Spin Hall effect clocking of nanomagnetic logic without a magnetic field

Transcription

1 SUPPLEMENTARY INFORMATION DOI: /NNANO Spin Hall effect clocking of nanomagnetic logic without a magnetic field (Debanjan Bhowmik *, Long You *, Sayeef Salahuddin) Supplementary Section S1- Modulation of the coercivity of CoFeB by varying in-plane current through underlying Ta layer Thin films of thermally oxidized Si substrate/ta (10 nm)/cofeb(1 nm)/mgo(1 nm)/ta(10 nm) are deposited through sputtering on Si substrates. Hall bars of length 500 microns and thickness (20-40 um for thicker bar, 5 um for thinner bar) are fabricated from that stack (Fig. S1a). Magnetic properties of the devices are characterized through Anomalous Hall Effect. Current is injected into the thicker Hall bar and voltage is measured from thinner bar (Figure S1a), the ratio between voltage and current being the Anomalous Hall Resistance ((V + -V - )/I) which is proportional to the out of plane magnetisation of CoFeB 1. When the current flowing through the device is very small and magnetic field is varied in the out of plane direction, we observe a square hysteresis loop with coercivity of 60 gauss. It shows that the magnetic thin film exhibits perpendicular magnetic anisotropy 2. When more current flows through the device, coercivity of the magnet is reduced. Coercivity can be modulated from 60 gauss to 2 gauss by varying the current density from A/cm 2 to A/cm 2 at room temperature (Fig. S1b). The effect is independent of direction of current (+x or x) as shown in Figure S1c. We observe similar effect in various devices with different areas of cross section. From an average linear fit of plots of coercivity vs current density for three such devices, we find out that for an increase of current density in Ta by 10 6 A/cm 2, coercivity decreases by approximately 17 gauss (Fig. S1d). Coercivity reduces with increase in current because in plane current flowing through Ta (x direction) separates electrons with +y and y directed spins across the thickness of Ta. This causes accumulation of +y spins at the Ta-CoFeB interface, which offers an in-plane spin torque to the magnetisation of CoFeB (green arrow). This spin torque (Spin Hall Effect Spin Torque or SHEST) assists in switching the magnetisation of CoFeB from out of plane to in-plane thereby reducing the coercivity of the magnet (Fig. S1a) 3,4. This effect is independent of polarity of current because for either polarity in-plane spin torque assists the external magnetic field in switching the magnet in the out of plane direction (Fig. S1b). Since we use SHEST to drive the magnet in-plane into a meta-stable state for clocking, polarity of the current pulse does not matter in our clocking experiments. However to verify that the modification of magnetic properties observed is not an effect of Joule heating or Oersted field, generated by the current, we observe the dependence of magnetisation on the polarity of current in the presence of an in-plane magnetic field along the direction of current. We observe a hysteric switching of magnetisation with current when 50 gauss of magnetic field is applied along the direction of current (Fig. S1e). Positive polarity of current beyond a certain magnitude (~ A/cm 2 ) switches the magnet upward (R AHE =1) NATURE NANOTECHNOLOGY 1

2 while negative polarity of current beyond that magnitude switches the magnet downward (R AHE =-1). On the other hand when -50 gauss of magnetic field is applied along the direction of current, negative current switches the magnet upward while positive current switches the magnet downward (Fig. S1f). This peculiar nature of magnetic switching, based on the polarity of current and the polarity of the magnetic field applied along current direction, cannot be an effect of thermal or Oersted field based switching 3. We also measured the Anomalous Hall Resistance of the Hall bars as a function of magnetic field applied in-plane instead of out of plane (Fig. S1g). Figure S1g shows that more than 4 kg of magnetic field needs to be applied in-plane to drive the magnetisation in-plane (R AHE =0), owing to the very strong perpendicular magnetic anisotropy of the material 2. The Oersted field generated by the current pulses in all our experiments (Fig. 2, Fig. 3, Fig. 4) is much smaller than that.

