Current-induced domain wall motion and magnetization dynamics in CoFeB/Cu/Co

nanostripes

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J. Phys.: Condens. Matter 24 (2012) 024213 (9pp) doi:10.1088/0953-8984/24/2/024213

Current-induced domain wall motion andmagnetization dynamics in CoFeB/Cu/Conanostripes

V Uhlır1,2, J Vogel1, N Rougemaille1, O Fruchart1, Z Ishaque1, V Cros3,J Camarero4, J C Cezar5, F Sirotti6 and S Pizzini1

1 Institut Neel, CNRS and UJF, BP 166, 38042 Grenoble Cedex 9, France2 Institute of Physical Engineering, Brno University of Technology, 61669 Brno, Czech Republic3 Unite Mixte de Physique CNRS/Thales, Route departementale 128, 91767 Palaiseau cedex, France4 Departamento Fısica de la Materia Condensada, Instituto ‘Nicolas Cabrera’ and IMDEA-Nanociencia,Campus Universidad Autonoma de Madrid, 28049 Madrid, Spain5 ESRF, BP200, 38043 Grenoble, France6 Synchrotron SOLEIL, L’Orme des Merisiers, Saint-Aubin, 91192 Gif-sur-Yvette, France

E-mail: stefania.pizzini@grenoble.cnrs.fr

Received 11 June 2011, in final form 6 October 2011Published 15 December 2011Online at stacks.iop.org/JPhysCM/24/024213

AbstractCurrent-induced domain wall motion and magnetization dynamics in the CoFeB layer ofCoFeB/Cu/Co nanostripes were studied using photoemission electron microscopy combinedwith x-ray magnetic circular dichroism (XMCD-PEEM). Quasi-static measurements show thatcurrent-induced domain wall motion in the CoFeB layer is similar to the one observed in theNiFe layer of NiFe/Cu/Co trilayers, although the threshold current densities for domain walldepinning are lower. Time-resolved XMCD-PEEM measurements are used as an efficientprobe of domain wall depinning statistics. They also reveal that, during the application ofcurrent pulses, the CoFeB magnetization rotates in the direction transverse to the nanostripe.The corresponding tilt angles have been quantified and compared to analytical andmicromagnetic calculations, highlighting the influence of magnetostatic interactions betweenthe two magnetic layers on the magnetization rotation.

(Some figures may appear in colour only in the online journal)

1. Introduction

Current-induced domain wall motion (CIDM) via thespin transfer torque effect has attracted enormous interestboth because of fundamental aspects [1–3] and for thepossible applications in future spintronic memories andregisters [4, 5]. While CIDM has been most widelystudied in NiFe nanostripes, other systems such as magneticsemiconductors [6, 7], spin-valves [8, 9], and metallicsystems with perpendicular anisotropy [10–14] have also beeninvestigated. However, understanding the microscopic originsof spin torque efficiency is still a challenging theoreticalissue [3].

In order to use CIDM in devices, the threshold currentdensity for depinning domain walls (DWs) should beminimized and the spin torque efficiency, defined as the ratiobetween domain wall velocity and current density, should beenhanced. This efficiency is strongly material dependent andoptimizing material properties or nanostructure design [15] inorder to enhance it is a challenging task. A large distributionof domain wall velocities (in general much lower than100 m s−1) and relatively high threshold current densities(of the order of 1 × 1012 A m−2) have been found for NiFenanostripes.

Higher spin torque efficiencies have been reported forspin-valve trilayers. Evidence of current-induced domain wallmotion for much lower current densities than for single

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J. Phys.: Condens. Matter 24 (2012) 024213 V Uhlır et al

NiFe was first given by Grollier et al [16] for NiFe/Cu/Conanostripes, with a threshold current density of about 2 ×1010 A m−2 in the NiFe layer. It was then shown that thethreshold current density can be further lowered to less than1×1010 A m−2 by employing CoFeB as a soft magnetic layerinstead of NiFe [17]. Lower pinning strengths and smallerthreshold current densities are indeed expected for CoFeB,respectively because of the amorphous nature of the magneticlayer and because of its lower damping constant [17].

