependence of the critical current of spin transfer torque-driven magnetization dynamics on the free-layer thickness was studied by taking into account both the finite penetration depth of the transverse spin current and spin pumping. We showed that the critical current remains finite in the zero-thickness limit of the free layer for both parallel and anti-parallel alignments. We also showed that the remaining value of the critical current of parallel to anti-parallel switching is larger than that of anti-parallel to parallel switching.
We study the influence of the spin torque, which depends on the space and time derivative of magnetization, on magnetization reversal time in a ferromagnetic fine particle. The spin torque operates to dissipate the angular momentum of the magnetization precession, and the torque increases in a spin vortex structure. We calculate the magnetization reversal time under a DC magnetic field using the Landau-Lifshitz-Gilbert equation containing a spin torque term. We found that the spin torque changes the magnetization switching speed significantly during the reversal process by maintaining a spin v…
We study current-induced torques in WTe2/permalloy bilayers as a function of WTe2 thickness. We measure the torques using both second-harmonic Hall and spin-torque ferromagnetic resonance measurements for samples with WTe2 thicknesses that span from 16 nm down to a single monolayer. We confirm the existence of an out-of-plane antidamping torque, and show directly that the sign of this torque component is reversed across a monolayer step in the WTe2. The magnitude of the out-of-plane antidamping torque depends only weakly on WTe2 thickness, such that even a single-monolayer WTe2 device provides…
The spin-torque ferromagnetic resonance (ST-FMR) in a bilayer system consisting of a magnetic insulator such as Y3Fe5O12 and a normal metal with spin-orbit interaction such as Pt is addressed theoretically. We model the ST-FMR for all magnetization directions and in the presence of field-like spin-orbit torques based on the drift-diffusion spin model and quantum mechanical boundary conditions. ST-FMR experiments may expose crucial information about the spin-orbit coupling between currents and magnetization in the bilayers.
We study the role of thermal fluctuations on the spin dynamics of a thin permalloy film with a focus on the behavior of spin torque and find that the thermally assisted spin torque results in new aspects of the magnetization dynamics. In particular, we uncover the formation of a finite, spin torque-induced, in-plane magnetization component. The orientation of the in-plane magnetization vector depends on the temperature and the spin-torque coupling. We investigate and illustrate that the variation of the temperature leads to a thermally-induced rotation of the in-plane magnetization.
In systems with small spin-orbit coupling, current-induced torques on the magnetization require inhomogeneous magnetization textures. For large spin-orbit coupling, such torques exist even without gradients in the magnetization direction. Here, we consider current-induced torques in ferromagnetic metals with both Rashba spin-orbit coupling and inhomogeneous magnetization. We first phenomenologically construct all torques that are allowed by the symmetries of the system, to first order in magnetization-direction gradients and electric field. Second, we use a Boltzmann approach to calculate the …
Oscillation frequency of spin torque oscillator with a perpendicularly magnetized free layer and an in-plane magnetized pinned layer is theoretically investigated by taking into account the field-like torque. It is shown that the field-like torque plays an important role in finding the balance between the energy supplied by the spin torque and the dissipation due to the damping, which results in a steady precession. The validity of the developed theory is confirmed by performing numerical simulations based on the Landau-Lifshitz-Gilbert equation.
The optimum condition of the magnetization alignment to maximize the spin torque diode voltage is derived by solving the Landau-Lifshitz-Gilbert equation. We show that the optimized diode voltage can be one order of magnitude larger than that of the conventional alignment where the easy axes of the free and the pinned layers are parallel. These analytical predictions are confirmed by numerical simulations.
Spin torque majority gates are modeled and several regimes of magnetization switching (some leading to failure) are discovered. The switching speed and noise margins are determined for STMGs and an adder based on it. With switching time of 3ns at current of 80uA, the adder computational throughput is comparable to that of a CMOS adder.
