A rich variety of specific multidomain textures recently observed in antiferromagnetically coupled multilayers with perpendicular anisotropy include regular (equilibrium) multidomain states as well as different types of topological magnetic defects. Within a phenomenological theory we have classified and analyzed the possible magnetic defects in the antiferromagnetic ground state and determine their structures. We have derived the optimal sizes of the defects as functions of the antiferromagnetic exchange, the applied magnetic field, and geometrical parameters of the multilayer. The calculated magnetic phase diagrams show the existence regions for all types of magnetic defects. Experimental investigations of the remanent states (observed after different magnetic pre-history) in [Co/Pt]/Ru multilayers with wedged Co layers reveal a corresponding succession of different magnetic defect domain types.
Antiferromagnetically coupled multilayers with perpendicular anisotropy, as [CoPt]/Ru, Co/Ir, Fe/Au, display ferromagnetic stripe phases as the ground states. It is theoretically shown that the antiferromagnetic interlayer exchange causes a relative shift of domains in adjacent layers. This ``exchange shift'' is responsible for several recently observed effects: an anomalous broadening of domain walls, the formation of so-called ``tiger-tail'' patterns, and a ``mixed state'' of antiferromagnetic and ferromagnetic domains in [CoPt]/Ru multilayers. The derived analitical relations between the va…
In antiferromagnetically coupled multilayers with perpendicular anisotropy unusual multidomain textures can be stabilized due to a close competition between long-range demagnetization fields and short-range interlayer exchange coupling. In particular, the formation and evolution of specific topologically stable planar defects within the antiferromagnetic ground state, i.e. wall-like structures with a ferromagnetic configuration extended over a finite width, explain configurational hysteresis phenomena recently observed in [Co/Pt(Pd)]/Ru and [Co/Pt]/NiO multilayers. Within a phenomenological th…
The thermodynamic properties of the electron gas in multilayer graphene depend strongly on the number of layers and the type of stacking. Here we analyse how those properties change when we vary the number of layers for rhombohedral stacked multilayer graphene and compare our results with those from a conventional two dimensional electron gas. We show that the highly degenerate zero energy Landau level which is partly filled with electrons and partly with holes has a strong influence on the value of the different thermodynamic quantities.
Strong magnetoresistance effects are often observed in ferromagnet-nonmagnet multilayers, which are exploited in state-of-the-art magnetic field sensing and data storage technologies. In this work we report a novel current-perpendicular-to-plane magnetoresistance effect in multilayer graphene as grown on a catalytic nickel surface by chemical vapor deposition. A negative magnetoresistance effect of 10^4% has been observed, which persists even at room temperature. This effect is correlated with the shape of the 2D peak as well as with the occurrence of D peak in the Raman spectrum of the as-gro…
We present a ferromagnetic resonance (FMR) study of the effect of Helium ion irradiation on the magnetic anisotropy, the linewidth and the Gilbert damping of a Co/Ni multilayer coupled to Co/Pd bilayers. The perpendicular magnetic anisotropy decreases linearly with He ion fluence, leading to a transition to in-plane magnetization at a critical fluence of 5x10^{14} ions/cm^2. We find that the damping is nearly independent of fluence but the FMR linewidth at fixed frequency has a maximum near the critical fluence, indicating that the inhomogeneous broadening of the FMR line is a non-monotonic fu…
We report the experimental observation of collective picosecond magnetization dynamics in [Co/Pd]8 multilayers with perpendicular magnetic anisotropy. The precession frequency shows large and systematic variation from about 5 GHz to about 90 GHz with the decrease in the Co layer thickness from 1.0 nm to 0.22 nm due to the linear increase in the perpendicular magnetic anisotropy. The damping coefficient 'alpha' is found to be inversely proportional to the Co layer thickness and a linear relation between the perpendicular magnetic anisotropy and 'alpha' is established. We discuss the possible re…
The effect of disorder on the perpendicular magnetoresistance of magnetic multilayers is investigated theoretically. Various kinds of disorder are considered: (i) interface substitutional disorder and (ii) bulk disorder in the various layers and in the leads. The calculations are based upon the non-equilibrium Green's function formalism, together with the recursion method for calculating the real-space Green's function.
