The field-induced asymmetric growth of magnetic bubble domains in Pt/Co/Pt out-of-plane magnetized films with Dzyaloshinskii–Moriya interactions (DMI) is used to control the lateral displacement of bubbles. We demonstrate experimentally that we can laterally translate bubbles away from their nucleation site by applying a series of alternating 3-dimensional field pulses with a controlled relative sign between the out-of-plane and in-plane components. Using magneto optical Kerr effect imaging, the domain wall velocity as a function of applied field strength was measured from which the magnitude of the DMI field was estimated.This work was supported by the European Community
under the Seventh Framework Programme '3SPIN' (ERC
contract 247368) and by EMRP JRP EXL04 SpinCal.
The EMRP is jointly funded by the EMRP participating
countries within EURAMET and the EU.This is the accepted manuscript. The final version is available from AIP at http://scitation.aip.org/content/aip/journal/apl/106/2/10.1063/1.4905600

Cowburn, RP

Mansell, R

Petit, D

Seem, PR

Tillette, M

Apollo (Cambridge)

2D control of eld-driven magnetic bubble movement usingDzyaloshinskii-Moriya interactionsDorothee Petit,1 Peter R. Seem,2 Marine Tillette,1 Rhodri Mansell,1 and Russell P. Cowburn11)Thin Film Magnetism group, Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue,Cambridge CB3 0HE, United Kingdom2)Durham Magneto Optics Ltd, Church Farm, Gransden Road, Caxton, Cambridge CB23 3PL,United KingdomThe eld-induced asymmetric growth of magnetic bubble domains in Pt/Co/Pt out-of-plane magnetized lmswith Dzyaloshinskii-Moriya interactions is used to control the lateral displacement of bubbles. We demonstrateexperimentally that we can laterally translate bubbles away from their nucleation site by applying a seriesof alternating 3-dimensional eld pulses with a controlled relative sign between the out-of-plane and in-planecomponents. Using magneto optical Kerr eect imaging the domain wall velocity as a function of appliedeld strength was measured from which the magnitude of the Dzyaloshinskii-Moriya interaction eld wasestimated.Domain walls in magnetic thin lms have been the ob-ject of intense research from the magnetism communityfor a number of years, due to their potential for spin-tronic devices, either as a possible route to low-powerswitching of magnetization1,2 or as an intrinsic element toshift-register-based data storage architectures3,4. Ultra-thin magnetic lms with perpendicular anisotropy andDzyaloshinskii-Moriya interactions (DMI)5,6 are receiv-ing renewed interest7 for these applications because ofrecent developments in the understanding of DMI's rolein controlling domain wall (DW) motion8: by stabilizingNeel DWs rather than Bloch DWs, the DMI is believedto be at the origin of the unusually high eciency of DWmotion in patterned strips9{11, with obvious benets toDW-based devices. Furthermore, DMI is at the originof the stabilization of complex magnetic textures such asskyrmions12,13. The prospect of their existence in thinlms opens up the possibility of using them as carriersfor data storage devices14.In thin lm systems, the DMI is due to the combi-nation of strong spin-orbit interaction in the adjacentheavy metal non-magnetic layer and broken symmetryat the interface of the magnetic material15. The DMIcouples two neighboring spins S1 and S2 via a neighbor-ing atom with large spin-orbit interaction and takes theform  D S1S2, with the DM vectorD perpendicularto the unit vector joining S1 and S2 and in the interfaceplane. The DM interaction favors a perpendicular align-ment between S1 and S2 such that both spins are in theplane perpendicular to the interface and perpendicularto D, with the chirality of the (S1;S2) arrangement setby the sign of D.Recently, the DMI was shown in Pt/Co/Pt andPt/Co/Ir/Pt systems to cause a sizable asymmetry inthe velocity of out-of-plane (OOP) eld-driven motion ofDWs in the presence of an in-plane (IP) eld, causingan asymmetry in the expansion of bubble domains16{18.This asymmetry was shown to depend on the direction ofan IP magnetic eld applied in conjunction to the OOPeld responsible for the motion. Because of the DMI, theDW around the bubble is forced into the Neel-type witha well-dened chirality. The relative direction betweenthe magnetization in the DW and the IP eld is there-fore also well-dened, and the DW velocity asymmetrywas shown to be due to the IP eld being parallel (in-creased velocity) or