3 Figure S1. a, Schematic showing the origin of Spin Hall Effect Spin Torque (SHEST) and the device geometry for Anomalous Hall Effect measurements on the thin film stack. b, Anomalous Hall Resistance measurements on devices of Figure S1a (magnetic field is in out of plane direction) show reduction of coercivity with increase in current density through Ta. c, Coercivity is reduced from 60 gauss to 40 gauss when A/cm 2 flows through the Hall bar. Reduction in coercivity is same for either polarity of current. Thus polarity of the current does not matter in this case. d, Coercivity of 1nm of CoFeB drops approximately at the rate of 17 gauss per 10 6 A/cm 2 of current density. e,f, In-plane magnetic field along the direction of current breaks the symmetry with respect to SHEST. The direction of magnetic field determines whether up or down magnetisation would be stabilized for a given polarity of SHEST i.e. polarity of current, as observed through our AHE measurements. g, Anomalous Hall Resistance plot as a function of in-plane magnetic field shows that more than 4 kg is needed to drive the magnet in-plane (R AHE =0). A very small angle (~1 o ) between the direction of applied magnetic field and the plane of the sample results in the presence of a small out of plane component of magnetic field. This helps the Hall bar structure to remain uniformly magnetised and its magnetisation to rotate coherently with applied magnetic field. Supplementary Section S2- Spatial sensitivity of Anomalous Hall Resistance signal of the magnetic dots

4 Anomalous Hall Resistance (R AHE ) measurement of the 3 dot structure shown in Figure 3a shows three jumps in the R AHE signal corresponding to the magnetic switching of the three dots. The jumps are of different magnitude. Intuitively the dot closest to the intersection of the two Hall bars should have the largest R AHE contribution while the farthest dot should have the smallest R AHE contribution. M.Alexondrou et al. showed experimentally that Anomalous Hall resistance signal of a nanodot is spatially sensitive and it decreases with increase in distance from the cross centre of the Hall bars 5. To compare our results in Figure 3, we have fabricated 3 dots of same size ( 200nm diamater) at the cross centre of the Hall bars (Fig. S2a). R AHE response of this device has three distinct jumps of equal magnitude unlike Figure 3 because here the dots are not at different distances from the cross centre (Fig. S2b). Figure S2. a, SEM image of 3 dots of diameter 200nm each at a separation of 30nm. b, Anomalous Hall Resistance (R AHE ) vs magnetic field (out of plane) plot shows equal jumps in R AHE, corresponding to switching of each magnet. Supplementary Section S3- Determining the magnetisation state of each magnetic dot after a current pulse The magnetic dots of the device in Figure 3a are first saturated in the vertically downward direction by -400 gauss of out of plane magnetic field (positive polarity refers to upward magnetic field, negative polarity refers to downward magnetic field). Then the magnetic field is changed to 0 gauss and current pulse (clock) of magnitude A/cm 2 and duration 1s is applied on the vertical Hall bar such that the same current flows through all the three dots (Fig. 3a). Thus all magnets experience the same SHEST from the clock pulse. Once the current pulse is removed, R AHE is measured by measuring the voltage across the horizontal Hall bar with a small amount of current flowing through the vertical bar to generate AHE response. The current density used for R AHE measurement is two orders of magnitude lower than the magnitude of current pulse used to generate SHEST. Then the magnetic field is swept from 0 gauss to -400 gauss (saturation) and R AHE is measured at every point of the sweep (Fig. S3). As the system goes to complete saturation (all