To address thermal stability issues for spintronic devices with a reduced size, we investigate spin-orbit torque in Co/Pt multilayers with strong perpendicular magnetic anisotropy. Note that the spin-orbit torque arises from the global imbalance of the spin currents from the top and bottom interfaces for each Co layer. By inserting Ta or Cu layers to strengthen the top-down asymmetry, the spin-orbit torque efficiency can be greatly modified without compromised perpendicular magnetic anisotropy. Above all, the efficiency builds up as the number of layers increases, realizing robust thermal stab…
Recently synthesized magnetic multilayers with strong perpendicular anisotropy exhibit unique magnetic properties including the formation of specific multidomain states. In particular, antiferromagnetically coupled multilayers own rich phase diagrams that include various multidomain ground states. Analytical equations have been derived for the stray-field components of these multidomain states in perpendicular multilayer systems. In particular, closed expressions for stray fields in the case of ferromagnetic and antiferromagnetic stripes are presented. The theoretical approach provides a basis…
We present an analytical theory to describe three-dimensional magnetic textures in perpendicularly magnetized magnetic multilayers that arise in the presence of magnetostatic interactions and the Dzyaloshinskii-Moriya interaction (DMI). We demonstrate that domain walls in multilayers develop a complex twisted structure, which persists even for films with strong DMI. The origin of this twist is surface-volume stray field interactions that manifest as a depth-dependent effective field whose form mimics the DMI effective field. We find that the wall twist has a minor impact on the equilibrium sky…
We use broadband ferromagnetic resonance spectroscopy and x-ray diffraction to investigate the fundamental origin of perpendicular anisotropy in Co90Fe10/Ni multilayers. By careful evaluation of the spectroscopic g-factor, we determine the orbital moment along the out-of-plane and in-plane directions. For the multilayers, we find a direct relationship between the orbital moment asymmetry and the perpendicular anisotropy, consistent with the theory of Bruno [P.Bruno, Phys. Rev. B, 39, 865 (1989)]. A systematic x-ray diffraction study revealed the presence of a trigonal strain as high as 0.7 % i…
The transverse anisotropy constant and the related Döring mass density are key parameters of the one-dimensional model to describe the motion of magnetic domain walls. So far, no general framework is available to determine these quantities from static characterizations such as magnetometry measurements. Here, we derive a universal analytical expression to calculate the transverse anisotropy constant for the important class of perpendicular magnetic multilayers. All the required input parameters of the model, such as the number of repeats, the thickness of a single magnetic layer, and the layer…
Multifunctional materials composed of ultrathin magnetic films with perpendicular magnetic anisotropy combined with ferroelectric substrates represent a new approach toward low power, fast, high density spintronics. Here we demonstrate Co/Ni multilayered films with tunable saturation magnetization and perpendicular anisotropy grown directly on ferroelectric PZT [Pb(Zr_xTi_1-x)O_3] substrate plates. Electric fields up to +/- 2 MV/m expand the PZT by 0.1% and generate at least 0.02% in-plane compression in the Co/Ni multilayered film. Modifying the strain with a voltage can reduce the coercive f…
We report on a strong perpendicular magnetic anisotropy in [CoFe 0.4nm/Pd t]6 (t = 1.0-2.0 nm) multilayers fabricated by DC sputtering in a ultrahigh vacuum chamber. Saturation magnetization, $M_s$, and uniaxial anisotropy, $K_u$, of the multilayers decrease with increasing the spacing thickness, with a $M_s$ of 155 emu/cc and a $K_u$ of 1.14$\times 10^5$ J/m$^3$ at a spacing thickness of t = 2 nm. X-ray absorption spectroscopy and X-ray magnetic circular dichroism measurements reveal that spin and orbital magnetic moments of Co and Fe in CoFe film decrease as function of Pd thickness, indicat…
We discuss a mesoscopic mechanism of exchange interaction in ferromagnet-normal metal-ferromagnet multilayers. We show that in the case when the metal's thickness is larger than the electron mean free path, the relative orientation of magnetizations in the ferromagnets is perpendicular. The exchange energy between ferromagnets decays with the metal thickness as a power law.
