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Highly asymmetric chiral domain wall velocities in Y shaped junctions Chirag Garg, Aakash Pushp, See-Hun Yang, Timothy Phung, Brian P. Hughes, Charles Rettner, and Stuart S. P. Parkin Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.7b05086 • Publication Date (Web): 08 Feb 2018 Downloaded from http://pubs.acs.org on February 10, 2018

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Highly asymmetric chiral domain wall velocities in Y-shaped junctions Chirag Garg1,2,3*, Aakash Pushp1*§, See-Hun Yang1, Timothy Phung1, Brian P. Hughes1, Charles Rettner1, and Stuart S.P. Parkin1,2,3§ 1

IBM Research - Almaden, San Jose, California 95120, USA.

2

Max Planck Institute of Microstructure Physics, Halle (Saale), D06120, Germany.

3

Institute of Physics, Martin Luther University Halle-Wittenberg, Halle (Saale), D06120,

Germany. *

These authors contributed equally to the work.

§

Correspondence to be addressed to: [email protected] (A.P.); stuart.parkin@mpi-

halle.mpg.de (S.S.P.P.)

ABSTRACT: Recent developments in spin-orbit torques allow for highly efficient current driven domain wall (DW) motion in nanowires with perpendicular magnetic anisotropy. Here, we show that chiral DWs can be driven into non-equilibrium states that can persist over tens of nanoseconds in Y-shaped magnetic nanowire junctions that have an input and two symmetric outputs. A single DW that is injected into the input splits and travels at very different velocities in the two output branches until it reaches its steady-state velocity. We find that this is due to the disparity between the fast temporal evolution of the spin current derived spin-orbit torque and a much slower temporal evolution of the DMI-derived torque. Changing the DW polarity inverts the velocity asymmetry in the two output branches, a property which we use to demonstrate sorting of domains. KEYWORDS : Spintronics; domain wall motion; spin-orbit torques; DMI; biplexer

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In ultrathin perpendicularly magnetized hetero-structures, the presence of spinorbit coupling (SOC) gives rise to chiral Néel walls that are stabilized by the Dzyaloshinskii-Moriya Interaction (DMI)1-5, and also to a highly-efficient spin Hall effect6 derived spin-orbit torque (SHE-SOT) mechanism4, 5, 7-9 that allows for ultra-fast DW motion4. Several recent experiments have explored the dynamics of such DWs in presence of electric currents and magnetic fields: by modifying the geometry of the structures10; by adjusting the material parameters to obtain hedgehog skyrmions11; or by creating synthetic anti-ferromagnetic structures where the DWs are found to be moved very rapidly via an exchange coupling torque7. There have also been other recent reports, which have demonstrated that DWs have effective mass and thus have inertia12, 13. In straight nanowires, the current-driven propagation of chirality-locked Néel DWs of alternating polarities is identical, leading to the lock-step motion of several DWs in a nanowire5. On application of current, the DW tilts in response to the canting of the DW moments induced by the spin accumulation until reaching an equilibrium tilt and steady-state motion14. Here, we use the Y-shape junction15 as a tool to explore the current-driven dynamics of a chiral DW which would ordinarily not be possible in a straight wire geometry. By causing the DW to travel through an abrupt turn in the Yshape, we obtain an out-of-equilibrium tilt of the DW with respect to the new spin accumulation direction (that is defined by the current direction in the nanowire). Depending on this tilt, a DW travels either faster or slower than it would do when starting from a rest state. This is succinctly captured in the snapshots of our modelling results as shown in Fig. 1a. Eventually, the DW accelerates or decelerates to reach steady-state motion and the associated timescales can vary distinctively depending on the initial out-


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of-equilibrium tilt and width of the wire. Thus, we design various Y-shape junctions and observe dramatic differences in the DW dynamics that we explain using an extended form of the 1D model. Fig. 1b shows an optical image of a representative Y-shaped device used to perform polar-Magneto Optical Kerr Effect (p-MOKE) microscopy measurements of the DW motion. The device is patterned (see methods) using standard lithography techniques from the magnetic stack: 100 AlOx | 20 TaN | 15 Pt | 3 Co | 7 Ni | 1.5 Co | 50 TaN (the numbers indicate the respective film thicknesses in Å) grown by magnetron sputtering on Si substrates with a 250 Å SiO2 layer for electrical isolation. Care is taken so that there is minimal roughness along the edges of the structure (see supplementary section 5 for an AFM scan of the Y-shape device) so that both output branches B and C, with an angle between them, are nominally identical for DW motion. The input A is designed to be twice in width as compared to the widths of the two output branches B and C to keep the current density across the entire Y-shaped structure constant (the current crowding near the bifurcation region is highly localized as obtained from finite element modeling as discussed in the supplementary section 1). A nanosecond voltage pulser is connected to the input branch whereas the two output branches are electrically grounded. Fig. 1c illustrates schematically the SHE16 derived spin accumulation profile at the Pt-Co interface due to the current flowing in the Pt underlayer along the different branches of the structure. A DW is first created in the input branch A (see supplementary section 2 for more details) and is then moved towards the bifurcation region of the Y-junction by a predetermined distance without any external magnetic field. Once the DW is at the


