Spin-torque critical current of graphene-based lateral spin valves

Influence of MgO Tunnel Barrier thickness in 3-terminal Spin Hall Nano-Oscillators

The current-induced magnetization precession dynamics provoked by the spin transfer torque (STT) in a spin valve device i.e. tri-layer device (commonly spin torque nano oscillator (STNO)) is investigated numerically by solving the governing Landau–Lifshitz–Gilbert–Slonczewski (LLGS) equation. In this study, we have devised an STNO device made of EuO-based ferromagnetic alloy in free and fixed magnetic layers. The copper acts as a nonmagnetic spacer. Here, we have introduced the current induced Oesterd field (CIOF), which is generated when a spin-polarized current passes through the STNO device. In the device, we have tuned the free layer angle [Formula: see text] from [Formula: see text] to [Formula: see text] as an increment of [Formula: see text]. For every individual [Formula: see text] ranging from [Formula: see text] to [Formula: see text], the generated Oersted field’s strength can be altered by increasing the STNO device’s diameter. Henceforth, it is apparent that the frequency tunability is achieved in the device for all the values of [Formula: see text]. The frequency and power of the device depend entirely on the material’s saturation magnetization, which inherently reflects the current density and coherence of spin-polarized DC. From the results, it is apparent that for a particular [Formula: see text], the frequency keeps increasing with the eventual decrease in power when we increase the strength of the Oersted field from 10[Formula: see text]kA/m to 50[Formula: see text]kA/m. By doing so, the maximum frequency can be tuned up to 212[Formula: see text]GHz for [Formula: see text] with [Formula: see text] as 50[Formula: see text]kA/m. The high frequency emitted by the device acts as a linchpin ingredient, as well as a launch pad element in much of scientific and technological point of view. It paves way for a new route in the areas such as high capacity, high precision, high density as well as the sensing applications.

Using the linearized Landau–Lifshitz-Gilbert (LLG) equation in the rotation coordinate, we calculate the critical switching current density of a perpendicular magnetic tunnel junction (MTJ), where magnetization switching is achieved by the interplay of spin-transfer and spin-orbit torques. In terms of the critical current density, we find that as the current density inducing the spin-orbit torque (jSOT) increases, the current density inducing the spin-transfer torque (jSTT) decreases nonlinearly. In the presence of the spin-orbit field-like torque (β), the critical switching current density by the spin-transfer torque is proportional to the damping constant (α) as the conventional spin-transfer torque switching, while the critical switching current density by the spin-orbit torque increases with α when Heff≫HSOT . We also investigated the β dependence of the critical switching current density. For a given jSOT , the critical switching current density for the spin-transfer torque, jSTT,c decreases linearly with increasing β and nonlinearly decreases with increasing jSOT for a given β. Further, we discuss the β dependence of the critical switching current density on energy.