5 three magnets vertically down polarised), the magnets which were vertically up polarised after the current pulse at 0 gauss show a sharp change in R AHE corresponding to the their switching. On the other hand, the magnets which were down polarised after the current pulse at 0 gauss do not contribute to any change in the R AHE signal. Also by looking at the size of the jump, we can conclude specifically which magnet was up polarised and which was down polarised after the current pulse. For example, when the resultant state after the current pulse at 0 gauss is ( ) state 6, saturation to all down takes place through the magnet, nearest to cross-centre of Hall bars, switching (large jump in R AHE of magnitude ~ 0.07 Ω) and magnet, farthest from cross centre, switching (small jump in R AHE of magnitude ~ Ω)(red plot in Fig. S3). When the resultant state after the current pulse at 0 gauss is ( ) state, saturation to all down (green plot) takes place through only the middle magnet switching (medium jump in R AHE of magnitude ~ 0.04 Ω). Thus looking at the number and magnitude of jumps, magnetisation direction of each of the dots can be found out after the current pulse is applied at 0 gauss. Figure S3. Anomalous Hall resistance (R AHE ) is measured while sweeping the magnetic field in the negative direction till all the three magnets become saturated in the downward magnetised state. The state of the three magnets after application of current pulse at 0 gauss is found out from the number and size of jumps in R AHE on their way to saturation and is shown with respect to each R AHE curve. Same notation is followed as that in text and Figure 3 to represent the state of the magnets (nearest magnet, middle magnet, farthest magnet) 6. Supplementary Section S4- Clocking three magnetic dots in the presence of bias magnetic field -multiple trials When current pulse is applied to the three dots (all polarised upward) at +20 gauss, they go to ( ) state. We do this experiment 5 times and we always get the same result (Fig S4a).

6 Similarly current pulse is applied to three dots (all polarised upward) at -20 gauss and they go to ( ) state. This experiment is also done 5 times and we always get the same result. In either case, none of the other 7 possible states is formed. Figure S4. a,b, Histogram, obtained from multiple trials of the experiment in Figure 3f (clocking the three magnetic dots of Figure 3a at a bias magnetic field), shows that ( ) state is always formed when current pulse is applied at +20 gauss and ( ) state is always formed when current pulse is applied at -20 gauss. Supplementary Section S5- Dependence of coercivity on the size of the magnet We have fabricated square dots of side length 500 nm and 2 μm to compare their coercivity. Hysteresis loop obtained through R AHE measurement on the 500nm square dot shows a coercivity of ~240 gauss (Fig S5a) while the coercivity of Hall bars of width μm (Fig. S1b) is 60 gauss and that of the 2 μm dot is ~160 gauss (Fig. S5b). This shows that micron size larger dots have smaller coercivity than the smaller dots (500 and 200nm) 2,7. Thus the sharp change of R AHE in Figure 4b corresponds to the large input dot while the three sharp changes of R AHE between 270 and 330 gauss correspond to the three smaller square dots. The coercivity of the three smaller dots is not identical and it deviates from the coercivity of the single 500nm square dot in Fig S5a because the defects in the dots are not identical.

7 Figure S5. a, Anomalous Hall Resistance measurement on a square dot of side length 500nm shows a coercivity of ~240 gauss. b, Same measurement on a square dot of side length 2 μm shows a coercivity of ~160 gauss. Supplementary Section S6- The input magnet is unaffected by the clock pulse while other magnets are affected. The input magnet in Figure 4a has dimensions much larger than the other magnetic dots of the 3- dot chain along which information is meant to propagate. The input magnet is a nearly rectangular dot with dimensions 2 μm by 5 μm, while the other magnets are squares of 500nm side length. An input magnet is supposed to be unaffected by the clock pulse. Larger size of the input magnet compared to other magnets serves this purpose. We have separately fabricated a 2 um square dot on a cross bar structure to study the properties of a large dot, like the input dot, independently (Fig. S6a). We start with the magnet being fully saturated in the upward direction. Application of a current pulse at 0 gauss results in the formation of a demagnetised state or mixed state (R AHE =0) with an equal number of up and down polarised domains. This happens because SHEST from the current pulse drives the magnet in-plane. Once the torque is removed, due to the absence of an external magnetic field, magnetic moments in some of the regions of CoFeB layer go upward while magnetic moments in other regions go downward. Thus a demagnetised state of up and down polarised domains is formed. Since R AHE measured is the average of all the domains in the dot, net R AHE is 0.When magnetic field is slowly increased in one direction the magnet gradually transitions from a mixed state to a saturated up state between 20 and 30 gauss (red plot- Fig. S6a). If we now apply the current pulse at 20 gauss instead, with the magnet initially up, no mixed state is formed. The final state of the magnet after the current pulse is same as the initial state (Fig. S6b). On the other hand we have already shown in Figure 2 that when current pulse is applied at 0 gauss on a 200nm side square magnet, it does not break into domains. It goes to either saturated upward or downward state with 50% probability for each. Similarly when current pulse is applied at 0 gauss on the device in Figure 4a the three square magnets of 500nm size do not go to a mixed state. They rather reach dipole-coupled states with each magnet saturated up or down just like the 200nm circular dots in Figure 3.On the other hand, the larger magnet (2 by 5 μm dot) expectedly breaks into a mixed state just like the 2 μm square dot of Figure S6a. Figure S6c shows these happening. The larger magnet and the three other dots are all saturated upward. After application of current pulse at 0 gauss, when the magnetic field is swept in the positive direction there is a gradual rise in R AHE around 20 gauss which is the signature of a magnet going from mixed state to the saturated state (red plot- Fig. S6c). We know that it is the larger magnet which is going from mixed state to saturated state and not the other magnets because the magnitude of the increase in R AHE (0.25 Ω) is larger than the magnitude of one small jump (0.08 Ω), corresponding to the switching of each small dot (Fig. 4b). On the other hand, the smaller dots show sharp switching at higher magnetic fields. The change in R AHE during the switching is 0.08Ω,which corresponds to one full switch of a smaller dot between up and down (Fig 4b). It shows that the smaller dots were saturated in either up or down states after the application of