We have recently shown [9, 18] that direct magneticimaging of DW motion by XMCD-PEEM allows elucidatingthe details of domain wall motion in layered systems.Measurements carried out on NiFe/Cu/Co nanostripesallowed us to reveal large DW velocities—above 600 m s−1—for relatively low current densities, below 5 × 1011 A m−2

in the NiFe layer. The reduction of the threshold currentdensities compared to those for single NiFe systems hasbeen attributed to two phenomena. The first one is basedon the existence of spin accumulation in the DW region,resulting in a local vertical spin current acting on the DW.The pure vertical injection of a spin polarized current has beentheoretically predicted [19] to yield a larger efficiency for thespin transfer-induced DW motion. This has been confirmedrecently by measurements of transport in NiFe/Cu/CoFeand Co/MgO/NiFe nanostripes with perpendicular currentinjection [20, 21]. A second origin of the enhanced CIDMin these multilayered structures might be the Oersted fieldassociated with the current [22]. Indeed, as the applied currentis largely flowing in the Cu layer of the trilayer system, atransverse Oersted magnetic field acts on the NiFe layer andthe DWs. For the layer thicknesses and stripe widths usedhere, transverse domain walls in the NiFe or CoFeB layersare expected to be more stable than vortex walls [23]. Theinternal structure of these transverse DWs is stabilized bythe action of the transverse magnetic field. As was alreadyshown for field-induced domain wall motion [24, 25], theprecessional transformation of the DWs taking place abovethe Walker breakdown can be suppressed, leading to higherDW velocities. A similar effect was recently reported forPt/Co/AlOx systems, where a current-induced Rashba fieldwas shown to stabilize Bloch domain walls [14].

The aim of this paper is to study domain wall motionin the CoFeB layer of CoFeB/Cu/Co nanostripes, as wellas the influence of the Oersted field on the CoFeBmagnetization. Our experimental tool is synchrotron-basedXMCD-PEEM magnetic microscopy, both in quasi-staticand in time-resolved mode. We first report quasi-staticmeasurements of domain wall motion, from which averagedomain wall velocities can be extracted. We will show thattime-resolved XMCD-PEEM measurements can be used asan efficient probe of the statistical behaviour of domainwall depinning. These time-resolved measurements also allowus to show that the CoFeB magnetization rotates into thedirection transverse to the stripe during the application ofcurrent pulses, and we quantify the tilt angles. Some of theresults on CoFeB/Cu/Co nanostripes will be compared withthe ones that we previously obtained on NiFe/Cu/Co [9, 22].

Figure 1. (a) Initial CoFeB domain structure in a 300 nm wideCoFeB/Cu/Co nanostructure; A and B denote the domain wallpositions in the initial state; (b) domain structure after theapplication of a single current pulse 30 ns long of average density5.8× 1011 A m−2 (1.8× 1010 A m−2 in CoFeB).

2. Experimental details

The multilayer stacks were patterned into 300 and 400 nmwide zigzag nanostripes, with 90◦ corners (see figure 1),using electron-beam lithography combined with ion-beametching or lift-off techniques. The stack composition wasCu(3 nm)/Al(3 nm)/Co72Fe8B20(5 nm)/Cu(8 nm)/Co(7 nm)/CoO(4 nm), deposited on highly resistive Si(100) (R >

300 � cm) by dc magnetron sputtering. The spontaneousmagnetizationµ0MS of the CoFeB was measured to be 1.02 T.The Cu/Al bilayer protects the CoFeB from oxidation and theCoO underlayer improves the stack growth and increases theCo coercivity.

XMCD-PEEM measurements were performed at beam-line ID08 at the European Synchrotron Radiation Facility(ESRF) and at beamline TEMPO at SOLEIL, using a FocusIS-PEEM microscope [22]. In order to avoid electricaldischarges, the voltage between the sample and the objectivelens of the PEEM was set to 5.4 keV instead of the nominal12 keV, limiting the spatial resolution to about 0.6 µm.The local XMCD intensity in the CoFeB layer was imagedby tuning the x-ray energy to the Co L3 absorption edge(778.6 eV). The XMCD intensity is determined by theprojection of the local magnetization on the x-ray incidencedirection. To optimize the magnetic contrast, the differencebetween two consecutive images obtained with 100% left- andright-circularly polarized x-rays was computed.