Spin torque from spin current applied to a nanoscale region of a ferromagnet can act as negative magnetic damping and thereby excite self-oscillations of its magnetization. In contrast, spin torque uniformly applied to the magnetization of an extended ferromagnetic film does not generate self-oscillatory magnetic dynamics but leads to reduction of the saturation magnetization. Here we report studies of the effect of spin torque on a system of intermediate dimensionality - a ferromagnetic nanowire. We observe coherent self-oscillations of magnetization in a ferromagnetic nanowire serving as the…
We report the thickness dependence of Dzyaloshinskii-Moriya interaction (DMI) and spin-orbit torques (SOTs) in Pt\Co(t)\AlOx, studied by current-induced domain wall (DW) motion and second-harmonic experiments. From the DW motion study, a monotonous decay of the effective DMI strength with an increasing Co thickness is observed, in agreement with a DMI originating at the Pt\Co interface. The study of the ferromagnetic thickness dependence of spin-orbit torques reveals a more complex behavior. The effective SOT-field driving the DW motion is found to initially increase and then saturate with an …
We use pulsed inductive microwave magnetometry to study the precessional magnetization dynamics of the free layer in CoFeB/MgO/CoFeB based magnetic tunnelling junction stacks with varying MgO barrier thickness. From the field dependence of the precession frequency we are able to derive the uniaxial anisotropy energy and the exchange coupling between the free and the pinned layer. Furthermore the field dependence of the effective damping parameter is derived. Below a certain threshold barrier thickness we observe an increased effective damping for antiparallel orientation of free and pinned lay…
We apply a recently developed quantum theory of spin transfer torque to study the effect of the quantum noise in spin transfer process on the magnetization switching in spin-torque-driven devices. The quantum noise induces considerable fluctuation of the switching time at zero temperature. By including the thermal noise, the temperature dependence of the expectation value and standard deviation of the switching time are obtained in the Monte Carlo simulations, and the results are fitted to an effective first passage model. We expect that the predictions here are observable in the single-shot m…
The critical current of the spin transfer torque-driven magnetization dynamics was studied by taking into account both spin pumping and the finite penetration depth of the transverse spin current. We successfully reproduced the recent experimental results obtained by Chen et al. [Phys. Rev. B {\bf 74}, 144408 (2006)] and found that the critical current remains finite even in the zero-thickness limit of the free layer. We showed that the remaining value of the critical current is determined mainly by spin pumping.
We demonstrate magnetization switching in out-of-plane magnetized Ta\CoFeB\MgO nanowires by current pulse injection along the nanowires, both with and without a constant and uniform magnetic field collinear to the current direction. We deduce that an effective torque arising from spin-orbit effects in the multilayer drives the switching mechanism. While the generation of a component of the magnetization along the current direction is crucial for the switching to occur, we observe that even without a longitudinal field thermally generated magnetization fluctuations can lead to switching. Analys…
We study current-induced switching in magnetic tunnel junctions (MTJs) in the presence of a field-like spin-transfer torque and titled pinned-layer magnetization in the high current limit at finite temperature. We consider both the Slonczewski and field-like torques with coefficients $a_J$ and $b_J $, respectively. At finite temperatures, $σ= b_J/a_J = \pm1$ leads to a smaller mean switching time compared that with $σ= 0$. The reduction of switching time in the presence of the field-like term is due to the alignment effect (for $σ> 0$) and the initial torque effect.
We demonstrate efficient current induced spin orbit torque switching in perpendicularly magnetized epitaxial MgO(001)//Pd/Co2FeAl/MgO heterostructures grown by magnetron sputtering. The advantage of such heterostructures for spin orbit torque MRAM devices is that they allow a unique combination of critical ingredients: i) low resistivity required for reduced electric energy consumption during writing, ii) high TMR ratio required for efficient reading and iii) strong perpendicular magnetic anisotropy for increased thermal stability.
In this article we analyze by modeling two possible mechanisms for magnetization switching using spin orbit torques, which have been reported to cause field-free deterministic switching in experiments. Here we compare the field-free magnetization switching due to a tilt of the anisotropy direction against the use of an antiferromagnetic bias field. Simple results obtained analytically show that a bias field not only causes the magnetization reversal but also reduces the corresponding energy barrier. The critical current required for magnetization switching is analyzed on the basis of a macrosp…
We investigate the current-induced spin-orbit torque in thin topological insulator (TI) films in the presence of hybridization between the top and bottom surface states. We formulate the relation between spin torque and TI thickness, from which we derived the optimal value of the thickness to maximize the torque. We show numerically that in typical TI thin films made of $\mathrm{Bi_2Se_3}$, the optimal thickness is about 3-5 nm.