8 current pulse at 0 gauss, but did not go to mixed state. If they were in mixed state, they would also have gradually saturated like the larger magnet at small magnetic fields instead of sharply switching at larger magnetic fields. If we now apply current pulse at 20 gauss instead of 0 gauss, the larger magnet (2 by 5μm dot) should be unaffected as we have shown in Fig. S6b. On the other hand, Figure 3f shows that smaller dots form dipole-coupled states when current pulse is applied at 20 gauss. Thus for the device of Figure 4a, the smaller dots are affected by the current pulse at 20 gauss while the larger dot is not. Thus the larger dot acts as fixed input bit in the system. Figure S6. a, Blue plot shows the hysteresis loop of a square dot of side length 2μm obtained by R AHE measurement. Current pulse with magnitude of A/cm 2 and duration 1s applied at 0 gauss drives the magnet from a saturated up state to a mixed state of up and down polarised domains (R AHE =0). After that, as magnetic field is swept upward the magnet gradually goes back to saturated up state between 20 and 30 gauss, represented by a gradual rise in R AHE (red plot). Similarly if magnetic field is swept downward, the magnet goes to saturated down state gradually between -20 and -30 gauss (green plot). b, Starting with the magnet in saturated up magnetisation state, application of current pulse with same magnitude and duration as before ( A/cm 2, 1 s) at 20 gauss does not change the

