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Current-Induced Switching in a Magnetic Insulator

Supplementary Information

Can Onur Avci, Andy Quindeau, Chi-Feng Pai1, Maxwell Mann,

Lucas Caretta, Astera S. Tang, Mehmet C. Onbasli, Caroline A. Ross2, and Geoffrey S. D.

Beach3

Department of Materials Science and Engineering, Massachusetts Institute of Technology,

Cambridge, Massachusetts 02139, USA

S1. Reciprocal space mapping of a 30 nm thick TmIG film on GGG(111)

The structural analysis is performed based on symmetric XRD scans (Fig. 1(a) in the

main text) and reciprocal space mapping (RSM) of TmIG film grown on GGG(111). As

illustrated in Fig. S1, the RSM result shows that, in case of a 30 nm-thick TmIG film on

GGG(111), the respective (246) asymmetric diffraction peaks lie on one vertical line,

sharing the same value for the interplanar spacing in [ 110 ]-direction. This can be

interpreted as the TmIG being fully strained on top of the GGG substrate, leading to a

rhombohedral distortion of its pseudocubic unit cell. The lattice parameter ratio of

( ) ( )film bulk film bulk444 444 220 220/ / / 0.985d d d d = is calculated using the structural data extracted from

the RSM and the structural data for bulk TmIG in Ref. 1 (visualized in the figure by a red

cross). 1 Current address: Department of Materials Science and Engineering, National Taiwan University, Taipei 10617, Taiwan 2 [email protected] 3 [email protected]

Current-induced switching in a magnetic insulator

© 2016 Macmillan Publishers Limited, part of Springer Nature. All rights reserved.

SUPPLEMENTARY INFORMATIONDOI: 10.1038/NMAT4812

NATURE MATERIALS | www.nature.com/naturematerials 1

http://dx.doi.org/10.1038/nmat4812

2

Figure S1 | Reciprocal space map of fully strained TmIG on GGG(111). RSM around

the (246) film- and substrate peaks. The dashed line is a visual guide to demonstrate that

film and substrate peaks have the same qx-values. A comparison with a (246) diffraction

peak of bulk TmIG is made by showing the value using a red cross in the figure.

S2. Longitudinal spin Hall magnetoresistance measurements

In the main text we mainly focused on the transverse measurements of the spin Hall

magnetoresistance (SMR). However, the SMR does also modulate the longitudinal

resistance as given in equation (1) [see main text]. In figure S2 we show the relative

change in the resistance (∆𝑅𝑅 𝑅𝑅) when the magnetization (𝐦𝐦) is tilted in the zx and zy

planes with an in-plane field applied along x (𝜑𝜑! = 0°) and y (𝜑𝜑! = 90°). We observe a

decrease in the resistance when magnetization is tilted along the y-axis whereas the

magnetoresistance is merely noticeable along the x-axis. This behavior is typical of the

2.26 2.27 2.28 2.29 2.30 2.315.55

5.60

5.65

5.70

q z // [1

11] (

nm-1)

qx // [110] (nm-1)

GGG

TmIG

(246)diffraction





3

SMR reported in YIG/Pt system2 and compatible with equation (1) given in the main text.

Simulation based on the macrospin approximation and experimental parameters

reproduce very well the angular dependence of the data expected from the SMR signal.

The small increase of the resistance when the external field is applied along the x-axis

can be interpreted in several ways. Due to the low signal-to-noise ratio and limitation in

the applied field amplitude, it is not clear to us whether the signal saturates at higher

fields or not. A non-saturating signal could indicate a field-induced Hanle

magnetoresistance3 (see further discussion in the next section). On the other hand, if the

signal saturates at higher fields, proximity-induced polarization of Pt could give rise to a

conventional anisotropic magnetoresistance, which would increase when m is tilted along

the x-axis. Nevertheless, this set of data validates that the longitudinal/transverse

resistance changes are mainly driven by the SMR as expected from magnetic

insulator/normal metal systems.

Figure S2 | Longitudinal resistance measurements of TmIG/Pt. Relative change of the

longitudinal resistance (∆𝑅𝑅 𝑅𝑅) is plotted as a function of in-plane field applied along





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(𝜑𝜑! = 0°) or across (𝜑𝜑! = 90°) the current injection direction. The resistance changes

significantly as a function of 𝐦𝐦 controlled by the external field when tilted across the

current direction, i.e. y axis, and it remains nearly constant when tilted along the current

direction. Green curve is a simulation based on macrospin approximation and the

experimental parameters.