A common ploy to reduce the switching current and energy dissipation in spin-transfer-torque driven magnetization switching of shape-anisotropic single-domain nanomagnets is to employ magnets with low saturation magnetization $M_s$ and high shape-anisotropy. The high shape-anisotropy compensates for low $M_s$ to keep the static switching error rate constant. However, this ploy increases the switching delay, its variance in the presence of thermal noise, and the dynamic switching error rate. Using the stochastic Landau-Lifshitz-Gilbert equation with a random torque emulating thermal noise, we s…
Strong magnetic field pulses associated with a relativistic electron bunch can imprint switching patterns in magnetic thin films that have uniaxial in-plane anisotropy. In experiments with Fe and FeCo alloy films the pattern shape reveals an additional torque acting on magnetization during the short (in the 100fs time scale) magnetic field pulse. The magnitude of the torque is as high as 15% of the torque from the magnetic field. The torque symmetry is that of a uniaxial anisotropy along the direction of the eddy current screening the magnetic field. Spin-orbit interaction acting on the conduc…
We predict the existence of a new metastable magnetization state in a single-domain nanomagnet with uniaxial shape anisotropy. It emerges when a spin-polarized current, delivering a spin-transfer-torque, is injected into the nanomagnet. It can trap the magnetization vector and prevent spin-transfer-torque from switching the magnetization from one stable state along the easy axis to the other. Above a certain threshold current, the metastable state no longer appears. This has important technological consequences for spin-transfer-torque based magnetic memory and logic systems.
To study the effect of spin-orbit coupling (SOC) on spin-transfer torque in magnetic materials, we have implemented two theoretical formalisms that can accommodate SOC. Using the "charge-pumping" formalism, we find two contributions to the out-of-plane spin-transfer torque parameter $β$ in ballistic Ni domain walls (DWs). For short DWs, the nonadiabatic reflection of conduction electrons caused by the rapid spatial variation of the exchange potential results in an out-of-plane torque that increases rapidly with decreasing DW length. For long DWs, the Fermi level conduction channel anisotropy t…
We present a comparative study of high frequency dynamics and low frequency noise in elliptical magnetic tunnel junctions with lateral dimensions under 100 nm presenting current-switching phenomena. The analysis of the high frequency oscillation modes with respect to the current reveals the onset of a steady-state precession regime for negative bias currents above $J=10^7 A/cm^2$, when the magnetic field is applied along the easy axis of magnetization. By the study of low frequency noise for the same samples, we demonstrate the direct link between changes in the oscillation modes with the appl…
We study the effects of the coupling between magnetization dynamics and the electronic degrees of freedom in a heterostructure of a metallic nanomagnet with dynamic magnetization coupled with a superconductor containing a steady spin-splitting field. We predict how this system exhibits a non-linear spin torque, which can be driven either with a temperature difference or a voltage across the interface. We generalize this notion to arbitrary magnetization precession by deriving a Keldysh action for the interface, describing the coupled charge, heat and spin transport in the presence of a precess…
Spin-orbit torques induced by spin Hall and interfacial effects in heavy metal/ferromagnetic bilayers allow for a switching geometry based on in-plane current injection. Using this geometry, we demonstrate deterministic magnetization reversal by current pulses ranging from 180~ps to ms in Pt/Co/AlOx dots with lateral dimensions of 90~nm. We characterize the switching probability and critical current $I_c$ as function of pulse length, amplitude, and external field. Our data evidence two distinct regimes: a short-time intrinsic regime, where $I_c$ scales linearly with the inverse of the pulse le…
In this paper we present an overview of recent progress made in the understanding of the spin-torque induced magnetization dynamics in nanodevices using mesoscopic micromagnetic simulations. We first specify how a spin-torque term may be added to the usual Landau-Lifshitz-Gilbert equation of magnetization motion and detail its physical meaning. After a brief description of spin-torque driven dynamics in the macrospin approximation, we discuss the validity of this approximation for various experimentally relevant geometries. Next, we perform a detailed comparison between accurate experimental d…
The critical current needed to destabilize the magnetization of a perpendicular ferromagnet via the spin Hall effect is studied. Both the dampinglike and fieldlike torques associated with the spin current generated by the spin Hall effect is included in the Landau-Lifshitz-Gilbert equation to model the system. In the absence of the fieldlike torque, the critical current is independent of the damping constant and is much larger than that of conventional spin torque switching of collinear magnetic systems, as in magnetic tunnel junctions. With the fieldlike torque included, we find that the crit…