9 state of the magnet since no change in R AHE is observed. When magnetic field is swept in the positive direction R AHE does not change (red plot). When magnetic field is swept in the negative direction after current pulse at 20 gauss, R AHE changes sharply at -180 gauss, corresponding to a switch from saturated up to saturated down state (green plot). This shows that when current pulse is applied at 20 gauss on a large magnet of similar dimensions (2 μm by 5 μm) saturated in one direction, the final state of the magnet is same as the initial state. So it can be used as fixed input magnet. c, All magnets, including the large input magnet, are saturated upward. Current pulse of magnitude A/cm 2 is applied on them at 0 gauss. Next magnetic field is applied in the positive direction and the magnets are driven back to saturation (upward), with simultaneous measurement of R AHE (red plot). Gradual transition for the large magnet is observed at ~20 gauss and sharper transition for the smaller magnets is observed at higher magnetic field (~ 300 gauss). Next, current pulse is again applied on the upward saturated magnets at 0 gauss. This time, magnetic field is next swept in the negative direction till all magnets become saturated down (green plot). Similar results are observed. d, Same experiment as in Figure S6c is performed on the same system of magnets, only difference being both for the orange and violet plots, the state of the magnets is all down before the application of current pulse. The large magnet again shows smooth transition to saturation, while the three smaller magnets show sharp switching. Supplementary Section S7- Determining the magnetisation state of a chain of magnetic dots with an input dot Starting from all the magnets in the initially up direction, current pulse of magnitude A/cm 2 and duration 1s is applied at 20 gauss (Fig. S7a). Next the magnetic field is swept in the positive direction till all dots reach saturation (red plot). We can see that unlike Figure S6c and Figure S6d, there is no gradual change of R AHE at lower magnitudes of magnetic field, which means that the input magnet does not go to mixed state. There are only two sharp changes in R AHE signal at a higher magnetic field with magnitude of each change equal to 0.08Ω. They correspond to the switching of two smaller dots. Absence of a bigger jump (~0.4Ω) means that the input magnet does not change its state when the magnetic field is increased in the positive direction, i.e, the input magnet has remained up after the current pulse at 20 gauss, which matches with our argument in Section S6. Since there are two small jumps, two out of the three smaller magnetic dots were down at 20 gauss after current pulse and one was up. Also by applying the current pulse on saturated up magnets again at 20 gauss and sweeping the magnetic field negative till saturation (green plot) we observe one large jump corresponding to the input magnet switching from up to down. We also observe one small jump at higher magnetic field, which further confirms that only one of the three smaller magnetic dots was up after the current pulse at 20 gauss and it has switched down during the negative field sweep, resulting in that single sharp change in R AHE. Thus we deduce that after the application of current pulse on all saturated up magnets, the input magnet is still up while the other three magnets are 2 down 1 up. The magnet next to the

10 input magnet should be down owing to the stray field from input magnet. Thus input magnet controls the state of the other magnetic dots. When same experiment is performed with all magnets initially down, we find out through the same procedure that the resultant state is 2 up 1 down because the input magnet is down now and it controls its adjacent magnet to be up (Fig. S7b). Figure S7. a, All magnets, including the input magnet, are saturated upward. Current pulse of magnitude A/cm 2 and duration 1s is applied on them at 20 gauss. Next magnetic field is applied in the positive direction and the magnets are driven back to saturation (upward), with simultaneous measurement of R AHE (red plot). Two small jumps and no big jump in R AHE show the formation of ( ) state after application of the current pulse, along with input magnet remaining up. Again current pulse is applied on the upward saturated magnets at 20 gauss. This time, magnetic field is next swept in the negative direction till all magnets become saturated down (green plot). One small jump further establishes the formation of ( ) state after the current pulse. The big jump corresponds to the input magnet switching from up to down when we sweep the magnetic field in negative direction. b, Same experiment as in Figure S6b is performed on three dots with input magnet, only difference being both for the orange and violet plots, the state of the magnets is all down before application of current pulse and the current pulse is applied at -20 gauss. This time, saturation to all saturated up polarised state takes place through one small jump, corresponding to one small magnet switching from down to up, and one big jump, corresponding to the input magnet switching from down to up (violet plot). This shows that ( ) state is formed after application of the current pulse at -20 gauss. It also shows that the input magnet did not change its state after the current pulse. Applying the current pulse again on downward saturated magnets at -20 gauss and sweeping the magnetic field in negative field further confirms the formation of ( ) state after the current pulse (two small jumps orange plot).