S3. Revealing the different contributions to the Hall voltage signal

A convenient way to determine SMR, SMR-induced anomalous Hall effect (AHE),

and the effective magnetic anisotropy field (𝐻𝐻!) is to measure the transverse Hall voltage

(𝑉𝑉!) with a nearly in-plane field sweep at 𝜑𝜑! = 45°, 𝜃𝜃! ≈ 90°. Figure S3a shows such

a measurement where we recognize several contributions, which we address individually.

First, we recognize a small negative linear background signal, which we associate with

the ordinary Hall effect (OHE, blue dashed line) due to the (unintentional) out-of-plane

component of the external field. We subtract this contribution together with the

sample-dependent offset (due to the misalignment of the Hall arms giving rise to a small

resistance) and plot the data in Fig. S3b. Second, we observe that even after the OHE

subtraction 𝑉𝑉! is continuously increasing well above 𝐻𝐻!. This field dependent signal

identifies itself as the Hanle magnetoresistance3 (MR) and follows approximately 𝐻𝐻!

(green curve). After subtraction of the Hanle MR we find the signal that is purely driven

by the SMR and SMR-induced AHE. Due to the small out-of-plane component of the

external field, 𝐦𝐦 switches between up and down states at 625±25 Oe, a value much

larger than the coercivity obtained with the out-of-plane field sweep, as expected from

PMA systems. When the external field is zero, 𝐦𝐦 points either up or down, and the

difference in 𝑉𝑉! (orange dashed lines) gives the AHE signal. The SMR signal indicated





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with the green bar is measured between the average 𝑉𝑉! at 𝐻𝐻 = 0 and the maximum 𝑉𝑉!

after 𝐦𝐦 is fully saturated in-plane.

Figure S3 | Contributions to the Hall voltage signal. a, Raw data corresponding to 𝑉𝑉!

recorded during a field sweep between ±5000 Oe applied at 𝜑𝜑! = 45° and 𝜃𝜃! ≈ 90°.

We recognize a small linear background due to the OHE (blue dashed line). b, 𝑉𝑉! after

subtraction of OHE and a sample-dependent constant offset. We identify the Hanle MR

∝ 𝐻𝐻! plotted in green. c, 𝑉𝑉! after removing the Hanle MR from which we determine

the AHE (orange dashed lines) and SMR (green dashed lines) contributions. The red

curve shows the macrospin simulation based on the experimental parameters and the 𝐻𝐻!

value best fitting the data.

By using the extracted AHE and the SMR values we performed macrospin

simulations by assuming different 𝐻𝐻! values. The red curve shows the best match to the

data with 𝐻𝐻! = 1500 Oe, which can also be approximately determined from the

measured data by the field required to saturate 𝐦𝐦 in-plane where 𝑉𝑉! shows no more

variation. We note that this measurement is performed at the same current density

(𝑗𝑗!"# = 2.1×10!! A/m2) used for the second harmonic measurements and therefore 𝐻𝐻!

is considerably lower than the one reported in Fig. 2 (𝐻𝐻! = 2700 Oe), which was





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measured at much lower current density. We conclude that the Joule heating considerably

changes the magnetic anisotropy in TmIG/Pt films and one should be cautious about this

when performing the second harmonic signal analysis.

S4. High field behavior of the second harmonic signal and the spin Seebeck effect

contribution

As extensively studied in Ref. 4 the second harmonic signals can have additional

contributions associated with the thermoelectric effects driven by random temperature

gradients in the Hall bar device. Due to larger thermal conductivity of the GGG/TmIG

bilayer with respect to the air surrounding the device, the accumulated heat from the

Joule heating in Pt mostly dissipates towards the substrate creating a significant

out-of-plane temperature gradient 𝛁𝛁𝑇𝑇!4,5. This 𝛁𝛁𝑇𝑇! gives rise to the spin Seebeck effect

(SSE) in TmIG creating a spin current 𝐣𝐣! ∥ 𝛁𝛁𝑇𝑇! with the polarization 𝛔𝛔 ∥ 𝐦𝐦. When 𝐣𝐣! is

injected into Pt a transverse voltage develops due to the inverse spin Hall effect with the

symmetry 𝑉𝑉!!"~𝐣𝐣!×𝛔𝛔 = 𝐳𝐳×𝐦𝐦. By assuming that 𝛁𝛁𝑇𝑇! ∝ 𝑇𝑇 ∝ 𝐼𝐼!𝑅𝑅 SSE is bound to

generate a voltage proportional to 𝐼𝐼! and which shows up in the second harmonic signal6

and mixes with the SOT-driven signal.

The main difference between the SSE and SOT-driven signals is that the former

depends only on the magnetization direction whereas the latter depends both on the

magnetization direction and magnetic susceptibility to the current-induced fields.

Therefore performing 𝑉𝑉!! measurements at large fields can help to determine the origin

of the second harmonic signals.