Temporal resolution was obtained using the timestructure of the x-ray beam (pulses 80 ps long at arepetition rate of 1.4 MHz in four-bunch mode at the ESRF,pulses 50 ps long at 6.67 MHz in eight-bunch mode atSOLEIL). Measurements were taken in a pump–probe mode,by synchronizing the (pumping) current and field pulseswith the (probing) x-ray pulses. The temporal evolutionof the magnetic configuration in the nanostripes uponapplication of the current pulses was obtained by recording

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Figure 2. Time-resolved images, taken before (a) and after positive (b) and negative (c) current pulses, for the current densities indicated inthe figure. The time schemes for the synchronization and the delays between the magnetic field, current and x-ray pulses are also given.

images for different delays between the current and photonpulses [26–28]. For a given delay, the total acquisition timefor each XMCD image was about 1 min (30 s for each circularpolarization), meaning that sequences of up to 2×108 currentand photon pulses were averaged.

Before the measurements, the magnetization wassaturated along the nanostripe direction using an externalmagnetic field, in order to avoid the presence of domain wallsin the hard Co layer. Two kinds of measurements were thencarried out. In the first experiment, a magnetic field pulse wasapplied in the direction transverse to the stripe, in order tocreate a DW in the corners. The magnetic field amplitudewas tuned to allow creating a DW in the CoFeB withoutmodifying the Co magnetization. Current pulses of differentlengths and amplitudes were then applied to move a DWfrom its initial position. In order to reset the DW at the sameposition before each current pulse, magnetic field pulses of11 mT, 40 ns long, were applied in the direction indicated infigure 2, at the same frequency as the current pulses (see thetiming scheme in figure 2). The DW position was observed, instroboscopic mode, after the end of each current pulse. Thesemeasurements provide information on the statistics of the DWdepinning process.

In a second series of experiments, our aim was to observethe dynamical behaviour of the CoFeB magnetization duringthe application of current pulses. In this case, only currentpulses were applied, and the tilt of the CoFeB magnetizationinduced by the Oersted field was measured as a functionof the current density. Since at the end of a current pulsethe magnetization turns back reversibly along the localdirection of the nanostripe, reinitialization of the magneticconfiguration before each current pulse is not necessary.

The current flowing through the nanostructures wasdeduced from the voltage measured across the 50 � inputof a 6 GHz LeCroy oscilloscope in series with the sample.Two different values of the current density are given inthe following. The average current density is defined as thecurrent divided by the total cross-section of the nanostripe, notconsidering differences in resistivity of the different layers.When the current density in the CoFeB layer is mentioned,

we refer to the current density estimated using the individuallayer resistivities: 600 µ� cm for CoFeB [29], 6 µ� cm forCu and 35 µ� cm for Co. The resistivities of the Cu andCo layers were measured experimentally using the van derPauw technique. For the layer thicknesses we used, the currentdensity in the CoFeB layer is about 30 times smaller than theaverage current density in the stack.

3. Current-induced domain wall motion in CoFeB

Domain wall motion in the CoFeB layer was studied fora 300 nm wide CoFeB/Cu/Co nanostripe. Like for theNiFe layer of NiFe/Cu/Co nanostripes [9], DW pinningplays an important role and prevents long distance domainwall displacements. While in polycrystalline NiFe, DWpinning can be caused by crystallographic defects likegrain boundaries, in amorphous CoFeB, this source ofpinning should be minimized. However, we observed thatthe application of short magnetic field pulses can induce arather large number of domain walls in the nanostripes, andthat the current-induced domain wall displacements are notproportional to the pulse length, like for the NiFe/Cu/Cosystem. This indicates that the pinning mechanisms aresimilar and that the barriers hindering domain wall motionin the soft layer are mainly due to the presence of anisotropydefects in the Co underlayer [9]. The quantitative advantage ofCoFeB over NiFe is that lower threshold currents for domainwall depinning were found, in agreement with the earlier workof Laribi et al [17].