11 Supplementary Section S8- Evidence of observed switching not being due to Joule heating or magnetic field generated by the current i. Joule heating- Anomalous Hall Resistance (R AHE ) versus out of plane magnetic field plot of a 200nm size dot, similar to the device of Figure 2, shows the existence of perpendicular magnetic anisotropy (Fig. S8a). When a current pulse is applied next in the presence of an in-plane magnetic field of 100 gauss along the direction of the current, we observe that a positive current pulse switches the magnetisation from down (-0.05Ω) to up (0.05Ω) whereas a negative current pulse switches the magnetisation from up (0.05Ω) to down (-0.05Ω) (Fig. S8b). On the other hand, in the presence of an in-plane magnetic field of -100 gauss, a positive current pulse switches the magnetisation from up (0.05Ω) to down (-0.05Ω) whereas a negative current pulse switches the magnetisation from down (-0.05Ω) to up (0.05Ω) (Fig. S8c). Thus the handedness of the hysteresis curve with respect to current can be reversed through switching the direction of the magnetic field. The applied in-plane magnetic field is much smaller than the anisotropy field, which is greater than 4000 gauss for this material 2. Hence it cannot drive the magnetisation inplane alone (Fig. S8f). Next, starting from the initial state of magnetisation being upward, we have applied a positive current pulse with 100 gauss of magnetic field along the direction of the current. We have observed that the magnet remains up every time the pulse is applied (Fig. S8d). Doing a similar experiment, starting from the magnet pointing down, a positive current pulse with the in-plane magnetic field applied opposite to the direction of the current, results in the magnet always remaining in the down direction (Fig. S8e). This is totally different from what happens when the same current pulse is applied at zero gauss of magnetic field (Fig. 2d of main manuscript). In that case, the magnet randomly goes to up and down state. If that indeed happened because of Joule heating which caused the magnet to cross the energy barrier, then the presence of 100 gauss of magnetic field (much smaller than the anisotropy field) would not have affected its behavior at all and Fig. S8d and S8e would show similar behavior as Fig. 2d. However that is clearly not the case. This peculiar behavior with respect to polarity of current and in-plane magnetic field along the current is a signature of Spin Hall Effect Spin Torque, also observed by Liu et al in their devices 3,8. The physics behind it is the addition of Spin Transfer Torque and torque by magnetic field in one case and the cancellation of the two in the other case, as explained in details through simulations in references 4 and 8. ii. Magnetic field generated by current (Oersted field) switching- Fig. S8g shows the magnetic field generated by a current through 10 nm thick layer of Ta with current density of 1x10 7 A/cm 2, obtained through simulation in COMSOL Multiphysics simulation software. A simple analytical calculation matches with the simulation results. Magnetic field close to a slab of finite thickness (t) with volume current of current density (J) flowing through it is given by 9 : H Oersted = μ 0 J (d/2) = T =6.28 gauss, for J=10 7 A/cm 2 and d=10nm. Thus the 1nm thick CoFeB layer on the top of the Ta layer should experience an in-plane magnetic field of 6 gauss for 10 7 A/cm 2 of current through Ta and 18 gauss for A/cm 2. Such magnetic field is order of magnitude lower than the coercivity of the magnet (~300 gauss).

12 Thus the magnetic field generated by the current pulses in our clocking experiment is too small to drive the magnet in-plane or switch it.

13 Figure S8. a, Anamolous Hall Resistance of a 200 nm size dot is measured with a varying magnetic field applied out of the plane. b, In the presence of a 100 gauss field along current direction, negative current pulses of A/cm 2 switch the magnetisation from up to down and positive current pulses of A/cm 2 switch the magnetisation from down to up. Current pulses below that magnitude has no effect on the state of the magnetisation. Thus a hysteresis loop can be obtained if we plot out of plane magnetisation (R AHE ) against the current density of the pulses applied. c, In the presence of a -100 gauss magnetic field, negative current pulses of A/cm 2 switch the magnetisation from down to up and positive current pulses of A/cm 2 switch the magnetisation from up to down. d, Starting from an initial state of upward direction of magnetisation, a series of positive and negative current pulses of magnitude A/cm 2 is applied with 100 gauss of field along the current direction. It is observed that a positive pulse always causes the magnetisation to be up while negative pulses always causes it to be down. e, When direction of the magnetic field is reversed, positive pulse causes the

