Spin-orbit torque magnetization switching controlled by ... · Spin-orbit torque magnetization...

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Supplementary Information

Spin-orbit torque magnetization switching controlled by

geometry

C.K.Safeer, Emilie Jué, Alexandre Lopez, Liliana Buda-Prejbeanu, Stéphane Auffret, Stefania Pizzini,

Olivier Boulle, Ioan Mihai Miron, Gilles Gaudin

Table of contents:

S1. Device fabrication

S2. Angular dependence of DW velocity, critical current and critical in-plane field.

S3. Dynamic DW deformation

S4. DW motion asymmetry at different current densities

S5. Imaging of DW motion during switching

S6. Switching: Size, speed and nucleation limits

SUPPLEMENTARY INFORMATIONDOI: 10.1038/NNANO.2015.252

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© 2015 Macmillan Publishers Limited. All rights reserved

http://dx.doi.org/10.1038/nnano.2015.252

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S1. Device fabrication

The sample fabrication process includes several steps of electron beam lithography

(EBL), electron beam physical vapor deposition (EBPVD) as well as mechanical and

chemical etching.

The Pt(3nm)/Co(0.6nm)/AlOx(2nm) trilayer was deposited by sputtering. On top of

this trilayer, two levels of masks were fabricated using EBL followed by the EBPVD

deposition. The first mask consists of Ti10nm and Au20nm (mask1) in the form of a rectangle.

On top of this, we placed a second Ti5nm mask (mask2) having the form desired for the

magnetic device. After a first step of mechanical etching everything outside the rectangle

defined by the mask1 was removed. A second step of selective chemical etching was used to

remove both AlOx and Co outside the area still covered by Ti (mask 2). A schematic diagram

of the different structures obtained after each etching is shown in figure S1. Ti5nmAu50nm

electrical contacts made by standard EBL and EBPVD were used to inject the electric current.

Figure S1. The schematic diagrams of the different structures after each level of etching. a.

The structure after the fabrication of the masks above the Pt/Co/AlOx layer. Mask 1 has

rectangular shape and mask 2 has the shape of final geometry expected for the magnetic

object. b. The structure after the mechanical etching. The rectangular part under the mask 1

was protected from etching. c. The final structure after chemical etching.

2 NATURE NANOTECHNOLOGY | www.nature.com/naturenanotechnology

SUPPLEMENTARY INFORMATION DOI: 10.1038/NNANO.2015.252



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S2. Angular dependence of DW velocity, critical current and critical in-plane

field.

Angular dependence of DW velocity. The angular dependence of non-collinear current

induced DW motion was shown in the figure 3 of the main text. To confirm that this angular

dependence is a characteristic feature of the DW velocities rather than an offset contribution

to the DW displacements, we performed additional measurements. We measure the DW

velocity following the same procedure as in I.M.Miron et al.14. For each wire, we measured

DW displacements at a constant current density (1.81x1012 Am-2) for three different current

pulse lengths. DW displacement varies linearly with pulse length as shown in Figure S2b. The

DW velocity is extracted from the slope of the linear dependence. We observe the same trend

as the DW displacement curves, confirming that the angular dependence is an intrinsic feature

of the DW velocity.

Angular dependence of critical current. Another important parameter that

characterizes the current induced DW motion is the critical current density. In our experiment

the critical current is defined as the current required to displace the DWs over the smallest

distance detectable using our microscope (200nm). We have performed measurements for

different pulse durations. Ideally one should use continuous current for this experiment, but

unfortunately increasing the length of the current pulses also increases the sample

temperature, which leads to nucleation of new domains. Therefore we have measured the

critical current for 1000 pulses with three different durations (1.8ns, 3.8ns and 6.3ns). The

critical current density shown in Figure S3c, mirrors the dependence of the DW velocity on

tilt angle of the wire. This result also excludes the tilt formation in the wires: not only the

pulses are too short, but also DWs do not move over a sufficiently long distance to form the

tilt.