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desired location, the background p-MOKE contrast is reset. Afterwards, a single pulse of voltage with a typical rise time of 300ps and a fall time of 700ps and pulse length is applied across the device, which makes the DW (i) move distance from its initial position in branch A, (ii) split into two DWs that then (iii) travel into the two output branches, represented by the p-MOKE contrast images (Fig. 2a). The distances traversed and by the two DWs in their respective output branches B and C are then measured. This single-shot experiment for a given and is repeated 50 times to build statistics. The experiment is repeated for 10 V ≤ ≤ 28 V and 20 ns ≤ ≤100 ns for devices with = 30°, 60°, 90° and 120° as summarized in Fig. 2b-d. The two distances and differ from each other in a systematic way as a function of , and . Note that the domains wall in Fig. 2a are oriented nearly perpendicular to the wire edges whereas in earlier experiments on similar wires the domain walls were found to have a significant tilt after current driven motion17. However, in these previous studies the magnetic layers were deposited on a TaN seed layer as compared to the Al2O3/TaN seed layers used in the current experiments. The latter seed layer has the effect of reducing the pinning of the domain walls so that after the current pulse is removed the tilt of the domain wall introduced by the spin-orbit torque relaxes back to its equilibrium state without any tilt. 1 Fig. 2a (left column) shows representative p-MOKE images of an up-down (UD) DW that travels much further in branch B than in branch C as is increased after a = 16 V and = 100 ns pulse is applied. Remarkably, in same devices, a down-up (DU) DW (Fig. 2a; right column) travels further in branch C than in branch B. Figure 2b

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represents the asymmetric behavior of an UD DW in a device with = 90° (see supplementary section 3 for detailed data for all ). Experimental data indicating the distance travelled by a DW into the branches A, B and C upon application of a single pulse is indicated by solid lines. Dashed lines of corresponding color indicate the displacement of a DW, had it travelled in a straight wire, with a constant steady-state velocity in the respective branches. Values of are obtained experimentally from current-induced DW motion experiments in the device. Clearly, in the branch B, the DW has travelled further and in the branch C, it has fallen behind compared to a DW traveling in a straight wire with the velocity, . Alternatively, we can plot − , which is the asymmetry in the distance traversed by the DWs in branches B and C as shown in Fig. 2c. We find that for = 15.8 V, − keeps increasing up to = 100 ns which is the range of our instrument. This indicates that the out-of-equilibrium DW dynamics which are responsible for this asymmetry are sustained for significant timescales and distances beyond the initial bifurcation region where the DW splits. The DWs reach an equilibrium state when they start moving at in both the branches and hence − saturates. This is seen more clearly for = 19.9 V and 25 V. For = 120°, − does not saturate at any (refer to supplementary section 3). − for an UD and DU DW also look remarkably like a mirror image of each other, i.e., the asymmetry in the branches is reversed (Fig. 2c). Although electrical measurements confirm that the branches B and C are symmetrical, this further suggests that this asymmetry is not due to spurious effects such as lithographic patterning, edge pinning, current crowding near the bifurcation region, or any other inhomogeneity in the magnetic structure that would make one branch


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more favorable over the other for DW motion. Fig. 2d shows a systematic increase in the asymmetry − with increasing for different voltages, which we will discuss later. We have developed a detailed 1D model18 extended in 2D (see supplementary section 4) to account for the observed experimental results (Fig. 3). From its inertial frame of reference, when a DW traveling in input branch A enters an output branch (B or C), it experiences an abrupt change in the SHE-SOT as well as the DMI torque. Specifically, upon entry of the DW into an output branch, the DMI effective field, (Fig. 3a,d) retains its direction (due to the tilt of the DW evolving slowly in time - being dependent on square of the width of the nanowire14), whereas the DW’s magnetization, ! , responds almost instantly (< 1ns) to the abrupt change in SHE-SOT (Fig. 3a,e). ) becomes instantaneously Consequently, the DMI-derived driving torque (∝ ! × higher for the UD (DU) DW in the upper (lower) branch resulting is higher instantaneous velocity, whereas it significantly decreases in the lower (upper) branch resulting in lower instantaneous velocity (Fig. 3a,c). This detail is accounted for in our model, which shows that for the dimensions of the wires used in our experiments, the DW acceleration or deceleration times to reach a steady-state can be significant (on the order of tens of nanoseconds). Subsequently, we see the evolving disparity in the DW displacements in the individual branches in agreement with our experimental results (Fig. 3b). The model also predicts that the acceleration time of the slow moving DW is significantly larger than the deceleration time of the fast moving DW, thereby, corroborating the experimental results (Fig. 2b). From our model, we also find that by increasing , we can launch the DW into the Y-shape branches at an angle further away from the steady-state DW configuration,