3.1. Quasi-static measurements

Two XMCD images representing domain wall motion inCoFeB are shown in figure 1. Before the application of currentpulses, two domain walls are present in the CoFeB layer.After the application of a single current pulse 30 ns long witha current density of 1.8 × 1010 A m−2 in the CoFeB layer(average current density 5.8× 1011 A m−2), the domain wallat one of the corners (A) is still pinned, while the domain

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wall found initially at position B moves by about 1.5 µmto position B′. The average domain wall velocity during thedisplacement is about 50 m s−1. The current density in theCoFeB layer is at least a factor of 2 smaller than the oneneeded to obtain similar DW velocities in the soft layer ofNiFe/Cu/Co trilayers [9, 18]. Note that the maximum DWvelocity during the pulse can be larger than the value of50 m s−1, since the measured average velocities can bestrongly influenced by DW pinning [9].

3.2. Dynamic measurements: depinning probability as afunction of current density

In order to obtain statistical information on the domainwall depinning process and the displacements induced bycurrent pulses, we have carried out time-resolved experimentsin pump–probe mode on a CoFeB/Cu/Co 400 nm widenanostripe. The results of these measurements are shown infigure 2. The initial magnetic configuration in the CoFeBlayer, shown in figure 2(a), is observed when setting thereinitializing magnetic field pulse before the photon pulse, thecurrent pulse coming after. A single domain wall is positionedin the corner of the nanostripe. Images were then collected forfour current density values, going from 1.19× 1010 A m−2 to1.30×1010 A m−2 in the CoFeB layer, with the delay time setsuch that the x-ray photon pulses probe the magnetic structureafter the application of the current pulses. For the lowestcurrent density for which DW displacements were observed,1.19 × 1010 A m−2 current pulses, 50 ns long, were applied,while current pulses 20 ns long were applied for larger currentdensities.

The images in figure 2(b), which show only the resultscorresponding to three current densities, illustrate that theXMCD intensity is modified in the neighbourhood of thenanostripe corner, indicating that the domain wall moves awayfrom its initial position, in the direction of the electron flow.On applying a current pulse of opposite polarity (figure 2(c))the DW moves from the same initial position in the oppositedirection, as expected from spin transfer torque theory.

Let us focus on the nanostripe region below the corner(defined by square boundaries in figure 2), where the domainwall moves during the application of current pulses. TheXMCD intensity in this region depends on the reproducibilityof the domain wall depinning and on the distance of thedisplacement. In figure 2(a), which represents the initial state,the XMCD intensity in the nanostripe corner is uniform andthe DW profile width (shown in figure 3(a)) is similar tothat found in quasi-static measurements. This means that thereinitializing magnetic field pulse reproducibly sets the DWin the same position x0, at a pinning site located in the cornerregion.

The XMCD intensity below the nanostripe cornerdepends on the current density value, and at first glanceit decreases, i.e. the region becomes darker, as the currentdensity increases. The XMCD intensities obtained from thelinescan profiles around the nanostripe corner, for the initialstate and the four current densities, are shown in figure 3. Foreach current density value, the XMCD intensity for the two

Figure 3. (a) Normalized XMCD intensity profiles in the regionaround the nanostripe corner obtained from the XMCD imagesshown in figure 2. (b) Derivatives of the curves in (a). Prior todifferentiation, the profiles in (a) were further smoothed by therunning average method to minimize artificial peaks in thederivative signal.

magnetization directions is normalized to the intensity foundfor the initial state (−0.025 for the black domain and 0.02 forthe white domain). Note that this intensity is not homogeneouswithin a domain (see figure 2 outside the square) becausethe CoFeB magnetization direction is not always well alignedalong the nanostripe. The width 1x of the region of transitionbetween negative and positive intensity (about 0.6 µm) isdetermined by the DW width and the distribution of initial DWpositions, convoluted with the resolution function. Figure 2(b)shows that when the current density increases, and thereforethe probability of depinning the DW from x0 increases, theintensity to the left of x0 decreases. If after depinning, thedomain wall moves systematically to a new position x1, aconstant intensity is expected between the initial and the finalposition. This is the case for the dotted and dash-dotted curvesin figure 3, where the domain wall appears to move to asecond pinning site located at approximately 1 µm from theinitial position. For the dashed curves, taken for larger currentdensities, the variation of intensity that is observed between