We study the spin-wave dynamics in nanoscale antidot lattices based on Co/Pd multilayers with perpendicular magnetic anisotropy. Using time-resolved magneto-optical Kerr effect measurements we demonstrate that the variation of the antidot shape introduces significant change in the spin-wave spectra, especially in the lower frequency range. By employing micromagnetic simulations we show that additional peaks observed in the measured spectra are related to narrow shell regions around the antidots, where the magnetic anisotropy is reduced due to the Ga+ ion irradiation during the focused ion beam…
Within the framework of a two-band tight-binding model, we have performed calculations of giant magnetoresistance, exchange coupling and thermoelectric power (TEP) for a system consisting of three magnetic layers separated by two non-magnetic spacers with the first two magnetic layers strongly antiferromagnetically exchange-coupled. We have shown how does the GMR relate with the corresponding regions of magnetic structure phase diagrams and computed some relevant hysteresis loops, too. The GMR may take negative values for specific layers thicknesses, and the TEP reveals quite pronounced oscill…
We present a calculation of current-induced torques in metallic magnetic multilayers derived from the spin-dependent transmission and reflection properties of the magnetic layers. A scattering formalism is employed to calculate the torques in a magnetic-nonmagnetic-magnetic trilayer, for currents perpendicular to the layers, in both the ballistic and diffusive regimes.
Perpendicular magnetic anisotropy (PMA) and dynamic magnetization reversal process in [CoFeB $t$ nm/Pd 1.0 nm]$_n$ ($t$ = 0.4, 0.6, 0.8, 1.0, and 1.2 nm; $n$ = 2 - 20) multilayer films have been studied by means of magnetic hysteresis and Kerr effect measurements. Strong and controllable PMA with an effective uniaxial anisotropy up to 7.7$\times$ 10$^6$ J.m$^{-3}$ and a saturation magnetization as low as 200 emu/cc are achieved. Surface/interfacial anisotropy of CoFeB/Pd interfaces, the main contribution to the PMA, is separated from the effective uniaxial anisotropy of the films, and appears …
Current induced spin-orbit torques have been studied in ferromagnetic nanowires made of 20 nm thick Co/Pd multilayers with perpendicular magnetic anisotropy. Using Hall voltage and lock-in measurements, it is found that upon injection of an electric current both in-plane (Slonczewski-like) and perpendicular (field-like) torques build up in the nanowire. The torque efficiencies are found to be as large as 1.17 kOe and 5 kOe at 108 A/cm2 for the in-plane and perpendicular components, respectively, which is surprisingly comparable to previous studies in ultrathin (~ 1 nm) magnetic bilayers. We sh…
We report on the controlled switching of domain wall (DW) magnetization in aligned stripe domain structures, stabilized in [Co (0.44 nm)/Pt (0.7 nm)]$_X$ ($X = 48$, 100, 150) multilayers with perpendicular magnetic anisotropy. The switching process, induced by an external magnetic field, is monitored by measuring the evolution of the in-plane magnetization. % We show that the remanent in-plane magnetization originates from the polarization of the Bloch-type DWs. With micromagnetic simulations, we reveal that the reversal of the DW polarization is the result of the emergence and collapse of hor…
We experimentally investigate the current-induced magnetization reversal in Pt/[Co/Ni]$_3$/Al multilayers combining the anomalous Hall effect and magneto-optical Kerr effect techniques in crossbar geometry. The magnetization reversal occurs through nucleation and propagation of a domain of opposite polarity for a current density of the order of 0.3 TA/m$^2$. In these experiments we demonstrate a full control of each stage: i)the Ørsted field controls the domain nucleation and ii) domain-wall propagation occurs by spin torque from the Pt spin Hall effect. This scenario requires an in-plane magn…
We have studied the magnetic properties of multilayers composed of ferromagnetic metal Co and heavy metals with strong spin orbit coupling (Pt and Ir). Multilayers with symmetric (ABA stacking) and asymmetric (ABC stacking) structures are grown to study the effect of broken structural inversion symmetry. We compare the perpendicular magnetic anisotropy (PMA) energy of symmetric Pt/Co/Pt, Ir/Co/Ir multilayers and asymmetric Pt/Co/Ir, Ir/Co/Pt multilayers. First, the interface contribution to the PMA is studied using the Co layer thickness dependence of the effective PMA energy. Comparison of th…
Centro Atómico Bariloche（巴里洛切原子中心）；Instituto Balseiro, Universidad Nacional de Cuyo–CNEA（巴尔塞罗研究所，门多萨国立大学-国家原子能委员会）；Instituto de Nanociencia y Materiales de Aragón (INMA-CSIC)（阿拉贡纳米与材料研究所）；Universidad de Zaragoza（萨拉戈萨大学）
Magnetic lateral multilayers have been fabricated on weak perpendicular magnetic anisotropy amorphous Nd-Co films in order to perform a systematic study on the conditions for controlled nucleation of topological defects within their magnetic stripe domain pattern. A lateral thickness modulation of period $w$ is defined on the nanostructured samples that, in turn, induces a lateral modulation of both magnetic stripe domain periods $λ$ and average in-plane magnetization component $M_{inplane}$. Depending on lateral multilayer period and in-plane applied field, thin and thick regions switch indep…