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leading to longer acceleration or deceleration times and consequently, greater − . This is seen most clearly in Fig. 2d where − at the end of a = 100 ns pulse for devices with various are summarized. A systematic increase in − follows with an increase in for all . We also find that − decreases monotonically after reaching a particular though that exact point does not appear for = 30°, 60° for the range of we were able to measure. This suggests that for a particular , while the DWs in the two branches move with disparate velocities and this difference grows with , they are also able to attain a steady-state motion faster. The acceleration or deceleration times increase with , and may cause the downturn in − to be seen at a higher as seen in Fig. 2d. Finally, this model also confirms that when the width of the nanowire is decreased, the acceleration/deceleration time for a DW decreases and the DW relaxes to its new equilibrium position much faster (see supplementary section 4). Thus, while we acknowledge that our 1D model simulations may not be able quantify the effects of pinning, or current crowding that may happen at the bifurcation point, by and large, they are able to qualitatively reproduce the key trends we see in our measurements. In both our experiments and model, we find that a chiral DW travels different distances when injected into the branches of a Y-shaped junction. For the opposite DW configuration, the asymmetry in DW propagation is a mirror inverse of the original one. Hence by incorporating two coupled chiral DWs of the opposite configurations in the same structure, we should be able to nullify the asymmetry caused in the two branches. We do this by forming a synthetic antiferromagnet (SAF) using a Ru spacer layer sandwiched between two Co/Ni/Co layers7 as follows: 100 AlOx | 20 TaN | 15 Pt | 3 Co | 7 Ni | 1.5 Co | 8Ru | 3Co | 7Ni | 3Co | 50 TaN | (Fig. 4a). By forming a Y-shape junction


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out of this film structure, we perform current driven motion of DWs and find that the DW travels identical distances in the two branches upon splitting (Fig. 4b). This further reinforces the concept that the asymmetry is caused due to the SHE-SOT torques. The controlled manipulation of magnetic domains and domain walls (DWs) by current forms the basis of a number of proposed memory and logic devices19-22 for conventional as well as neuromorphic23 computing. We now demonstrate (Fig. 5) that our findings above can be utilized to sort domains of opposite polarities (pair of DWs rather than individual DWs as reported earlier in in-plane soft magnetic nanowires15, 24) on the basis of significantly different velocities of UD and DU DWs upon entering an output branch. Instead of bringing a single DW near the bifurcation region as in our earlier experiments, we now bring a pair of DWs, i.e., a domain of a predetermined length, and monitor its motion as a pulse of = 25 V and either (i) a series of = 15 ns or (ii) a single pulse of = 100 ns is applied across the device. In case (i), the domain splits into two and travels into both output branches B and C (see supplementary movie S1 and S3). This is because both the DWs constituting a domain have time to relax to their zero-current equilibrium state before a subsequent electrical pulse arrives, thereby leading to the lock-step motion of both the DWs. In case (ii), however, in presence of a continuous electrical pulse, an UD DW travels faster in branch B upon entry while it slows down in branch C, whereas a DU DW does the inverse; the DU DW moving faster in branch C can overcome and annihilate the slow moving UD DW for appropriate domain and pulse lengths (see supplementary movie S2). For the same reason, due to the velocity difference, the distance between the UD and DU DW gets increased in branch B. This results in sorting of an up domain in branch B (Fig. 5a(ii)). Similarly, a down


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domain can be split (see supplementary movie S3) into both the branches or can be sorted (see supplementary movie S4) in branch C (Fig. 5b(ii)). By utilizing symmetry breaking, we have shown that a DW, depending on its polarity, can be simultaneously accelerated or decelerated in two identical output branches of Y-shaped magnetic nanowires over rather long time scales and distances, which depends on the angle between the output branches, the current density used to move the DW and the width of the nanowire. Using this simple technique, we can indirectly visualize the temporal evolution of the various torques and their respective effects on the magnetization vector and the velocity of the DW, since ours is a post-facto rather than a real time technique. Furthermore, by designing a voltage pulse sequence, we show that the domain length in a nanowire can be manipulated without any magnetic field thereby allowing for all electrical complex logic in memory devices, where timing of electrical pulses can be encoded in domain lengths. Finally, the asymmetry can be eliminated in a synthetic antiferromagnetic structure having two opposite DWs coupled together.