Angular dependence of critical in-plane field. The standard method for characterizing

the DMI field in the DMI-SOT model is to apply a longitudinal field (parallel to the electric

current and perpendicular to the DW). We have performed a similar measurement. In our case

the magnetic field is parallel to the electric current while the angle with respect to the DW

varies from wire to wire. In the 1D geometry, the usual interpretation of this data is to

consider that zero velocity corresponds to a Bloch DW, that is to say the component of the

DW magnetization along the current is zero (Figure S3f).





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Figure S2. The DW displacement and DW velocity a. The variation of DW displacements

with respect to the angle of the wire for a current pulse of 3.75 ns, 3.14 ns, and 2.67 ns. Here

we plot DW displacements corresponding to single current pulses, calculated by dividing the

total DW displacement for each wire by the total number of pulses used for each case. Red

curves correspond to positive current, while blue curves stand for negative current. b. DW

displacement variation vs. the pulse length for each wire. Note that for – I, we do not plot the

displacements for wires with φ > 30° because all the displacements were zero. c. DW velocity

vs. φ the tilt angle of the wire. Each DW velocity value in this graph is extracted from the

slope of the corresponding linear plot from panel b. d. critical current dependence on tilt

angle. The inset shows the data corresponding to the 3 pulse durations normalized to the value

obtained for the straight wire. the solid line is the result expected from the DMI-SOT model e.

DW displacement obtained for 30 pulses of 2,6 ns at a current density of 1.6x1012 Am-2 as a

function of the in-plane field, for five of the wires. The wires tilted at 15° and 30° exhibit

faster DW velocity compared to the straight wire independently of the value of HX. The inset

shows the value of the interpolated critical field Hc required to stop the motion. We observe a

significant discrepancy compared to the DMI-SOT model that predicts a simple cosine

variation. f. Schematic representation of the effect of HX on the DW structure in the DMI-

SOT model. When the external field is sufficient of compensate the internal DMI field, the

DW in the straight wire becomes Bloch, its mX component vanishes and the DW motion

stops. For the same HX value, the mX component of the DW magnetization in the tilted wires

has already changed sign. This means that the critical field required to stop the DW motion in

the tilted wires must be smaller than in the straight wire. This is opposite to what we observe.





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In the non-collinear geometry, this does not mean that the DW has a Bloch structure; it

only means that the component of the DW magnetization along the current is zero. Depending

on the wire orientation, the SOT will be zero for different degrees of DW distortion.

Experimentally, we observe that contrary to expectations from the DMI-SOT model, stopping

the DW motion in the tilted wires requires in-plane fields significantly larger than the parallel

wire Figure S3e. This is consistent with the observation of asymmetric velocity and the

critical current dependence on the tilt angle.

S3. Dynamic DW deformation

The current induced DW motion within the SOT-DMI model can be illustrated using a

graphical construction, as shown in Figure S3. When the current is applied through the DW,

the damping-like SOT induces a distortion of the Néel DW structure. The restoring internal

field (HDMI) creates an out of plane torque that displaces the DW. The dissipative torque

associated to the DW motion is opposed to the TDL.

In steady state, the in-plane torques must cancel each other

DMIDL TT ⋅= α

and the out-of-plane torque dictates the DW velocity

DMITv ∝

As explained in the main text, a possible cause of the velocity asymmetry that we observe

experimentally may be the DW distortion by the TDL.

Both TDMI and TDL depend on θ, the angle between the actual DW magnetization and its static

equilibrium position dictated in this case by the DMI

)sin(θDMIDMI HT ∝ and )cos(θDLDL HT ∝

Here HDMI and HDL are the corresponding effective fields. In this case, the deformation angle

is: ( )DMI

DL

HH⋅

=α

θtan

and the DW velocity in steady motion is: )sin(θDMIDW Hv ∝





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An important specificity of the SOT-DMI model is that a significant DW dynamic distortion

in steady motion is synonym of large velocity. If the DW velocity is small, the accompanying

DW distortion is also small.