Spin-orbit torque magnetic RAM (SOT-MRAM) is affected by read disturbances due to spin current in the heavy metal layer that arises from spin-orbit interaction at the time of reading [1]. To resolve this issue, we have proposed a stabilized structure with a bi-directional read path, based on the idea that spin currents flowing in opposite directions on either side of the heavy metal layer cancel each other’s effects, that improves the read reliability of SOT-MRAM. We have already reported that this structure reduces the read disturbance [2]. In this study, we evaluated the movement of the magnetization of the free layer at the time of reading in a bi-directional read SOT-MRAM by using an LLG simulator. It was found that the read disturbance caused by SOT is removed in the free layer, as shown in Fig. 1 (a). In other words, the spin currents generated in opposite directions in the heavy metal layer directly affect the magnetization of the free layer, and the free layer functions as if it were two ferromagnets, whose balanced magnetizations cancel the read disturbance. To clarify this mechanism, Fig. 1 (b) shows the simulated magnetization for only the free layer at extremely large currents. The free layer is a ferromagnet magnetized in two opposite directions due to the central vortex magnetization, and the magnetization does not reverse to either side. (That is, it is not a mechanism in which the spin currents cancel themselves in both directions in the heavy metal layer.)Toward the realization of this bidirectional read SOT-MRAM structure, we evaluated the effect on the read disturbance of the size of the direction in which current flows through the heavy metal layer of an SOT structure. The device structure had an magnetic tunnel junction (MTJ) with two ferromagnets (cobalt), in which a pinned layer with a thickness of 3.5 nm and a free layer with a thickness of 1.5 nm sandwiched an insulating layer with a thickness of 1.0 nm, and a heavy metal layer (tungsten) with a thickness of 2.0 nm under the free layer. The magnetization of the two ferromagnetic layers directed toward the short side direction of the device, and the current passed from the pinned layer to both ends in the long side direction of the heavy metal layer. The width in the short side direction was uniformly 30 nm, and there were four device widths for the long side direction, i.e., 30 nm, 60 nm, 120 nm, and 180 nm. We evaluated the magnetization reversal probability of a conventional SOT-MRAM structure and the stabilized SOT-MRAM structure for a read time of 5 ns. Fig. 2 shows that the stabilized SOT-MRAM was about 6 to 10 times more effective than the conventional structure. In the conventional SOT-MRAM, the threshold current was proportional to the width of the device, whereas in the stabilized SOT-MRAM, the threshold current decreased as the width of device increased. The magnetization reversal of the conventional SOT-MRAM was strongly affected by the SOT disturbance due to the spin Hall effect, and the difference in thermal stability depending on the device size also had an influence. On the other hand, in the stabilized SOT-MRAM, the disturbance was canceled out at the free layer and only spin transfer torque in MTJ affected the magnetization reversal. Thus, we expected that the relationship between thermal stability and device size would have a large effect on magnetization reversal, but the result was contrary to that. These results indicate that the force exerted by the spin Hall effect on the magnetization of the free layer is relatively large and easy to act when the device is small. Therefore, a small device of the conventional SOT-MRAM tend to easily occur magnetization reversal, whereas in a smaller device of the stabilized SOT-MRAM, the effect on the magnetization of the free layer is strong enough to cancel the SOT disturbance and the magnetization reversal becomes more difficult.AcknowledgmentsThis work was partly supported by a Grant-in-Aid for Scientific Research (19K04536) from Japan Society for the Promotion of Science. **

Materials with perpendicular magnetic anisotropy have been intensively investigated due to their potential applications in the nonvolatile magnetic memory and spin-torque oscillators. Hear in this paper, we report a special interesting spin-transfer-driven magnetic behavior in perpendicularly magnetized (Co/Ni) -based spin-valve nano-pillars due to the reduced symmetry of easy axis in the free layer. The micromagnetic simulations indicate that a dip in the average magnetization curve can take place due to the reduced symmetry such as tilt of the magnetic field as well as the easy axis of the free and polarizer layers. In order to further clarify the physics mechanism of the dip, we carry out a series of new simulation studies. In our simulations, we consider a spin-valve nano-pillar with perpendicular anisotropy free layer and a 3 tilted polarizer layer. A negative perpendicular magnetic field and a positive perpendicular current are both applied simultaneously. In the average magnetization curves mz as a function of the magnetic field with various currents, three dips are observed. Note that although the spin-transfer torque is essential to the appearance of the dips, the position of the dips is less affected by the current in a certain current range. For three dips, we notice that the mz values are almost identical at a special magnetic field for different currents. At this special magnetic field, the magnetization oscillation modes in the free layer are similar to each other for different currents. The corresponding frequency spectra show that the amplitude of the main frequency peak decreases with the increasing of current due to the enhanced spin-transfer torque. In addition, the frequency shows a blue-shift with the increasing of applied current. Our simulations show that the main frequency f1 corresponding to the highest peak is approximately equal to the precession frequency of the local magnetization in the free layer. Several high-order frequency peaks are also observed in the frequency spectrum with fn=nf1, where n is an integer. Therefore the periodic oscillation of mz is a harmonic oscillation. Further simulations indicate that the dip appearance is also affected by the thickness of free layer. The spin-transfer torque effect decreases with the thickness of the free layer increasing. As a consequence, the dips shift to a low magnetic field range with the increase of the thickness. And for larger thickness t=8.0 nm, no dip appears. This result suggests that the spin-transfer torque is necessary for the dip, rather than the unique effect factor, to occur. In the dip region, the magnetic oscillation modes of the free layer show interesting frequency spectrum characters:harmonic frequency or inter-harmonic frequency. As a consequence, the periodic oscillation of the free layer is accompanied by the harmonic waves.