We present a time-resolved study of the magnetization dynamics in a microstructured Cr$|$Heusler$|$Pt waveguide driven by the Spin-Hall-Effect and the Spin-Transfer-Torque effect via short current pulses. In particular, we focus on the determination of the threshold current at which the spin-wave damping is compensated. We have developed a novel method based on the temporal evolution of the magnon density at the beginning of an applied current pulse at which the magnon density deviates from the thermal level. Since this method does not depend on the signal-to-noise ratio, it allows for a robus…
We compute the spin-orbit torque in a transition metal heterostructure using Slater-Koster parameterization in the two-center tight-binding approximation and accounting for d-orbitals only. In this method, the spin-orbit coupling is modeled within Russel-Saunders scheme, which enables us to treat interfacial and bulk spin-orbit transport on equal footing. The two components of the spin-orbit torque, dissipative (damping-like) and reactive (field-like), are computed within Kubo linear response theory. By systematically studying their thickness and angular dependence, we were able to accurately …
We present measurements of spin orbit torques generated by Ir as a function of film thickness in sputtered Ir/CoFeB and Ir/Co samples. We find that Ir provides a damping-like component of spin orbit torque with a maximum spin torque conductivity 1.4e5 in SI unit and a maximum spin-torque efficiency of 0.04, which is sufficient to drive switching in an 0.8 nm film of CoFeB with perpendicular magnetic anisotropy. We also observe a surprisingly large field like spin orbit torque. Measurements as a function of Ir thickness indicate a substantial contribution to the FLT from an interface mechanism …
We consider current-induced spin-transfer torque on an antiferromagnet in a dual spin-valve setup. It is demonstrated that a net magnetization may be induced in the AFM by partially or completely aligning the sublattice magnetizations via a current-induced spin-transfer torque. This effect occurs for current densities ranging below 10$^6$ A/cm$^2$. The direction of the induced magnetization in the AFM is shown to be efficiently controlled by means of the magnetic configuration of the spin-valve setup, with the anti-parallell configuration yielding the largest spin-transfer torque. Interestingl…
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 orb…
We address the nature of spin-orbit torques at the magnetic surfaces of topological insulators, using both Kubo formula and Keldysh formalism. Through the analysis of the derived spin-charge equations, we find that the so-called Dirac torques possess a different symmetry compared to their Rashba counterpart, as well as a high anisotropy as a function of the magnetization direction. In particular, the damping torque vanishes when the magnetization lies in the plane of the topological insulator surface. This peculiarity has important consequences in terms of magnetization dynamics and switching,…
Current-induced magnetization switching by spin-orbit torque (SOT) holds considerable promise for next generation ultralow-power memory and logic applications. In most cases, generation of spin-orbit torques has relied on an external injection of out-of-plane spin currents into the magnetic layer, while an external magnetic field along the electric current direction is generally required for realizing deterministic switching by SOT. Here, we report deterministic current-induced SOT full magnetization switching by lateral spin-orbit torque in zero external magnetic field. The Pt/Co/Pt magnetic …
For graphene nanoribbons with Rashba spin-orbit coupling, the peculiar magnetic response due to the presence of a magnetization and geometric confinement are analyzed within a tight-binding model. We observe a sizable transverse susceptibility that can be considered as a gate voltage-induced magnetoelectric torque without the need of a bias voltage, with different directions for zigzag and armchair ribbons. The local torque generates non-collinear spin polarization between the two edges and/or along the ribbon, and the net torque averages to zero if the magnetization is homogeneous. Neverthele…
We study deterministic magnetic reversal of a perpendicularly magnetized Co layer in a Co/MgO/Ta nano-square driven by spin Hall torque from an in-plane current flowing in an underlying Pt layer. The rate-limiting step of the switching process is domain-wall (DW) depinning by spin Hall torque via a thermally-assisted mechanism that eventually produces full reversal by domain expansion. An in-plane applied magnetic field collinear with the current is required, with the necessary field scale set by the need to overcome DW chirality imposed by the Dzyaloshinskii-Moriya interaction. Once Joule hea…