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Figure 4. (a) Time constant τ for depinning of the DW in the CoFeB layer from the initial position in the nanostripe corner, calculated fromthe depinning probabilities obtained with the two methods described in the text. (b) Simulated dependence of the energy barrier height andDW width on the Oersted field for 100 nm wide nanostripes. Dashed vertical bars define the range of Oersted fields causing a transverse tiltof the magnetization in the 100 nm wide nanostripe which is the same as the tilts experimentally observed in the 400 nm wide nanostripe,for the current densities in (a) (see also figure 6(a)).

these two sites is indicative of a larger distribution of DWdisplacements.

The intensity linescans presented in figure 3 thus containinformation on the probability distribution of the DWdepinning and the associated displacements. In the case ofthe dotted and dash-dotted curves, the depinning probabilitiescan be easily inferred from the relative XMCD intensity at theinitial DW position x0 = 0.4 µm. This is more difficult for thehigher current densities, where DWs that moved to a positionclose to x0 still give a contribution to the XMCD intensity atx0. Alternatively, the probabilities can be obtained from thederivative of the linescan profiles (figure 3(b)). In these plots,the profiles represent the DW position probability distributionconvoluted with the derivative of the DW intensity profile7.The contrast normalization in figure 3(a) implies that forany current density the area below the differentiated curve isconstant. This allows us to deduce the probability of finding aDW in a given interval. If the initial DW position is accuratelydefined without a significant variance and the shape of theresponse function is approximately Gaussian, one can obtainthe DW depinning probability for each of the current densitiesdirectly from the relative peak heights. However, this is validonly if the peaks at the initial DW position are isolated (dottedand dash-dotted curves). For the higher current density values,the peaks at x0 overlap with the tails of the Gaussian peaksmore to the left, and the depinning probability was obtainedby subtracting the intensity due to these tails from the peaks atx0. The probabilities obtained from the linescan intensities infigure 3(a) and the derivatives in figure 3(b) differ by about15%. The probabilities obtained using the derivatives were30%, 35%, 79% and 89% for increasing current densities.

The thermally activated depinning over a single energybarrier 1E at a temperature T can be described by theArrhenius law, where the probability of overcoming the

7 (f ∗ g)′ = f ∗ g′ where f is the DW position probability distribution and gthe DW profile.

barrier is characterized by a time constant τ = τ0e1E/kT .This time constant expresses the mean waiting time for theDW to depin, with 1/τ0 being an attempt frequency whosevalue is 108–1012 Hz for most magnetization processes [30].The probability of depinning a domain wall with a currentpulse of duration t is given by P = 1 − e−t/τ . The timeconstants τ obtained from the probabilities extracted with thetwo methods described above are plotted in figure 4(a).

Note that the time constants, of the order of 10 to150 ns for CoFeB current densities between 1.19 and 1.30 ×1010 A m−2 and no applied field, are eight orders ofmagnitude smaller than those reported for FePt nanostructureswith perpendicular anisotropy [31]. Using 1/τ0 = 109 Hz, asis usually done in the literature, energy barriers of the orderof 0.06–0.12 eV are found for the different current densities.These energy barriers are about one order of magnitudesmaller than those found by Himeno et al for depinning DWsfrom ∼300 nm wide constrictions in 500 nm wide NiFenanostripes using an applied field [32]. Although both thecurrent density and the pulse length ranges are too short toallow drawing quantitative conclusions, the effective energybarrier does not appear to scale in a linear way with thecurrent density. Some recent theories have indeed predicteda quadratic term in the current density dependence of theenergy barrier [33, 34], though this quadratic term should besmall with respect to the linear term [33]. It should be takeninto account that in our case an increase in current densityincreases both the spin transfer torque and the transverseOersted field (see section 4). This increase in the transversefield leads to an increase of the effective domain wallwidth (smaller dθ/dx) and thus to easier depinning, whichcontributes to the nonlinearity. The DW width as a functionof transverse field, calculated using Thiele’s formula [35]using data from micromagnetic simulations performed withOOMMF [36] on 100 nm wide nanostripes, is shown by thecurve with circles of figure 4(b). This increase of the DW