antiparallel (decreased velocity) tothe magnetization inside the DW.In this paper, we show that this eect can be extendedto an arbitrary two-dimensional IP applied eld18. Usingmagneto-optical Kerr eect (MOKE) microscopy19 and a3D magnetic eld setup, we demonstrate 360-degree con-trol of the direction of the asymmetric growth of bubblesin a similar Pt/Co/Pt multilayer. Furthermore, we showthat we can use this eect to laterally translate a bubbledomain in arbitrary directions. This work demonstratescontrol of the movement of bubbles without using pat-terned structures, opening up the possibility for arbitrarypaths recongurable on-the-y.FIG. 1. (a), (b): Dierential MOKE microscopy images ofOOP eld-driven expanding bubble domains with an IP biaseld H of 1.4 kOe applied in the +Y (a) and  Y (b) direc-tions, as indicated by the white arrows. The perpendicularcomponent of the eld pulse is 125 Oe. Inset: denition ofthe (X;Y; Z) directions. (c): illustration of the DMI in thecase of a DW. (d): Circular upwards bubble domain and DW(dotted line). The arrows (both IP and pointing in and outof the plane) show the directions of the magnetization in theDW.The sample studied here consists of a Ta (4 nm) / Pt(10 nm) / Co (0.8 nm) / Pt (3 nm) multilayer grownat room temperature by DC magnetron sputtering ontoa Si substrate at an Ar pressure of 8  10 3 millibars.The MOKE microscopy setup allows the application ofa 2D (X;Y ) magnetic eld using a quadrupole electro-2magnet. The sample holder has an integrated air-coil forthe application of the perpendicular Z eld. See gure1 (a) for the denition of (X;Y; Z). Correct alignmentof the quadrupole and the sample was ensured by con-rming the symmetry of the eect upon application ofa positive and a negative eld in both the horizontal Xdirection and the vertical Y direction. Figure 1 (a) and(b) show images of bubble domains expanding under theinuence of a 150 ms 125 Oe +Z-eld applied in con-junction with an IP eld of 1.4 kOe pointing in the +Y(a) or the  Y direction (b). The images are dierentialimages obtained by subtracting the initial image with abubble domain present (small dark disk) from the nalimage after the domain has expanded under the inu-ence of the eld pulse. Thus, bright regions show wherethe bubble domain has grown. It is clear that the DWexpands asymmetrically: in the presence of a positive(negative) Y eld the DW travels faster in the +Y ( Y )direction. This eect is attributed to the presence of DMIin the following way16. First, the eect of DMI on themorphology of a DW is illustrated in gure 1 (c), whichshows three interacting spins across a DW. S1 (S3) isin the upward (downward) domain and S2 is in the DWitself. The DM vectors point in the plane of the interfaceand perpendicularly to the vector joining the two inter-acting spins15. For S1, S2 and S3 here, D12 and D23point in the same direction, causing spins S1, S2 andS3 to form a Neel DW rather than a Bloch one, and torotate around the relevant D with the same well-denedchirality. In the case of a DW enclosing a bubble do-main, such as is illustrated gure 1 (d), the Dij vectorsat any point across the DW are tangential to the DW,causing the well-dened chirality to be preserved for thewhole DW. The sign of D sets whether the Neel DWaround an upward domain points inwards or outwards.While an IP eld cannot act on the reversed domain it-self, it breaks the rotational symmetry of the DW whichencloses it, allowing the possibility of anisotropic expan-sion of the bubble. Within the creep regime formalism,it was found that the velocity dependence of the DWupon the IP eld and DMI strength could be attributedto the dependence of the DW energy density upon theIP eld and DMI strength16. More practically, the partsof the DWs which have their magnetization aligned withthe IP eld have a higher velocity than the parts of theDW which are anti-aligned. We note that all the bub-bles present in the eld of view are distorted in the samedirection, conrming the homogeneity of the sign of theDMI vector.We have used a series of images obtained when apply-ing a Y bias eld in order to extract the DW velocity asa function of the IP bias eld strength for an OOP prop-agation eld of 110 Oe. The velocity is extracted fromdierential images such as gure 1 (a) and (b), where thechange between images is one eld pulse of either 300 or350 ms duration. The velocity of the DW is measuredalong the center of each bubble (dotted line in gure 1(a)), and the results