Spin transport in magnetic tunnel junctions comprising a single magnetic layer in the presence of interfacial spin-orbit interaction (SOI) is investigated theoretically. Due to the presence of interfacial SOI, a current-driven spin torque can be generated at the second order in SOI, even in the absence of an external spin polarizer. This torque possesses two components, in-plane and perpendicular to the plane of rotation, that can induce either current-driven {\em magnetization switching} from in-plane to out-of-plane configuration or {\em magnetization precessions}, similarly to Spin Transfer…
We investigate theoretically the spin torque and magnetization dynamic in a thin ferromagnetic (FM) layer with spatially varying magnetization. The FM layer is deposited on the surface of a topological insulator (TI). In the limit of the adiabatic relaxation of electron spin along the magnetization, the interaction between the exchange interaction and the Rashba-like surface texture of a TI yields a topological gauge field. Under the gauge field and an applied current, spin torque is induced according to the direction of the current. We derived the corresponding effective anisotropy field and …
Pure spin currents transport angular momentum without an associated charge flow. This unique property makes them attractive for spintronics applications, such as torque induced magnetization control in nanodevices that can be used for sensing, data storage, interconnects and logics. Up to now, however, most spin transfer torque studies focused on metallic ferromagnets, while magnetic insulators were largely ignored, in spite of superior magnetic quality factors. Here, we report the observation of spin torque-induced magnetization dynamics in a magnetic insulator. Our experiments show that in u…
Current-driven magnetization dynamics in ferromagnetic metals are studied in a self-consistent adiabatic local-density approximation in the presence of spin-conserving and spin-dephasing impurity scattering. Based on a quantum kinetic equation, we derive Gilbert damping and spin-transfer torques entering the Landau-Lifshitz equation to linear order in frequency and wave vector. Gilbert damping and a current-driven dissipative torque scale identically and compete, with the result that a steady current-driven domain-wall motion is insensitive to spin dephasing in the limit of weak ferromagnetism…
We study spin accumulation and spin transfer torque in a domain wall by solving the Boltzmann equation with a diffusion approximation. We obtained the analytical expressions of spin accumulation and spin transfer torque. Both the adiabatic and the non-adiabatic components of the spin transfer torque oscillate with the thickness of the domain wall. We show that the oscillation plays a dominant role in the non-adiabatic torque when the domain wall thickness is less than the spin-flip length, which is defined by the product of the Fermi velocity and the spin-flip scattering time.
Using the Kubo linear-response formalism we derive expressions to calculate the heat current generated by magnetization dynamics in magnets with broken inversion symmetry and spin-orbit interaction (SOI). The effect of producing heat currents by magnetization dynamics constitutes the Onsager reciprocal of the thermal spin-orbit torque (TSOT), i.e., the generation of torques on the magnetization due to temperature gradients. We find that the energy current driven by magnetization dynamics contains a contribution from the Dzyaloshinskii-Moriya interaction (DMI), which needs to be subtracted from…
We investigate the magnetization dynamics that arise when a thin-film ferromagnet is deposited on a topological insulator (TI), focusing in particular on domain-wall motion via current and the possibility of a spin-wave torque acting on the magnetization. We show analytically that the coupling between the magnetic domain wall and the TI removes the degeneracy of the wall profile with respect to its chirality and topological charge. Moreover, we find that the threshold for Walker breakdown of domain wall motion is substantially increased and determined by the interaction with the TI, allowing f…
We theoretically study electrical responses of magnetization in Weyl semimetals. The Weyl semimetal is a new class of topological semimetals, possessing hedgehog type spin textures in momentum space. Because of this peculiar spin texture, an interplay of electron transport and spin dynamics might provide new method to electrical control of magnetization. In this paper, we consider the magnetically doped Weyl semimetals, and systematically study current- and charge-induced spin torque exerted on the local magnetization in three-dimensional Dirac-Weyl metals. We determine all current-induced spi…
The ability of spintronic devices to utilize an electric current for manipulating the magnetization has resulted in large-scale developments, such as, magnetic random access memories and boosted the spintronic research area. In this regard, over the last decade, magnetization manipulation using spin-orbit torque has been devoted a lot of research attention as it shows a great promise for future ultrafast and power efficient magnetic memories. In this review, we summarize the latest advancements in spin-orbit torque research and highlight some of the technical challenges for practical spin-orbi…