There have been several recent experiments involving spin injection and accumulation in mesoscopic metal samples, using lateral spin valve structures. The results have been interesting from the perspectives of both fundamental physics and applications. The resistance change associated with spin accumulation, ▵R, has been predicted to scale inversely with sample volume and this inverse scaling has been observed over ten decades. A value of ▵R = 1 Ohm has been reported, at room temperature, in a thin film Al wire structure with transverse dimensions of roughly 100 nm. High values of ▵R have been observed in samples characterized by electrode interface resistances that vary by 6 decades. Results are discussed within the framework of Johnson-Silsbee theory, and factors that limit inverse scaling are identified. Lateral spin valves with dimensions of tens of nm may be competitive for device applications. Structures with ▵R of order 1 Ohm are superior to CPP spin valves of comparable dimensions. Prospects for improved performance, the plausibility of a lateral spin valve with output levels of 10 Ohms and output impedance of 50 Ohms, and relevance to hard drive read heads and integrated nonvolatile random access memory applications are discussed.

In this thesis we make use of the Spin Transfer Torque effect from a continuous microwave current to induce and study the spin dynamics of an individual sub-100 nm nanostructure. The idea that an electrical current can carry a spin angular momentum was introduced in the 1980 with the advent of Spintronics. In 1996, Slonczewski and Berger predicted that, when flowing through a metal ferromagnet, such a spin polarized current can exert a torque on the magnetization. This effect is known as Spin transfer Torque (STT) and implies the possibility to manipulate the magnetization by means of an electrical current. One of the characteristics of the STT effect is that it allows for the magnetization dynamics to be excited and detected electrically. This makes the STT a perfect tool for the investigation of spin dynamics at the nano-scale. Indeed, the intrinsic local character of transport measurements permits a single nanostructure to be addressed and studied. This thesis is devoted to the study of the STT effect induced by a microwave current (AC STT). Our experiment focuses on two main aspects: the intrinsic dynamics of the magnetization and the role of a microwave current in assisting the magnetization reversal. We perform our measurements on Co/Cu nanowires electrodeposited in nanoporous polycarbonate templates. The electrical contact to a nanostructure is realized thanks to a home-made sample-holder, without the use of any lithographic technique. In the first part of the thesis a continuous microwave current is used to both drive and probe the magnetization dynamics of a pseudo spin valve nanostructure. Our measurements show that the magnetization dynamics in such a structure is extremely complex and arises from the excitation of both magnetic layers in the pseudo spin valve. In the dynamical spectrum we identify the fundamental modes of both magnetic layers, as confirmed by macrospin simulations. Higher frequency modes are attributed to spatially non-uniform spin wave excitations, in agreement with that observed by others in arrays of nanoelements. These results validate our technique for making samples and contacting them for AC STT-induced dynamical studies. The second part of this work is aimed at testing the effect of AC STT on the static switching field of magnetic nanoelements. The magnetoresistive curve of a pseudo spin valve structure is recorded with and without an additional microwave current. Our results prove the effectiveness of AC STT in assisting the magnetization reversal. We measured a reduction of the switching field up to 80 mT by injecting a microwave current of about 100 µA. This experiment suggests that the range of sensitivity of magnetoresistive devices could be tuned by simply injecting a continuous microwave current. This point is particularly interesting for the prospect of technological applications such as magnetic sensors.

The dynamics of the magnetization switching in magnetic tunnel junctions (MTJs) designed for spin-transfer-torque (STT) magnetoresistive random access memory (MRAM) was investigated using micromagnetic simulations. It was found that for short pulses (<∼10ns), the switching current threshold does not correlate with the switching field threshold and it is, therefore, essentially insensitive to MTJ shape (aspect ratio) and edge roughness. However, if the magnetization reversal is thermally activated for longer pulses, the switching current and the switching field are directly correlated. For a relatively large MTJ, the distribution is wide due to the excitation of high-order spin wave modes.

Efficient generation and detection of the spin current is a crucial issue for the application of spintronic devices. In addition, integrating spintronic circuit with conventional semiconductor devices is another important milestone for the practical application of the spin devices. Recently, the interplay between the heat and spin has attracted great attention because the temperature gradient is found to generate the spin current [1]. Since the heat can generate and propagate without electricity, this novel approach using the heat may open a new avenue for simplifying integration of spin devices. The precise estimation of the spin-dependent Seebeck coefficient (S s ), which is one of the important factors for the efficient generation of the thermal spin current, is indispensable to develop and optimize the spin device structure using the heat. However, it is still a hard nut to crack for the conventional ferromagnet because of its small magnitude and tiny related spin signal. Moreover, the related spin signal is smeared out by the spurious signals induced by classical thermoelectric effects especially at room temperature. Recently, we have shown that both the electrically and thermally driven spin injection efficiencies have been dramatically enhanced by the CoFeAl electrodes because of the excellent property for the thermal spin injection and electrical spin detection of CoFeAl [2]. In this presentation, by using the excellent CoFeAl, we develop the precise evaluation method for the thermal spin injection properties of Permalloy (Py)/Cu hybrid in lateral spin valve structure.