are averaged between all the bub-bles present in the eld of view. In gure 2 we show thedomain wall velocity as a function of bias eld. We mea-sure the velocity of the top of the bubble, expanding inthe +Y direction, shown in red, and the bottom of thebubble, expanding in the  Y direction, shown in blue.The in set in gure 2 shows this schematically. The datais symmetric around zero eld, as expected, and the ve-locities show minima at around  500 Oe, correspondingto the IP applied eld necessary to balance the DMI eldand restore symmetry to the system. The DMI eld istherefore of the order of 500 Oe in our multilayer. Thesign agrees with previous work16 for a similar system,and our simple estimate of the DMI eld strength is ofthe same order of magnitude, conrming that we are ob-serving the same eect.FIG. 2. DW velocity as a function of IP bias eld for a +Zpropagation eld value of 110 Oe. Red symbols give the ve-locity in the +Y direction, blue symbols in the  Y direction.The solid lines are a guide to the eye. Inset: Schematic of themeasurement geometry.Figure 3 (a)-(d) shows how the asymmetric growth ofbubble domains can be controlled by applying a 2D IPeld in arbitrary directions (shown by the white arrowsin each image). In our experiment, the nucleation of bub-bles is not controlled, rather we use naturally occurringdefects to act as nucleation centers. After an initial nega-tive saturation a +Z-eld pulse is applied in the positivedirection. The amplitude and duration of the eld pulse(125 Oe for  150 ms in this case) is adjusted so thatonly a few bubbles are activated within the 500500m2eld of view used for subsequent imaging. The initial do-main is then expanded using a 75 Oe, 150 ms pulse andthe Kerr image taken after this pulse is used as a back-ground subtracted from subsequent images. Four 150 mspulses at 125 Oe in +Z are then applied with a 1 kOein-plane eld in the direction shown by the white arrowin the gure. Each image is binarized and normalizedbefore being added to form the composite image. As ex-pected, the eect seen in Figure 1 is seen for every eld3FIG. 3. (a-d): MOKE microscopy images of OOP eld-drivenexpanding bubble domains with an IP bias eld of 1 kOe ap-plied in dierent directions, as indicated by the white arrowson each image. Each image is obtained by adding 4 consec-utive Kerr images each corresponding to the application of a150 ms long eld pulse.direction in the plane of the sample: the bubbles growfaster along the direction of the IP bias eld.The next step is to transform this controlled distortionof bubble domains into controlled movement. Figure 4(a) is a schematic of the experiment performed in gure1 (a), where an upward bubble (black) grows asymmet-rically under the inuence of an +Z eld and an IP biaseld in the +Y direction (red). The small black arrowsindicate the magnetization direction in the DW. If bothcomponents of the eld are reversed (gure 4 (b)), thebubble will shrink since the OOP component of the eldis now opposite to the magnetization inside the bubble.Because the IP component of the eld has also reversed,the side of the bubble which points in the same directionas the IP component of the eld is now also reversed.The bottom of the bubble therefore shrinks faster thanthe upper part, causing the bubble to go from the ini-tial black shape to the nal blue shape. The nal lateralposition of the bubble in (b) is dierent from the initialposition of the bubble in (a). The bubble was laterallytranslated in a controlled direction set by the IP compo-nent of the applied eld.The experimental realization of this is shown in gure4 (c-s). Figure 4 (c-s) shows a series of MOKE imagestaken as symmetric pulses of alternating magnetic eld(indicated at the bottom-right corner of each image) aresequentially applied in order to grow and shrink magneticbubbles in an asymmetric fashion. First, a  Z eld pulseis applied for  1s in order to saturate the magnetizationdownwards - (c) is taken at remanence after negative sat-uration. The magnetization is uniformly pointing down.A +Z eld pulse of 110 Oe amplitude is then appliedduring 200 ms in order to nucleate bubble domains - (d)is then taken at remanence. Subsequently, 200 ms pulsesof alternating elds with an Z component of 110 Oe andan IP component of 1.1 kOe at 36 clockwise from the Xaxis is applied. Figure 4 (e-s) are taken at remanence af-ter each eld pulse. The sign of the IP component of theeld relative to the OOP component is chosen such