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Figure S4 | High field behavior of the second harmonic signals. We note that 𝑉𝑉!! is

an order of magnitude larger when 𝐦𝐦 ∥ 𝐱𝐱 with respect to the signal when 𝐦𝐦 ∥ 𝐲𝐲. This is

due to the fact that the SSE dominates the signal in the former geometry and generates a

much larger signal with respect to the SOT which mainly drives the signal in the latter

geometry. Inset shows a zoom-in to the red curve.

In Fig. S4 we compare the 𝑉𝑉!! signals measured with a swept field of ±2300 Oe,

at two different configurations. We note that this field value is considerably larger than

the anisotropy value determined in the previous section (𝐻𝐻! = 1500 Oe), hence we

expect that the SOT-driven 𝑉𝑉!! significantly decreases at high fields. Signal at 𝜑𝜑! = 0°

increases (decreases) with the increasing (decreasing) field and saturates at 𝐻𝐻 ≅ 𝐻𝐻!

where the magnetization is expected to be saturated in-plane. This behavior is typical of

the SSE-driven thermal voltage where the SOT-driven signal is negligibly small. On the

other hand the signal at 𝜑𝜑! = 90° (red) is relatively smaller but consistent with the

SOT-driven signal (see inset for a zoom-in to the data): i) The sign changes depending on

whether 𝐦𝐦 is in the up or down state, ii) The maximum signal is observed at 𝐻𝐻 ≅ 800





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Oe which is approximately half of 𝐻𝐻! where 𝐦𝐦 has maximum susceptibility to

current-induced fields, iii) at high 𝐻𝐻 the signal drops to around its value recorded at

𝐻𝐻 = 0 where no SOT-driven signal is expected. We observe an asymmetry in 𝑉𝑉!!

taken at 𝜑𝜑! = 90° (more visible in the inset) which we associate with a small SSE

signal contribution due to the misalignment of 𝐻𝐻 with respect to the y-axis and will be

discussed in more details in the following section.

S5. Simulations of the second harmonic signals

In order to understand the different slopes observed in second harmonic

measurements which also contribute to the asymmetry reported in Fig. S4-inset we

performed macrospin simulations. We therefore computed the equilibrium magnetization

position by considering all effective torques acting on it, i.e. the external field (𝐓𝐓!),

perpendicular magnetic anisotropy (𝐓𝐓!), demagnetizing field (𝐓𝐓!"#) which are the static

parameters, and field-like (𝐓𝐓!") and damping-like (𝐓𝐓!") torques as dynamic

(current-induced) parameters. In equilibrium the sum of these torques is equal to zero:

𝐓𝐓! + 𝐓𝐓! + 𝐓𝐓!"# + 𝐓𝐓!" + 𝐓𝐓!" = 0 . (S1)

At each simulation point, i.e. a different external field, we compute the equilibrium angle

of the magnetization (𝜃𝜃 and 𝜑𝜑) in an iterative way, in order to satisfy the torque

equation above in 3D space. Once the sum of the torques satisfies the convergence

criterion for equilibrium we use the computed angles to calculate the Hall effect voltage

given by Equation (2) of the main text by inserting the SMR, AHE and OHE coefficients

as determined in Sect. S3. We repeat this procedure for positive and negative current by





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changing the sign of 𝐓𝐓!" and 𝐓𝐓!". The difference of these two signals computed for

opposite polarity of the current gives 𝑉𝑉!, and the sum gives 𝑉𝑉!! due to the SOT. Finally,

we add the voltage contribution from the SSE to 𝑉𝑉!! as determined from Fig. S4.

Figure S5 shows the raw data (a) and the simulations performed for two different

field angle and SOT scenarios (b and c). First, we address the two SOT scenarios. The

blue curves are the simulations where only the damping-like SOT is considered, whereas

the red curves show the simulations when both damping-like and field-like SOT are taken

into account. As discussed in the main text, we observe that the signal is dominated by

𝐻𝐻!" even though 𝐻𝐻!" is chosen to be as large as 𝐻𝐻!". This result is due to the fact that

the SMR coefficient is much larger than the AHE coefficient, therefore 𝑉𝑉!! is mainly

driven by the in-plane oscillations to the magnetization which is generated by 𝐻𝐻!" in

this geometry.

Figure S5 | Comparison between measured and simulated second harmonic signals.

a, Raw 𝑉𝑉!! data taken with the field supposedly applied along y-axis. b, Simulations by

considering 𝐻𝐻!" (blue curve) and 𝐻𝐻!" + 𝐻𝐻!" (red curve). We note that the signal is

mainly driven by 𝐻𝐻!" and adding 𝐻𝐻!" to the simulations makes a difference of approx.