We investigate the influence of Au capping layer on the spin accumulation in a lateral spin valve consisting of Permalloy and Cu wires. The nonlocal spin valve measurements show that the Au capping significantly suppresses the spin accumulation in the Cu wire, although it improves the electrical conductivity. This is understood as a result of the small spin-flip resistance of Au whereby absorbed spins are successively flipped.

<sec><p indent="0mm">Magnetic random-access memory (MRAM) has emerged as a leading candidate for next-generation storage technology, offering high speed, high density, non-volatility, low power consumption, and radiation resistance. MRAM has evolved through three generations: field-driven toggle MRAM, spin-transfer torque (STT)-MRAM, and the experimental spin-orbit torque (SOT)-MRAM. The current commercial MRAM products primarily rely on STT-MRAM, which is based on Ta/CoFeB/MgO multilayers with the interfacial perpendicular magnetic anisotropy (PMA). However, STT-MRAM performance deteriorates at sub<sc>-10 nm</sc> size due to thermal instability. In contrast, the tetragonal Mn-based binary alloys exhibit stable bulk PMA and enhanced properties for sub<sc>-10 nm</sc> tunnel junction devices. Previous research has demonstrated the potential of these alloys for high-density MRAM, with magnetization switching achieved via SOT without the need for external magnetic fields. Among Mn-based binary alloys, <italic>L</italic>1₀-MnAl stands out due to its strong PMA, high spin polarization, and low magnetic damping, making it a promising material for next-generation MRAM. On the other side, the <italic>B</italic>2-CoGa alloy serves as both an ideal buffer layer and a spin current source for the epitaxial growth of PMA <italic>L</italic>1₀-MnAl thin films on GaAs substrates. Our study demonstrates that doping <italic>B</italic>2-CoGa with Pt significantly enhances the SOT efficiency in (CoGa)_{1−<italic>x</italic>}Pt<italic>_x</italic>/<italic>L</italic>1₀-MnAl bilayers while preserving the excellent PMA properties of <italic>L</italic>1₀-MnAl. </sec><sec> Experimental results show that Pt doping up to <italic>x</italic> = 0.1 keeps the PMA characteristics while simultaneously reducing the critical current density required for magnetization switching from <sc>4.63×10⁷ A/cm²</sc> to <sc>2.59×10⁷ A/cm².</sc> SOT efficiency increases from 0.042 to 0.080. This enhancement is attributed to the increased resistivity of the (CoGa)_{1−<italic>x</italic>}Pt<italic>_x</italic> layer, which does not compromise its effective spin Hall conductivity. The optimized bilayer, with <italic>x</italic> = 0.075, supports magnetic tunnel junctions with lateral size as small as <sc>8.09 nm,</sc> reducing power consumption by 37%. The SOT effect utilizes spin currents generated by phenomena such as the spin Hall effect to switch local magnetization in adjacent ferromagnetic layers. The damping-like SOT efficiency (<italic>ξ</italic>_DL), a crucial parameter for reducing device power consumption, is influenced by both spin Hall conductivity and resistivity of the material. The introduction of Pt impurities into (CoGa)_{1−<italic>x</italic>}Pt<italic>_x</italic> bilayers optimizes this balance, significantly enhancing <italic>ξ</italic>_DL. Compared to traditional heavy metals used as buffer layers, the (CoGa)_{1−<italic>x</italic>}Pt<italic>_x</italic> layer provides better lattice matching with Mn-based binary alloys, preserving their crystalline quality and PMA. This work systematically investigates the structural, magnetic, and SOT-driven magnetization switching properties of epitaxially grown (CoGa)_{1−<italic>x</italic>}Pt<italic>_x</italic>/<italic>L</italic>1₀-MnAl bilayers, focusing on the dependence of magnetization switching on Pt concentration. Deterministic SOT-induced switching is achieved for <italic>x</italic> ≤ 0.1, with optimal PMA and SOT performance observed at <italic>x</italic> = 0.075. These results demonstrate the feasibility of incorporating Pt-doped CoGa layers into MRAM designs to enhance performance and scalability. This study provides valuable insights into improving SOT efficiency in Mn-based MRAM structures by incorporating Pt-doped CoGa buffer layers. These findings contribute to the development of high-density, high-performance MRAM devices with reduced power consumption. </sec>