References (1) Bode, M.; Heide, M.; von Bergmann, K.; Ferriani, P.; Heinze, S.; Bihlmayer, G.; Kubetzka, A.; Pietzsch, O.; Blugel, S.; Wiesendanger, R. Nature 2007, 447, 190-193. (2) Crépieux, A.; Lacroix, C. J. Magn. Magn. Mat. 1998, 182, 341-349. (3) Emori, S.; Bauer, U.; Ahn, S.-M.; Martinez, E.; Beach, G. S. D. Nat. Mater. 2013, 12, 611-616. (4) Miron, I. M.; Moore, T.; Szambolics, H.; Buda-Prejbeanu, L. D.; Auffret, S.; Rodmacq, B.; Pizzini, S.; Vogel, J.; Bonfim, M.; Schuhl, A.; Gaudin, G. Nat. Mater. 2011, 10, 419-423. (5) Ryu, K.-S.; Thomas, L.; Yang, S.-H.; Parkin, S. S. P. Nat. Nano. 2013, 8, 527– 533. (6) Hirsch, J. E. Phys. Rev. Lett. 1999, 83, 1834-1837. (7) Yang, S.-H.; Ryu, K.-S.; Parkin, S. S. P. Nat. Nano. 2015, 10, 221-226.


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(8) Manchon, A.; Zhang, S. Phys. Rev. B 2009, 79, 094422. (9) Parkin, S. S. P.; Yang, S.-H. Nat. Nano. 2015, 10, 195-198. (10) Safeer, C. K.; Jué, E.; Lopez, A.; Buda-Prejbeanu, L.; Auffret, S. p.; Pizzini, S.; Boulle, O.; Miron, I. M.; Gaudin, G. Nat. Nanotech. 2016, 11, 143-146. (11) Jiang, W.; Upadhyaya, P.; Zhang, W.; Yu, G.; Jungfleisch, M. B.; Fradin, F. Y.; Pearson, J. E.; Tserkovnyak, Y.; Wang, K. L.; Heinonen, O.; te Velthuis, S. G. E.; Hoffmann, A. Science 2015, 349, 6245. (12) Thomas, L.; Moriya, R.; Rettner, C.; Parkin, S. S. P. Science 2010, 330, 18101813. (13) Torrejon, J.; Martinez, E.; Hayashi, M. Nat. Commun. 2016, 7, 13533. (14) Boulle, O.; Rohart, S.; Buda-Prejbeanu, L. D.; Jué, E.; Miron, I. M.; Pizzini, S.; Vogel, J.; Gaudin, G.; Thiaville, A. Phys. Rev. Lett. 2013, 111, 217203. (15) Pushp, A.; Phung, T.; Rettner, C.; Hughes, B. P.; Yang, S.-H.; Thomas, L.; Parkin, S. S. P. Nat. Phys. 2013, 9, 505-511. (16) Liu, L.; Pai, C.-F.; Li, Y.; Tseng, H. W.; Ralph, D. C.; Buhrman, R. A. Science 2012, 336, 555-558. (17) Ryu, K.-S.; Thomas, L.; Yang, S.-H.; Parkin, S. S. P. Appl. Phys. Expr. 2012, 5, 093006. (18) Ryu, K.-S.; Yang, S.-H.; Thomas, L.; Parkin, S. S. P. Nat. Commun. 2014, 5, 3910. (19) Malozemoff, A. P.; Slonczewski, J. C., Magnetic Domain Walls in Bubble Material. Academic: New York, 1979. (20) Allwood, D. A.; Xiong, G.; Faulkner, C. C.; Atkinson, D.; Petit, D.; Cowburn, R. P. Science 2005, 309, 1688-1692. (21) Gallagher, W. J.; Parkin, S. S. P. IBM J. Res. & Dev. 2006, 50, 5-23. (22) Parkin, S. S. P.; Hayashi, M.; Thomas, L. Science 2008, 320, 190-194. (23) Locatelli, N.; Cros, V.; Grollier, J. Nat. Mater. 2014, 13, 11-20. (24) Phung, T.; Pushp, A.; Rettner, C.; Hughes, B. P.; Yang, S.-H.; Parkin, S. S. P. Appl. Phys. Lett. 2014, 105, 222404.