14 magnetisation to be down and negative pulses makes it up. f, When Anomalous Hall resistance of the dot is measured with a varying magnetic field applied in the plane of the dot, we see that more than 4000 gauss of magnetic field is needed to drive the magnetisation in-plane. Here R AHE going towards 0 means the magnetisation is going in-plane since R AHE is proportional to the out of plane magnetisation. We clearly see that a 100 gauss of in-plane magnetic field is much smaller than the anisotropy field and does not affect the magnet when there is no current pulse through Ta. g, Simulations performed on COMSOL showing magnetic field generated by 10 7 A/cm 2 of current flowing through a 10nm thick and 1μm wide bar. Arrows indicate direction of the magnetic field at a point while the color bar indicates magnitude and polarity of the component of magnetic field along the x-direction of the figure. Thus we see that 10 7 A/cm 2 of current generates around 6 gauss of magnetic field just above it. Supplementary Section S9- Comparison of on-chip current needed for Spin Hall Effect based clocking and current generated magnetic field (Oersted field) based clocking Magnets used in our experiments have dimensions either of 200 nm or 500 nm. Current pulse needed for clocking is ~2mA for our experiments. The width of our Ta bars is ~1 μm (varies among devices in that range) and thickness is 10 nm. So the current density is ~ A/cm 2. If we consider clocking a 60 nm 90 nm magnet instead (same lateral dimensions as that used for current generated magnetic field based clocking experiment of Alam et al. 10 ) and make the width of the Ta bar same as that of the magnet (60 nm) in the ideal case, the current is reduced to 0.12mA. Since Spin Hall Effect has been demonstrated for thicknesses of Ta up to 1 nm 11, we can reduce the thickness of our Ta bars and reduce the clocking current. Thus for 2nm thickness of Ta bar, current can be further reduced to 24 μa. On the other hand, Alam et al 10 performed on-chip clocking on 60 nm 90 nm magnets by applying 600 ma and 760 ma current pulses on Cu bars. Optimistic projections of such a scheme calculate current amplitude of 6.8 ma 10 and 4 ma 12. Thus, both in terms of direct experimental data and projections of both schemes based on certain assumptions and idealizations, Spin Hall clocking needs more than 100 times lower current than Oersted field clocking. Supplemenary Section S10 Variation of coercivity of dots of identical size The three magnetic dots of the device in Figure 3a have roughly identical size. However each of the dots switches at a different value of the external out of plane magnetic field. We have performed multiple scans on the device of Figure 3a to find out the order of switching of the three magnets (Fig. S10a and Fig. S10b). The middle magnet switches last in all the occasions. This is because the coercivity of the magnets that have perpendicular anisotropy like CoFeB- MgO bilayers and Co-Pd or Co-Pt multilayers is determined by the nature of the defects in the dots 13,14, which in turn depends on the method of fabrication (ion-milling, patterning, etc.). Since the exact value of the coercivity is defect dependent, the middle magnet can have a slightly

15 higher coercivity than the other two magnets. So it switches after the other two magnets. If the three magnets had the exact same coercivity, then the middle magnet would have switched before the other two magnets because it experiences the maximum dipole coupling being in between two other magnets. But in the practical case, this dipole coupling is not larger than the difference of coercivities of these magnets owing to defects. So the phenomenon of dipole coupling is not observed here. However when the magnets are driven in-plane by the current pulse, they are on their hard axis. Then a small magnetic field can drive them to its direction. In this case, the middle magnet experiences a stronger dipole coupling from the two adjacent dots than the other two magnets experience. Thus the three dots arrange themselves in their least energy configurationthe dipole coupled antiparallel state (Fig. 3c, 3d, 3e and 3f of the main paper). Coercivity of the magnets due to defects does not play a role in this case. Figure S10. a, Initially the magnetisations of all the three dots (device of Fig. 3) are in the upward direction. The out of plane magnetic field is slowly changed from ~ -170 gauss to ~-350 gauss and switching of the three magnets is observed. The experiment is repeated thrice. In all three cases, the rightmost magnet switches first, followed by the leftmost magnet. The middle magnet switches last. b, Starting from all magnets initially down, magnetic field is increased from ~170 gauss to ~350 gauss. The experiment is repeated thrice. 2 of out of 3 times, the rightmost magnet switches first followed by leftmost magnet (red and black plots). 1 out of 3 times, leftmost magnet switches first followed by rightmost magnet. The middle magnet switches last in all the 3 trials. Supplementary Section S11- Energy consumption for Spin Hall Effect clocked nanomagnetic logic and comparison with CMOS circuits Energy dissipation internal to the magnet while switching is very small 15,16. In nanomagnetic logic, most of the energy dissipation occurs in external circuits in the form of Joule heating during clocking 17,18. In this section, we calculate the energy dissipation for Spin Hall clocking scheme in nanomagnetic logic (NML) with a feature size of 15 nm and compare it with CMOS. We follow the methodology used by Nikonov et al. 19. Since the architecture for on-chip magnetic field clocked NML and SHE clocked NML would be similar, this methodology provides a way to compare energy dissipation from a common platform. Energy dissipation in wiring, parasitics, etc. has been considered in the calculation by Nikonov et al., and hence it is automatically included in our calculation.