Experimentally, even a moderate reduction of the current density, leads to a large

decrease of the velocity. This is due to the imperfections in the material structure, which

create local pinning centers for the DW and decrease its velocity. The pinning field does not

act uniformly along the DW trajectory. Because of the spatial variations of the pinning

potential, the DW motion is fast between pinning sites, but is interrupted by long waiting

times at each pinning center. As a consequence, the average velocity is largely determined by

the density of pinning centers and their depinning time, but only marginally affected by the

short periods of fast DW motion. Therefore we can effectively model consider that the DW

pinning acts as an internal field opposing the DW motion.

If pinnDL HH ≈ the DW deformation becomes ( ) 0tan ≈⋅−

=DMI

pinnDL

HHH

αθ

and the velocity 0≈DWv

Figure S3. a. Schematic representation

of the dynamic DW distortion in the

SOT-DMI model. The orientation of the

DW magnetization (black arrow in the

grey area), initially pointing along HDMI,

is modified by the presence of TDL. As

the DW equilibrium structure is distorted,

the effective restoring field (HDMI in this

case) exerts a torque pointing out-of the

plane. The perpendicular magnetization variation that moves the DW, also produces a

dissipative torque αTDMI. In steady state motion the in-plane orientation of the DW

magnetization is fixed by the balance of in-plane torques TDL and αTDMI. b. In the presence of

forces that oppose the DW motion, such as pinning to defects, the effect of TDL on the DW

distortion is inhibited by the effective pinning torque, THpinn. Since there is no DW distortion,

there cannot be any out-of plane torque and thus the velocity must be zero.





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S4. DW motion asymmetry at different current densities

In Figure 2 of the main text, we have shown the angular dependence of current

induced DW motion in the case of circular magnetic bubble domains. The physics behind this

effect could be explained by the DW distortion due to the combined action of DMI and SOT.

But this DW deformation is expected to be large only when the DW is moving fast. If so, for

slow DW motion the angular dependence of circular bubbles should disappear.

In order to check this, we performed the same experiment at large and small current

densities. For the DW motion shown in the Figure 2, the applied current density was 1.6x1012

Am-2. We repeated the same experiment for current densities of 1.1x1012 Am-2 and 2.1x1012

Am-2 and the corresponding images are shown in Figure S4. For small current density the DW

motion was slowed down approximately by three orders of magnitude. Nevertheless, the

angular dependence of DW motion is still preserved. This indicates that the physical origin of

the velocity variation is certainly more complex than the DMI-SOT model.

Figure S4. The Kerr differential images of the DW

motion in the case of the bubble domains. The white

arrows show the current direction. The dotted lines

show the initial DW position. a. The down/up DW

motion for current density 2.1x1012 Am2. Here the

maximum DW velocity was approximately 70m/s b.

The up/down DW motion for current density 1.1x1012

Am-2 and c. Down to up DW motion for the same

current. Here the domain wall velocity was very small,

approximately 0.1m/s. The images show that the

up/down and down/up cases, the asymmetric angular

dependence of DW motion is opposite (towards right

and left respectively). The maximum DW displacement

is always at an angle (approximately 30°) irrespective

to the strength of the current densities.





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S5. Imaging of DW motion during switching

In Figure 4 of the main text, we have shown images of the switching after applying a

series of 8 current pulses. Additional to this, we also imaged step by step DW motion during

the switching. For this we divided the 8 pulse series into 4 series of 2 pulses and made

differential imaging after each series. The corresponding images are shown in Figure S5.

Initially we saturated the magnetization of the devices by applying a magnetic field. Then we

applied current that induce nucleation and domain wall motion. In all the cases, DW motion

was initiated in one of the pins, and DW propagation lead to the magnetization reversal, as

described in the figure 3 of the main text.

Figure S5: Step by step imaging of the DW motion during the switching a. for “u” shape b.

for “s” shape. The length of the current pulse used for “u” shape and “s” shape was 4.4ns and

5ns respectively. The first raw contains the images of the initial magnetic states of the

switches. The black arrows show the direction of applied current. The further consecutive

images in each column are corresponding to the step by step DW motion after applying a

series of 2 current pulses at each step. These images confirm that the switching occurs

according to the nucleation and DW propagation mechanism explained in figure 3 of the main

text.