The spin-orbit torque (SOT) arising from materials with large spin-orbit coupling promises a path for ultra-low power and fast magnetic-based storage and computational devices. We investigated the SOT from magnetron-sputtered BixSe(1-x) thin films in BixSe(1-x)/CoFeB heterostructures by using a dc planar Hall method. Remarkably, the spin Hall angle (SHA) was found to be as large as 18.83, which is the largest ever reported at room temperature (RT). Moreover, switching of a perpendicular CoFeB multilayer using SOT from the BixSe(1-x) has been observed with the lowest-ever switching current dens…
Stripe states in multilayer systems with perpendicular polarization are investigated by analytical calculations within a general continuum approach, applicable to ferromagnetic, ferroelectric, or ferroelastic nanoscale superlattices. The competition between the long-range depolarization effect and short-range interlayer couplings can stabilize monodomain states and unusual stripe phase ground states with antiparallel polarization in adjacent layers. Geometric parameters of stable stripe domain states and the phase transitions lines between single domain states, aligned and antialigned stripe s…
We experimentally study spin-Hall nano-oscillators based on [Co/Ni] multilayers with perpendicular magnetic anisotropy. We show that these devices are capable of single-frequency auto-oscillations at current densities comparable to those in the in-plane magnetized oscillators. The demonstrated oscillators exhibit large magnetization precession amplitudes, and their oscillation frequency is highly tunable by the electric current. These features make them promising for applications in high-speed integrated microwave circuits.
Tailoring Ultrathin Magnetic Multilayers at Terraced Topologically Insulating Interfaces for Perpendicularly Magnetized Domains
University of Leeds（利兹大学）；ISIS Neutron and Muon Source, STFC Rutherford Appleton Laboratory（STFC卢瑟福阿普尔顿实验室中子与μ子源）；Diamond Light Source（钻石光源）；Imperial College London（伦敦帝国理工学院）
The magnetization dynamics in nanostructures has been extensively studied in the last decades, and nanomagnetism has evolved significantly over that time, discovering new effects, developing numerous applications, and identifying promising new directions. This includes magnonics, an emerging research field oriented on the study of spin-wave dynamics and their applications. In this context, thin ferromagnetic films with perpendicular magnetic anisotropy (PMA) offer interesting opportunities to study spin waves, in particular, due to out-of-plane magnetization in remanence or at relatively weak …
We consider the optical properties of finite systems composed of a series of graphene sheets separated by thin dielectric layers. Because these systems respond as conductors to electric fields in the plane of the graphene sheets and as insulators to perpendicular electric fields, they can be expected to have properties similar to those of hyperbolic metamaterials. We show that under typical experimental conditions graphene/dielectric multilayers have enhanced Purcell factors, and enhanced photonic densities-of-states in both the THz and mid-IR frequency range. These behaviors can be traced to …
We address two finite size effects in perpendicular transport through magnetic multilayers. When the magnetic layer thickness in spin valves becomes of the order or smaller than the spin-flip diffusion length, structural asymmetries affect the transport properties. A magnetic layer with thickness approaching the magnetic coherence length becomes transparent for spin currents polarized perpendicular to the magnetization. We use the generalized magnetoelectronic circuit theory to investigate both effects on the angular magnetoresistance (aMR) and spin transfer torque. We analyze recent aMR exper…
Nanopillar spin valve devices are typically comprised of two ferromagnetic layers: a reference layer and a free layer whose magnetic orientation can be changed by both an external magnetic field and through the introduction of spin-polarized electric current. Here we report the continuous repeated switching behavior of both the reference and free layers of a perpendicular spin valve made of Co/Pd and Co/Ni multilayers that arises for sufficiently large DC currents. This periodic switching of the two layers produces an oscillating signal in the MHz regime but is only observed for one sign of th…
Two series of [Ru10/Cox)]12 and [Ru6/Cr3/Cox)]12 x=16-60 easy-plane anisotropy multilayers (all thicknesses in Å), prepared by sputter deposition, are studied by cavity FMR. The acoustic modes are excited by setting the RF field perpendicular to the saturating in-plane field. Their resonance fields are in good agreement with the values predicted for acoustic modes by macrospin models, using the interlayer RKKY exchange and anisotropy fields derived by the magnetic measurements. The resonance fields of the modes excited by setting the RF field parallel to the saturating field, are lower than th…