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width does indeed lead to lowering of the effective barrierupon increasing the current (figure 4(b)). In the case of apinning site based on an anisotropy defect in the Co layer (inour simulations defined by a block of 50 × 50 × 7 nm3 inthe middle of the stripe, with a uniaxial anisotropy constantK = 520 kJ m−3 and an easy axis at 45◦ with respect to thestripe length), the decrease in energy barrier upon increasingthe current shows a trend that is similar to the one that weobserved experimentally (black curve in figure 4(b)). Theseanisotropy defects constitute the main source of pinning inthese nanostripes, as suggested in [9]. In the case of pinning bya constriction (defined by two 16×8 nm2 notches at the edgesof the stripe), the trend is linear (red curve in figure 4(b)),which suggests that the effect of the transverse field is smallerfor DW depinning arising from edge roughness than fordepinning arising from an anisotropy defect. Nevertheless,it was shown that the depinning from natural or lithographydefects in similar trilayer systems can also be considerablymodified by the Oersted field [37].

Although the XMCD intensity away from the nanostripecorner indicates the presence of a large distribution ofdisplacements, as expected for current densities close to thedepinning threshold (i.e. in the creep regime [13, 38]), forthe lowest two current density values the depinned domainwall appears to move on average by about 1.2 µm. Takinginto account that the two pulses are applied for respectively50 ns and 20 ns, this gives average DW velocities of 24 m s−1

and 60 m s−1, for CoFeB current densities of 1.19 and1.21×1010 A m−2, respectively. Our previous experience withNiFe/Cu/Co trilayers and the fact that the displacements donot scale with the pulse length indicate that the domain wallmovements are strongly hindered by pinning. It is thereforevery likely that the instantaneous DW velocity is much largerthan the average velocity over the length of the pulse forCoFeB also.

4. Oersted field-induced magnetization rotation

XMCD-PEEM measurements in the stroboscopic mode canalso be carried out with the x-ray bunches arriving during theapplication of current. In this case, the measurements shouldgive information on the dynamical behaviour of domain wallsduring the current pulses. Our previous measurements [22]have however revealed that in our samples, the domainwall dynamics is hidden by another effect. In NiFe/Cu/Cotrilayered nanostripes, the Oersted field associated withthe current pulses leads to a large tilt of the soft layermagnetization in the direction transverse to the stripes(perpendicular to the current direction). This magnetizationtilt is reinforced by the magnetostatic interaction betweenthe NiFe and Co layers, which acts in opposite directionsdue to the opposite direction of the Oersted field in thetwo layers. Because of the large magnetization tilt, whichdominates the XMCD contrast along the nanostripes, thedirect observation of the domain walls during the currentpulses becomes often impossible when high currents, beyondthe depinning threshold, are applied.

Figure 5. Magnetic images obtained in stroboscopic mode for theCoFeB layer of a 400 nm wide CoFeB/Cu/Co nanostripe. Theimages were acquired with the photon pulses set at the end of theplateau of current pulses 2 ns long, with current densities averagedover the stack of +2.1× 1011 A m−2 (b), +4.2× 1011 A m−2 (c),−4.2× 1011 A m−2 (d) and +6.3× 1011 A m−2 (e). No currentpulses were applied during the acquisition of the image in (a). Theapproximate magnetization directions and the electron flowdirection are indicated in the images.

For a better understanding of this effect, the magnetiza-tion tilt as a function of current density has been measured forthe CoFeB layer of a 400 nm wide CoFeB/Cu/Co nanostripe.In figure 5 we illustrate the evolution of the XMCD-PEEMintensity as a function of the current density. The stroboscopicimages were collected setting the photon pulse at the endof the plateau of a current pulse 2 ns long. It shouldbe noted that the Oersted field induces oscillations of themagnetization vector about the effective field, which arehowever largely damped out after a few nanoseconds. Theimages in figure 5 are thus representative for the quasi-staticmagnetic configuration of the CoFeB stripe for a constantvalue of the current and thus of the Oersted field. In theinitial state (figure 5(a)), apart from the presence of twosmall domains, the two sections of the stripe show globallythe same magnetic contrast. Without applied current or field,the shape anisotropy is expected to orient the magnetizationalong the stripe axis, and the observed magnetic contrastcorresponds to the magnetization directions indicated in thefigure. The images in figures 5(b)–(d), taken for current