The flow of in-plane current through ultrathin magnetic heterostructures can cause magnetization switching or domain-wall nucleation owing to bulk and interfacial effects. Within the magnetic layer, the current can create magnetic instabilities via spin transfer torques (STT). At interface(s), spin current generated from the spin Hall effect in a neighboring layer can exert torques, referred to as the spin Hall torques, on the magnetic moments. Here, we study current-induced magnetization switching in perpendicularly magnetized CoFeB/MgO heterostructures with a heavy metal (HM) underlayer. Depending on the thickness of the HM underlayer, we find distinct differences in the in-plane field dependence of the threshold switching current. The STT is likely responsible for the magnetization reversal for the thinner underlayer films whereas the spin Hall torques cause the switching for thicker underlayer films. For the latter, we find differences in the switching current for positive and negative currents and initial magnetization directions. We find that the growth process during the film deposition introduces an anisotropy that breaks the symmetry of the system and causes the asymmetric switching. The presence of such symmetry-breaking anisotropy enables deterministic magnetization switching at zero external fields.

Spin torque transfer structures with new spin switching configurations are proposed, fabricated and investigated in this paper. The non-uniform current-induced magnetization switching is implemented based on both GMR and MTJ nano devices. The proposed new spin transfer structure has a hybrid free layer that consists of a layer with conductive channels (magnetic) and non-conductive matrix (non-magnetic) and traditional free layer(s). Two mechanisms, a higher local current density by nano-current-channels and a non-uniform magnetization switching (reversal domain nucleation and growth) by a magnetic nanocomposite structure, contribute in reducing the switching current density. The critical switching current density for the new spin transfer structure is reduced to one third of the typical value for the normal structure. It can be expected to have one order of magnitude or more reduction for the critical current density if the optimization of materials and fabrication processes could be done further. Meanwhile, the thermal stability of this new spin transfer structure is not degraded, which may solve the long-standing scaling problem for magnetic random access memory (MRAM). This spin transfer structure, with the proposed and demonstrated new spin switching configurations, not only provides a solid approach for the practical application of spin transfer devices but also forms a unique platform for researchers to explore the non-uniform current-induced switching process.

Review: 120 refs.

All Optical Helicity Independent Switching (AO-HIS) of magnetization, using single femtosecond laser pulses, has been demonstrated in GdFeCo ferrimagnetic alloys for various concentrations [1] as well as in other structures with antiferromagnetic coupling, Gd/Co, [Tb/Co]n/Ta/CoFeB and Mn2RuxGa [2,3,4]. Up to now, AO-HIS has never been observed for ferromagnetic layers. However, it was shown that a single pulse magnetization reversal of a ferromagnet could be observed in a spin-valve structure [5]. The switching is then achieved by the ultrashort spin current pulse generated from the ultrafast demagnetization of GdFeCo [5,6].In this work, we study Gdx(FeCo)1-x/Cu/FM spin-valve structures, where FM can be different ferromagnetic layers [7] and the composition x of the GdFeCo alloy is also changed [8]. By increasing the Gadolinium concentration x, we aim at increasing the spin current injected in the copper layer [6]. We show that this can reduce the laser fluence threshold required to observe the FM magnetization reversal. In particular, no AO-HIS of the GdFeCo layer is required and the threshold fluence for the FM layer is around 1.6 mJ/cm2 i.e. comparable to GdFeCo and Gd/Co multilayers [1,2] and smaller than what is achieved for Tb/Co/CoFeB [2] and Mn2RuxGa [3]. We also show that by changing the Curie temperature, the laser pulse duration and the Cu/FM interface, one can control the interaction between the spin current and the FM layer and so the laser fluence threshold. Finally, we measured the dynamics of the reversal of the FM layer, which happens in around a picosecond. We show a model, based on a recent theory for the ultrafast magnetization dynamics of ferromagnets [9], that explains this behavior. We thus designed spin-valve structures that could provide technological advantages regarding both speed and energy efficiency of data storage.