A set of stacked two-dimensional electron systems in a perpendicular magnetic field exhibits a three-dimensional version of the quantum Hall effect if interlayer tunneling is not too strong. When such a sample is in a quantum Hall plateau, the edge states of each layer combine to form a chiral metal at the sample surface. We study the interplay of interactions and disorder in transport properties of the chiral metal, in the regime of weak interlayer tunneling. Our starting point is a system without interlayer tunneling, in which the only excitations are harmonic collective modes: surface magne…
Nanodots with magnetic vortices have many potential applications, such as magnetic memories (VRAMs) and spin transfer nano-oscillators (STNOs). Adding a perpendicular anisotropy term to the magnetic energy of the nanodot it becomes possible to tune the vortex core properties. This can be obtained, e.g., in Co nanodots by varying the thickness of the Co layer in a Co/Pt stack. Here we discuss the spin configuration of circular and elliptical nanodots for different perpendicular anisotropies; we show for nanodisks that micromagnetic simulations and analytical results agree. Increasing the perpen…
Spin-orbit torque (SOT) magnetization switching of ferromagnets with large perpendicular magnetic anisotropy has a great potential for the next-generation non-volatile magnetoresistive random-access memory (MRAM). It requires a high-performance pure spin current source with a large spin Hall angle and high electrical conductivity, which can be fabricated by a mass production technique. In this work, we demonstrate ultrahigh efficient and robust SOT magnetization switching in all-sputtered BiSb topological insulator - perpendicularly magnetized Co/Pt multilayers. Despite fabricated by the indus…
We investigate multilayer systems of a normal insulator and a Weyl semimetal. We calculate the bulk band structure and determine phase diagrams by changing the thickness of the normal insulator and that of the Weyl semimetal layer using two models; one is from the effective model for a Weyl semimetal, and the other is the lattice model. We compare the results between the two models, and found that they agree well. As a result, we find that the multilayer system shows a qualitatively different behavior depending on the stacking direction relative to the displacement vector connecting between tw…
The scattering theory of transport has to be applied with care in a diffuse environment. Here we discuss how the scattering matrices of heterointerfaces can be used to compute interface resistances of dirty magnetic multilayers. First principles calculations of these interface resistances agree well with experiments in the CPP (current perpendicular to the interface plane) configuration.
We present temperature dependent switching measurements of the Co/Ni multilayered free element of 75 nm diameter spin-valve nanopillars. Angular dependent hysteresis measurements as well as switching field measurements taken at low temperature are in agreement with a model of thermal activation over a perpendicular anisotropy barrier. However, the statistics of switching (mean switching field and switching variance) from 20 K up to 400 K are in disagreement with a Néel-Brown model that assumes a temperature independent barrier height and anisotropy field. We introduce a modified Néel-Brown mod…
Magnetic bilayers with different magnetic anisotropy directions are interesting for spintronic appli- cations as they offer the possibility to engineer tilted remnant magnetization states. We investigate the ferromagnetic resonance (FMR) linewidth of modes associated with two interlayer exchange- coupled ferromagnetic layers, the first a CoNi multilayer with a perpendicular magnetic anisotropy, and the second a CoFeB layer with an easy-plane anisotropy. For antiferromagnetic interlayer ex- change coupling, elevated FMR linewidths are observed below a characteristic field. This is in contrast t…
The perpendicular magnetic anisotropy at the Co/oxide interface in Pt/Co/MOx (MOx = MgOx, AlOx, TbOx) was modified by an electric field using a 10 nm-thick ZrO2 as a solid electrolyte. The large voltage-driven modification of interfacial magnetic anisotropy and the non-volatility of the effect is explained in terms of the migration of oxygen ions towards/away from the Co/MOx interface. While the effect is reversible in Pt/Co/AlOx and Pt/Co/TbOx, where the Co layer can be oxidised or reduced, in Pt/Co/MgOx the effect has been found to be irreversible. We propose that these differences may be re…
We examine transport properties of a magnetic superlattice with current perpendicular to the planes. In the limit that the phase-breaking and spin flip scattering lengths are greater than the system size, a multiple-scattering approach is used to calculate the 4-probe conductance. We show that by tuning the strength of tunnel barriers placed between the current and voltage probes giant magnetoresistance ratios of arbitrary strength and size are achievable.