thatthe top-left of the bubble moves faster than the bottom-right as the bubble grows while the bottom-right movesfaster than the top-left as the bubble shrinks. This re-sults in an inching movement of the bubbles towards theupper-left quadrant. This is clear when following thebubble highlighted in green for instance. In this partic-ular experiment, the eld used to propagate the bubbleis strong enough, for the particular nucleation sites ac-tivated here, to nucleate new domains each time a pulseis applied. This is clear if again we follow the bubblehighlighted in green. In (d) the just-nucleated bubble iscentered on the nucleation site in the middle of the im-age. In (e), because of the IP bias eld, it expands asym-metrically and grows faster in the ( X;+Y ) direction.In (f), a reverse eld has been applied which is strongenough to nucleate a downward domain exactly wherethe initial upward domain was nucleated in (d) - high-lighted in yellow. The resulting upward domain is thesmall crescent highlighted in green at the top left of theyellow disk. This pattern occurs for all bubbles withinthe eld of view - three of these crescents are highlightedwith a blue arrow. In (g), the eld is reversed again inorder to grow the bubbles asymmetrically towards thetop-left of the image, which also nucleates a new upwarddomain under the yellow disk. The new yellow bubbleand the expanded crescent merge. This pattern of nu-cleating new domains back and forth under the yellowdisk while moving the initial green bubble towards thetop-left of the image continues. From (o) onwards, theinitial green bubble has moved far enough away from thenucleation center that it does not merge with the upwardyellow bubble upon application of the upward eld (o, q,s). The white cross in (o-s) is placed at the center of thegreen bubble in (o), emphasizing its displacement duringthe last three eld pulses. The lateral bubble speed ishalf the dierence in domain wall velocity for the oppo-site sides of the bubble in the bias eld direction. Thelateral bubble speed will, therefore, scale with the do-main wall speed, which would allow much higher lateralbubble speed with greater magnitude pulse elds. For a1.1 kOe in-plane bias eld, the data in gure 2 gives alateral speed of around 40m=s, which, for the 15 pulsesof 200 ms length used in gure 4, leads us to expect travelof around 120m, similar to the 130m travel observed.A few points need commenting on. Firstly, the factthat only the green bubble appears to be able to es-4FIG. 4. (a), (b): Schematics showing the eect of applying alternating in-plane and out-of-plane magnetic elds. (c-s):Sequential series of MOKE images after pulses of alternating magnetic eld (indicated at the bottom-right corner of eachimage) are applied. The OOP component of the applied eld is 110 Oe, the IP component is 1.1 kOe.cape the nucleation area to travel in the direction of theIP eld. None of the subsequently-created yellow bub-bles are moving. This is because the green bubble goesthrough an additional growing step (nucleation in (d)followed by growing in (e)), as compared to the yellowbubbles which only go through a nucleation / annihila-tion cycle. Secondly, the size of the bubbles decreases asthey move, as shown by the green bubble, for instance,after it becomes independent from the nucleation center(compare (o), (q) and (s)). Some bubbles even annihi-late in the process, see for instance the traveling bubblehighlighted by a blue arrow in (k), which does not reap-pear at the subsequent growing step (m), where only itsassociated intermittent bubble is present at the corre-sponding nucleation site (yellow arrow in (k) and (m)).This behavior may be due to the eect of domain walltension, which tends to increase the domain wall velocityof a shrinking bubble at small sizes20.In conclusion, we have used MOKE microscopy and a3D magnetic eld setup to demonstrate 360-degree con-trol of the direction of the asymmetric growth of mag-netic bubble domains in a Pt/Co/Pt multilayer withDMI. We have estimated the strength of the DMI eldpresent in our lm, and shown that we can use this asym-metric growth to move a bubble in arbitrary directions byapplying alternating eld pulses with both IP and OOPcomponents of a dened relative sign. 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Two-dimensional control of field-driven magnetic bubble movement using Dzyaloshinskii-Moriya interactions

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