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Figure 1 | Out-of-equilbrium motion of DWs and device structure. a, Time-resolved 1D model snapshots of the current-induced motion of a chiral DW in wires with different initial DW states at = 0 ns, each having a different tilt angle. Reference lines (white) are drawn to compare the displacements of DWs = 50 and 100ns. Depending on the initial tilt, a DW travels either faster or slower compared to a DW which starts from a rest state. Modelling parameters are described in the supplementary section b, Micrograph and electrical circuit of the Y-shape structure with its three branches labelled as A, B and C. The width of input branch A (5%m) is twice that of output branches B and C (2.5%m) that subtend an angle between them. All the branches are 20 % m long. Branch A is electrically connected to a nanosecond pulser while branches B and C are electrically grounded. c, Schematic showing a typical Y-shape structure and the spin Hall derived spin accumulation (green) which changes direction at the Y-junction. The current density & is uniform across all branches except for narrow regions near the bifurcation region.


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Figure 2 | Asymmetric DW propagation. a, (left column) The dark region shows the wake of an up-down (UD) DW that moves from branch A into branches B and C upon splitting into two DWs when a single pulse of = 16 V and = 100 ns is applied across the devices with = 30°, 60°, 90°, 120° . (right column) The bright region indicates the same but for a down-up (DU) DW. b, ' and ' measured as a function of and for = 90° . Each data point is obtained after performing 50 repetitions to build statistics. The dashed lines indicate the distance that the DW should have moved at its steady-state velocity in the respective branches. Only those combinations of and have been considered where the DW in branch A splits into two and travels into the two output branches B and C. c, Asymmetry defined as − for = 90° for UD (top-half panel) and DU (bottom-half panel) DWs. d, Asymmetry as a function of for = 100 ns for devices with = 30°, 60°, 90° and 120° . Measurements for UD are in the top-half panel and DU are in the bottom-half panel.


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Figure 3 | Extended 1D model. a, Schematic of a device with an UD (left) and a DU (right) DW initially in the branch A (dashed white line) when current is applied. Spin accumulation (violet) causes the canting of the DW magnetization unit vector, ! (green) and subsequently the DW tilt. Black arrow indicates the effective DMI field , which is always perpendicular to the DW front. After splitting at the Ydirection shape junction, the DW (solid white line) makes different angles with the ! in the two branches () *+ ) ) than it made initially () ) and thus experiences different effective torques which gives rise to different velocities. Extended 1D simulation for a device (width of branch A is 5%m, width of branches B and C is 2.5%m and = 90°) showing time evolution of b, displacement, with the asymmetry − shown in inset c, , - and e, DW magnetization angle, . for an Instantaneous velocity, , d, angle of up-down DW as it travels from branch A (solid green) into branches B (blue) and C (red) upon splitting. Results of the motion of a DW in a straight wire are also shown in comparison (dashed green).


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Figure 4 | Symmetric DW motion in Synthetic-Anti-Ferromagnetically (SAF) coupled racetracks a, Schematic of a SAF structure used in our experiment b, Representative image for = 90° , = 16 V and = 50 ns showing symmetric injection of the DW into the Y-shape output branches.


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Figure 5 | DW splitting versus sorting. a, Splitting (i) or sorting (ii) of an up domain by modifying the pulse waveform. For a series of short pulses, both the DWs move in lockstep and during the time the pulse is turned off, the DW magnetization as well as DW profile for both the DWs relax into their respective equilibrium positions before the subsequent short pulse arrives. (ii) For a single pulse, the two DWs travel at different velocities in the two output branches leading to annihilation of the two domain walls in the bottom branch, whereas increase in the domain length in the top branch. b, Splitting (i) or sorting (ii) of a down domain by modifying the pulse waveform just as discussed in a. The up domain gets sorted in the top branch B, whereas the down domain gets sorted in the bottom branch C. Red and blue dashed lines show the positions of a DU and UD domain wall, respectively, in any given frame.


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Author contributions A.P., T.P. and C.G. conceived the experiment. C.G. performed the experiments and analyzed the data. S.-H.Y. grew the films and performed the extended 1D modeling. B.P.H. and C.R. patterned the devices. S.S.P.P. supervised and wrote the manuscript with A.P. and C.G. All authors discussed the results and contributed to the manuscript. The authors declare no competing financial interest.

Acknowledgments We acknowledge having stimulating discussions with M. Scheinfein and O. Tretiakov.

Supporting Information Available: PDF includes modelling of current density distribution in the device, additional experimental data not included in the main text, results based on one-dimensional DW model and AFM scan of our device. Videos show motion of a pair of DWs showing either a splitting or sorting operation depending on the timing of pulses.


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