For deterministic magnetization switching by spin-orbit torque (SOT) in a perpendicular magnetic anisotropy system, an additional in-plane direction magnetic field is essential for deterministic switching by breaking the magnetization symmetry. Realizing chirality in a magnetic ordering system can be one approach for achieving asymmetry in the lateral direction for field-free magnetization switching. However, systematic analysis of the influence of the chiral spin system on deterministic switching is still scarce. In this report, the achievement of field-free SOT-induced magnetization switchin…
So far, studies of spin-orbit torques (SOT) in ferromagnets with perpendicular magnetic anisotropy (PMA) have been restricted to ultra thin samples, while a systematic study of its thickness dependence is still lacking in literature. In this article we discuss the thickness dependence of SOT in GdFeCo samples with bulk PMA. We show that the effective SOT fields are decreasing inversely as a function of thickness while the spin-Hall angle stays constant, as expected from angular momentum conservation. Further we show that even 30nm thick GdFeCo samples can be switched with SOT. This has importa…
The dynamics of magnetization in the presence of spin-transfer torque was studied. We derived the equation for the motion of magnetization in the presence of a spin current by using the local equilibrium assumption in non-equilibrium thermodynamics. We show that, in the resultant equation, the ratio of the Gilbert damping constant, $α$, and the coefficient, $β$, of the current-induced torque, called non-adiabatic torque, depends on the relaxation time of the fluctuating field $τ_{c}$. The equality $α=β$ holds when $τ_c$ is very short compared to the time scale of magnetization dynamics. We app…
Impact of spin transfer torque (STT) on the write error rate of a voltage-torque-based magnetoresistive random access memory is theoretically analyzed by using the macrospin model. During the voltage pulse the STT assists or suppresses the precessional motion of the magnetization depending on the initial magnetization direction. The characteristic value of the current density is derived by balancing the STT and the external-field torque, which is about 5$\times$ 10$^{11}$ A/m$^{2}$. The results show that the write error rate is insensitive to the STT below the current density of $10^{10}$ A/m$…
In large magnetoresistance devices spin torque-induced changes in resistance can produce GHz current and voltage oscillations which can affect magnetization reversal. In addition, capacitive shunting in large resistance devices can further reduce the current, adversely affecting spin torque switching. Here, we simultaneously solve the Landau-Lifshitz-Gilbert equation with spin torque and the transmission line telegrapher's equations to study the effects of resistance feedback and capacitance on magnetization reversal of both spin valves and magnetic tunnel junctions. While for spin valves para…
Spin-transfer torque (STT) effects on the stationary forced response of nanoscale ferromagnets subject to thermal fluctuations and driven by an ac magnetic field of arbitrary strength and direction are investigated via a generic nanopillar model of a spin-torque device comprising two ferromagnetic strata representing the free and fixed layers and a nonmagnetic conducting spacer all sandwiched between two ohmic contacts. The STT effects are treated via the Brown magnetic Langevin equation generalized to include the Slonczewski STT term thereby extending the statistical moment method [Y. P. Kalm…
We simulate the stochastic Landau-Lifshitz-Gilbert (LLG) dynamics of a uniaxial nanomagnet out to sub-millisecond timescales using a graphical processing unit based micromagnetic code and determine the effect of geometrical tilts between the spin-current and uniaxial anisotropy axes on the thermally assisted reversal dynamics. The asymptotic behavior of the switching time ($I\rightarrow 0$, $<τ>\propto\exp(-ξ(1-I)^2)$) is approached gradually, indicating a broad crossover regime between ballistic and thermally assisted spin transfer reversal. Interestingly, the mean switching time is shown to …
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…
A free electron description of spin-dependent tranport in magnetic tunnel junctions with non collinear magnetizations is presented. We investigate the origin of transverse spin density in tunnelling transport and the quantum interferences which give rise to oscillatory torques on the local magnetization. Spin transfer torque is also analyzed and an important bias asymmetry is found as well as a damped oscillatory behaviour. Furthermore, we investigate the influence of the s-d exchange coupling on torque in particular in the case of half-metallic MTJ in which the spin transfer torque is due to …