S6. Switching: Size, speed and nucleation limits

The switching scheme that we propose is based on heat induced domain nucleation

and selective DW propagation. The speed of the switching depends on the total length of the

device as well as on the DW velocity. The smaller the size of the bit length and larger the DW

velocity, the faster will be the switching. Due to the resolution limit of the optical microscope,





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we chose the 2 µm length for all the straight wire in all the devices. Ideally it should be

possible to make switches with smaller size that work using exactly the same principle as long

as their length remains larger than the DW width. A second way of improving the switching

time is to increase the DW velocity. The maximum DW velocity reported in Pt/Co/AlOx was

around 400 m/s. In our experiments the maximum DW velocity achieved was around 100

m/s. This is because the sample resistance limited the maximum current density that we could

apply. By using devices with less resistance, it can be possible to improve the DW velocity

and thus the switching speed.

Figure S6. The current density required for the switching a. The graph showing the variation

of pulse length required for switching with respect to the current density. The dark and light

blue regions correspond to the saturated and non-saturated initial states of the switches. Note

that the switching pulse length window becomes narrow as the current density increases. This

is because for large current density, a small change in the pulse length produces large a

variation in Joule heating and nucleation becomes easier. b. A schematic diagram of

switching from a saturated state. The reversal begins with a nucleation (upper panel) followed

by DW propagation through the straight wire and into the second tilted wire, where it stops

(lower panel). c. Since a DW is already present, the high current density required for

nucleation is not required. Therefore, the object can be switched back with lower current

density. This phenomenon increases the switching range (light blue area in panel a).

The range of pulse width and height where controlled switching occurs is limited by

domain nucleation. As discussed in Figure 3 of the main text, the shape of the switch contains

two tilted wires and a straight wire. The switching is only possible if the nucleation takes

place on the tilted wires; not on the straight wire. As discussed before, the tilted ones have a

pin shape in order to decrease the thermal stability in the narrower regions. Thus the current

required to nucleate the DW in the tilted wires is always smaller than that in the straight wire.





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At the upper limit, when the current becomes large enough to create nucleation in the straight

wire, the switching becomes stochastic.

The critical current density required for switching depends on the initial magnetic state

of the switches. For all the switching experiments that we discussed so far, magnetization was

initially saturated using an external magnetic field. But there is also another possible initial

state where DW is already present in the tilted wires. In this case no nucleation is required for

switching. One such possible situation is schematically shown in Figure S6. To switch our

device, we apply a current such that the nucleated DW in one tilted wire propagates through

the straight wire and reaches the second tilted wire. Here, because of the opposite tilt, the DW

will stop. Now if we want to do a second switching to the opposite direction, since there is

already a DW present in the tilted wire, there is no need of nucleation. Instead we only need

to apply current to propagate the DW in opposite direction. Since the current required for

propagation is smaller than that for the nucleation, the critical switching current becomes

smaller. Note that the possibility to have DWs that remain in the pins depends on the relative

magnitude of two effects. The retaining force is given by the strength of the pining to defects.

The expelling force is derived from the DW energy reduction corresponding to the shortening

of the DW as it moves toward the end of the triangle. To obtain saturation of the tilted wires

they could be shortened, thereby increasing the pin angle and the resulting expelling force.

We chose to work with long tilted wires such that the DWs do not move out by themselves,

since we can easily saturate the samples using external field.

In order to evidence these different types of behavior, we systematically studied the

switching as a function of the length and the intensity of the current pulses. The result shown

in figure S6 indicates the existence of three different regions: no switching, switching and

nucleation regions. For a particular current density, an increase in the length of the current

pulse increases the joule heating. For short pulses, there is not enough heat for the nucleation

and thus no switching. When we increase the pulse length, the heating becomes sufficient to

nucleate on the tilted wires and the switching begins. The upper limit is given by the pulse

length where nucleation occurs in the straight wire. Above, the switching becomes stochastic.

The critical current dependence on the initial state is also illustrated in Figure S6a where the

switching region is further divided into two. The dark and light blue region corresponds to the

switching window for saturated and non-saturated initial. Note that he DW pinning field in the

tapered region is found to be almost identical to the propagation field in the straight section

Htapered=16mT and Hstraight=15.5mT.





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