We present a comprehensive micromagnetic model of isolated axisymmetric skyrmions in magnetic multilayers with perpendicular anisotropy. Most notably, the essential role of the internal dipolar field is extensively considered with a minimum amount of assumptions on the magnetization profiles. The tri-dimensional structure of the multilayered skyrmions is modeled by their radial profiles in each layer. We first compare the results of the model against a full micromagnetic description in Cartesian coordinates. Our model combines information on both layer-dependent size and chirality of the skyrm…
Multilayers of heavy metals and ferromagnets are the basis for the formation of various structures with inhomogeneous chiral magnetic distributions. The most informative method for studying magnetic states in such structures with a high spatial resolution is Lorentz transmission electron microscopy (L-TEM). Here, we report on the observation of chiral Néel domain walls by means of L-TEM in Co/Pt multilayers with perpendicular magnetic anisotropy. We explain the existence of chiral Néel internal structure due to the overcritical, giant interfacial induced Dzyaloshinskii-Moriya interaction. Our …
Transport properties of magnetic multilayers in current perpendicular to the plane of the layers geometry are defined by diffusive scattering in the bulk of the layers, and diffusive and ballistic scattering across the interfaces. Due to the short screening length in metals, layer by layer treatment of the multilayers is possible, when the macroscopic transport equation (Boltzmann equation or diffusion equation) is solved in each layer, while the details of the interface scattering are taken into account via the boundary conditions. Embedding the ballistic and diffusive interface scattering in…
We demonstrate the existence of a new type of zero energy state associated to vacancies in multilayer graphene that has a finite amplitude over the layer with a vacancy and adjacent layers, and the peculiarity of being quasi-localized in the former and totally delocalized in the adjacent ones. In a bilayer, when a gap is induced in the system by applying a perpendicular electric field, these states become truly localized with a normalizable wavefunction. A transition from a localized to an extended state can be tuned by the external gate for experimentally accessible values of parameters.
Thickness modulation at the edges of nanostructured magnetic thin films is shown to have important effects on their perpendicular magnetic anisotropy. Thin film wires with tapered edges were made from [Co/Pd]20 multilayers or L10-FePt films using liftoff with a double layer resist. The effect of edge taper on the reversal process was studied using magnetic force microscopy and micromagnetic modeling. In [Co/Pd]20 the anisotropy was lower in the tapered edge regions which switched at a lower reverse field compared to the center of the wire. The L10-FePt wires showed opposite behavior with the t…
We study the spectral characteristics of spin current nano-oscillators based on the Pt/[Co/Ni] magnetic multilayer with perpendicular magnetic anisotropy. By varying the applied magnetic field and current, both localized and propagating spin wave modes of the oscillation are achieved. At small fields, we observe an abrupt onset of the modulation sidebands. We use micromagnetic simulations to identify this state as a dynamical magnetic skyrmion stabilized in the active device region by spin current injection, whose current-induced dynamics is accompanied by the gyrotropic motion of the core due…
We investigate the spin-transfer torque in a magnetic multilayer structure by means of a spin-diffusion model. The torque in the considered system, consisting of two magnetic layers separated by a conducting layer, is caused by a perpendicular-to-plane current. We compute the strength of the field-like and the damping-like torque for different material parameters and geometries. Our studies suggest that the field-like torque highly depends on the exchange coupling strength of the itinerant electrons with the magnetization both in the pinned and the free layer. While a low coupling leads to ver…
We report that strong perpendicular magnetic anisotropy of the ferromagnetic layer in a W/CoFeB/MgO multilayer structure can be established by inserting a Hf layer as thin as 0.25 nm between the W and CoFeB layers. The Hf spacer also allows transmission of spin currents generated by an in-plane charge current in the W layer to apply strong spin torque on the CoFeB, thereby enabling current-driven magnetic switching. The antidamping-like and field-like components of the spin torque exerted on a 1 nm CoFeB layer are of comparable magnitudes in this geometry. Both components originate from the sp…
In magnetic multilayers, a dc current induces a spin precession above a certain critical current. Drive torques responsible for this can be calculated from the spin accumulation $\bar{Δμ}$. Existing calculations of $\bar{Δμ}$ assume a uniform cross section of conductors. But most multilayer samples are pillars with current leads flaring out immediately to a much wider cross-section area than that of the pillar itself. We write spin-diffusion equations of a form valid for variable cross section, and solve the case of flat electrodes with radial current distribution perpendicular to the axis of …