16 The assumptions and numbers we use for our calculation are as follows: i. We assume a 15 nm feature size, as Nikonov et al. 19 did for all their benchmark devices. ii. The same width for the Ta wire and the magnet is assumed. iii. The thickness of the Ta layer is 1 nm. Spin Hall Effect has been demonstrated at this thickness of Ta. 11 iv. The thickness of the magnet is 1 nm (same as our experiments). v. The current density needed for the clocking is A/cm 2 (similar to our experiments). vi. Resistivity of the Ta is 200 Ohm-cm, as measured in our experiments and similar to values reported by Liu et al. 3 For simplicity, we assume that the higher resistance Ta is only under the magnet. The wire everywhere else is made of Cu. vii. For calculation of energy dissipation, we need to make an assumption for the width of the clock pulse. We are not aware of any available data on fast switching of CoFeB/Ta heterostructures using spin Hall effect. Using available data for spin transfer torque an estimate for a required pulse width of pico seconds 20 for a current density of 10 7 A/cm 2 can be made. At a slower limit, 1 ns of pulse width seems reasonable. Therefore, we have calculated our results with 1ns, 100 pico seconds and 500 picoseconds. These three points provide a picture of the limiting cases for energy dissipation. Notably Nikonov et al. assumes a reasonably aggressive pulse width of 100 pico seconds in their calculation of field clocked NML. Fig. S11a and Fig. S11b show the results of our calculation for a FANOUT 4 inverter and a 32- bit adder circuit respectively. CMOS HP indicates high performance CMOS and CMOS LP indicates low performance CMOS. SHE clocked NML is projected to be within a factor of 10 of CMOS circuits in terms of energy cost. Improved energy efficiency for the larger 32-bit adder circuit is expected as logic density for NML and most spintronic circuits is much higher compared to CMOS 19. Note also that all these calculations are based on simple geometric scaling of the physical dimensions of metallic wires. As the spin Hall angle improves in time and new materials with higher spin Hall angle and lower resistivity such as CuBi mature 21, the total current needed for clocking and therefore the energy dissipation is expected to go down even more. Although the above calculation involves complex layouts, interconnects and devices together, the end result can be obtained intuitively. Most of the resistance and delay comes from the long interconnect wires. Also, highly resistive Ta is only needed underneath the magnet and perhaps a few tens of nanometers on its two sides. The bulk of the wires could be made of low resistance Cu and could also be thicker. Thus compared to conventional field clocked NML, the resistance changes only by a few times. On the other hand, due to more than two orders of magnitude reduction in current (i), the i 2 reduces by more than 4 orders of magnitude. In total, the energy dissipation goes down by almost 3 orders of magnitude. If we compare our results in Figure S11a

17 (for 100 pico second pulse width as in Nikonov et al.) to that of Figure 53 in Nikonov et al. 19, a roughly 3 orders of magnitude reduction in the energy dissipation is observed that corroborates the intuitive scenario. Fig. S11.a.

18 Fig. S11.b. Figure S11 a, Energy comparison between Spin Hall Effect clocked Nanomagnetic Logic (SHENML), high performance CMOS (CMOSHP) and low performance CMOS (CMOSLP) for FANOUT 4 inverter. b, Similar energy comparison for 32 bit adder circuit.

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