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Figure 6. (a) Tilt angles of the CoFeB magnetization as a function of the average current density (empty squares), compared to the tiltdetermined for a 400 nm wide stripe of NiFe(5 nm)/Cu(5 nm)/Co(5 nm) trilayer (full squares). The lines are guides to the eye.(b) Theoretical transverse field dependence of the tilt angle, for a single 5 nm thick and 400 nm wide CoFeB layer with µ0MS = 1.02 Tusing an analytical model (empty circles) and micromagnetic simulations (OOMMF code, full circles). The tilts calculated with theanalytical model (respectively OOMMF) taking into account the magnetostatic interaction between the CoFeB and Co layers, with anopposite Oersted field acting on the two layers, are shown with empty squares (respectively full squares) for CoFeB and empty triangles(respectively full triangles) for Co (the tilt angle for the Co layer is in the direction opposite to the CoFeB one).

pulses of increasing amplitudes, show a gradual change of themagnetic contrast of the two sections of the nanostripe. Asthe magnetic contrast is proportional to the projection of themagnetization on the x-ray incidence direction, a clockwisetilt of the magnetization direction, transverse to the stripe axis,can be inferred from the images taken during the applicationof positive current pulses. Accordingly, a counterclockwiserotation can explain the opposite change in contrast obtainedwhen negative current pulses are applied (figure 5(e)). It canbe noticed that for the highest current density, one of thewhite domains in the bottom branch has disappeared due toirreversible motion of one of the domain walls.

In figure 6(a) the tilt angles obtained as a functionof the current density from the images measured forthe CoFeB(5 nm)/Cu(8 nm)/Co(7 nm) nanostripe (imagespartially reported in figure 5) are compared with thoseobtained for NiFe(5 nm)/Cu(5 nm)/Co(5 nm) nanostripes of400 nm width. The tilt angles measured for the CoFeB layerare very similar to the ones obtained for the NiFe layer of thesame width.

Let us comment on the absolute values of theexperimental tilt angles compared with the results ofcalculations. The curve with empty circles in figure 6(b)shows the tilt angle obtained using an analytical calculationfor a single 5 nm thick, 400 nm wide CoFeB nanostripe,subject to a transverse magnetic field, supposing that themagnetization tilt is uniform over the width and the thicknessof the stripe. This calculation predicts a magnetization tiltangle of 70◦ for a transverse magnetic field of about 22 mT,while in the experiment this tilt angle is reached for anOersted field of about 6 mT. The calculated angle reaches90◦ for a transverse field of 23.5 mT, determined by thedemagnetizing factor of a stripe of such geometry (0.023) [39]and the CoFeB spontaneous magnetization of 1.02 T (Hd =

µ0Ms × 0.023). Two facts should be emphasized when

comparing experimental and calculated angles: (i) for agiven Oersted field, the experimental tilt angles found forthe CoFeB in the trilayer are much larger than the onescalculated for a single CoFeB layer; (ii) the dependenceof the angle on the transverse field calculated with thisuniform magnetization model is also very different from thatobserved experimentally. The inhomogeneous distribution ofthe demagnetizing field, which is much larger at the stripeedges than in the centre, is taken into account using aOOMMF micromagnetic simulation [36] (curve with fullcircles in figure 6(b)). The OOMMF results were obtainedusing an exchange constant A of 2.8 × 10−11 J m−1 forCoFeB [40] (3 × 10−11 J m−1 for Co), and a spontaneousmagnetization µ0MS of 1.02 T (1.76 T for Co). The fieldvariation of the tilt angles is in better agreement withexperiments than the analytical calculation, but the orderof magnitude of the tilt angles is the same. The simpleranalytical model can therefore be used to understand thephysical reasons for the discrepancy between the experimentaltilts angles and the ones expected for a single CoFeB layer.

This difference is mainly due to the presence of theCo underlayer in the CoFeB/Cu/Co trilayers, leading tomagnetostatic interactions between the CoFeB and Co layersthat should be taken into account. These magnetostaticinteractions lead to a partial flux closure and thereforean increased susceptibility in the transverse direction. Inthe model with uniform magnetization, this interactionbetween the two layers leads to a negative cross-term inthe demagnetizing term, given by NcM1M2 (the Mi beingthe transverse components of magnetization in each layer).Nc can be analytically evaluated [41] and depends on thedistance between the two magnetic layers, their thicknessesand the stripe width. This cross-term adds up to the usualdemagnetizing terms of each layer, given by NiM2

i . This is a

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generalization of demagnetizing coefficients in trilayers, thusyielding a quadratic form in M1 and M2.

The tilt angles, calculated within this model as a functionof current density for the CoFeB layer of the 400 nmCoFeB/Cu/Co nanostripe, are shown by the curve withempty squares of figure 6(b). Including the magnetostaticinteractions improves the quantitative agreement with theexperimental values considerably. A CoFeB tilt angle of 70◦,obtained experimentally with 6 mT, requires a field of 9 mTin this model, compared with a field as high as 22 mT whenconsidering the CoFeB layer alone. The important role of themagnetostatic interactions between the two magnetic layers inthe magnetization tilt is confirmed by the results of OOMMFsimulations comprising the complete trilayer stack (curve withfull squares in figure 6(b)).

We also emphasize that the Oersted fields acting on theCoFeB layer have been calculated supposing a homogeneouscurrent distribution. If we suppose that, due to the high CoFeBresistivity, the current flows only in the Cu and Co layers, theaverage Oersted field acting on the CoFeB layer is about 30%higher than the one indicated in figure 6(a), giving a betteragreement with the theoretical model.

5. Conclusions

We have used XMCD-PEEM microscopy to study thequasi-static and dynamic behaviours of domain walls in theCoFeB layer of CoFeB/Cu/Co nanostripes. The quasi-staticbehaviour is similar to that of domain walls in the NiFe ofNiFe/Cu/Co trilayers, although the threshold current densitiesfor domain wall depinning are lower. The time-resolvedmeasurements allowed obtaining information on the statisticalbehaviour of DW depinning and propagation over manymillions of events, using an acquisition time of the order ofone minute. In the rather narrow range of current densitiesthat we could study, the effective energy barrier does notvary in a linear way with the current density. The observedtrend is compatible with an increase of the domain wallwidth upon increasing the current density, due to the increaseof the transverse Oersted field. These results clearly showthat carrying out these measurements over a large currentdensity range would provide a reliable way to obtain accurateinformation on the current density dependence of the effectiveenergy barrier.

The time-resolved images taken during the applicationof current pulses, for different values of the current density,have allowed us to quantify the Oersted field-inducedrotation of the CoFeB magnetization. The observed CoFeBmagnetization tilt for an average current density of 5 ×1011 A m−2, induced by the combined effects of the Oerstedfield and the magnetostatic interaction with the Co layer, issimilar to the one expected for a single CoFeB layer with thesame thickness and width upon application of a transversemagnetic field as large as 20 mT. This internal transversefield may contribute to the enhancement of the spin torqueefficiency in the soft layer of magnetic trilayers, similarly tothe increased efficiency of field-induced motion in single NiFelayers when a transverse external field is applied [24].

Acknowledgments

We acknowledge invaluable technical and experimental helpfrom E Wagner, M Bonfim, D Lepoittevin, C Hoarau,E Jimenez, L Delrey, T Fournier and A Hrabec. VU is gratefulto R Kalousek for discussions. Samples were patterned atthe NANOFAB facility of the Institut Neel (CNRS). VU wasfinancially supported by the grants No. MSM0021630508,No. KAN400100701, No. 2E13800101-MSMT and by theproject INGO No. LA287 of the Czech Ministry of Education.This work was partly supported by the Agence Nationalde la Recherche under Grant No. ANR-07-NANO-034‘DYNAWALL.’ ZI is grateful to the Higher EducationCommission (HEC) of Pakistan for a scholarship.

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