7% which remains within the error bar of 𝐻𝐻!" reported in the main text. c, Simulations

at slightly different in-plane angle of the applied field. We observe that a non-negligible





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SSE signal gives rise to the asymmetry very similar to the raw data shown in a.

Second, we discuss the influence of the in-plane field angle on 𝑉𝑉!!. When the field

is applied at 𝜑𝜑! = 90° the second harmonic signal is perfectly symmetric for positive

and negative fields, as expected. On the other hand, when we simulate the same signal for

𝜑𝜑! = 89.2° (the angle is arbitrarily chosen) we obtain a slight asymmetry very similar to

the raw data reported in (a). This asymmetry is due to the SSE contribution when 𝐦𝐦 has

a +𝐱𝐱 (−𝐱𝐱) component with positive (negative) applied field. Furthermore the

simulations corresponding to 𝑉𝑉! reproduce very well the asymmetry reported in Fig. 3b

of the main text (not shown). These results further support our initial assumptions made

on neglecting 𝐻𝐻!" and the SSE origin of the different slopes in Fig.3c (main text), and

validates our analysis to accurately quantify 𝐻𝐻!".

Finally we would like to comment on the quantitative comparison between the

simulations and the measurement. Since the parameters used in the simulations are very

similar to that measured, we expect that they are quantitatively comparable. We notice

that the total amplitude of the signal in Fig. S5a and c are very close to each other within

10% of accuracy. This result corroborates with our analysis and validate the SOT

quantification.

S6. Switching measurement protocol and reference measurements

In this section we explain in detail the switching measurements procedures and

compare the switching polarity to that of a reference sample with well-known

characteristics. In order to observe the switching effect we have created a measurement

sequence where we apply an in-plane field (𝐻𝐻!) simultaneously with the current pulse of





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5 ms, and then we apply a negative and positive out-of-plane field (±𝐻𝐻!) which serve as

reference measurements for 𝐦𝐦!" and 𝐦𝐦!"#$. Figure S6a upper panel shows such a

sequence which takes 1 s in total. 𝐻𝐻! shown in magenta is ramped (rather than pulsed)

due to experimental limitations, and at the peak of 𝐻𝐻! a short voltage pulse is applied to

the sample along the x-axis. The system was then allowed to settle any transient

discharging effects and the Hall voltage (𝑉𝑉!) is averaged for 30 ms (gray region #3) just

before the 𝐻𝐻! pulses. We then applied −𝐻𝐻! and +𝐻𝐻! after which we acquired 𝑉𝑉!

during 30 ms (regions #1 and #2, respectively). We finally compare 𝑉𝑉! recorded after

the pulse injection to the difference of 𝑉𝑉! between region #2 and #1 which gives a value

between 1 and 0 corresponding to switching and non-switching events, respectively. This

sequence is repeated ten times for a given pulse amplitude and/or 𝐻𝐻! to construct the

data set reported in Fig. 4b and c of the main text.

In Fig. S6a bottom panel we show an exemplary 𝑉𝑉! signal recorded during one

measurement sequence. We observe several interesting features. First, we recognize a

very large transient signal during pulse injection which goes out of the scale of this plot.

The transient signal relaxes during the next 300 ms (approx.) and by the time that the

measurement is performed at 750 ms, there is no more transient signal and 𝑉𝑉! is

representative of the magnetization state driven by AHE. We note that magnetization

does (does not) switch with a positive (negative) pulse. We also observe an increase

(decrease) of 𝑉𝑉! during −𝐻𝐻! (+𝐻𝐻!). This is due to the OHE contribution which

disappears after removing the field. Overall, we find that for TmIG/Pt sample a positive

𝐻𝐻! together with a positive current 𝑗𝑗 stabilizes 𝐦𝐦!"#$ whereas opposite polarity of

𝐻𝐻! and 𝑗𝑗 stabilizes 𝐦𝐦!".





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Figure S6 | Acquisition of exemplary data points for the SOT switching hysteresis

loop and comparison with reference data. a, Top panel: Field and applied voltage vs.

time during a single data point acquisition sequence. Bottom panel: Hall voltage

measured throughout the sequence. Gray regions indicate data utilized to determine

whether switching has occurred or not. Region #3 measures the effect of the pulse

injection, region #1 and #2 are references for 𝐦𝐦!"#$ and 𝐦𝐦!", respectively. b, Similar

measurements performed on Pt/Co layers, serving as reference.

In Fig. S6b we show similar measurements performed in Pt/Co PMA layers in

exactly the same field and pulse configurations. In this system the switching is

demonstrated by several groups (see e.g. references 7,8) and it is know to be mediated by

the torque from the spin Hall effect in Pt. Therefore this can be used as a reference

measurements to confirm the switching polarity and examine whether the switching in

TmIG/Pt is driven by the SHE in Pt or not. We note that due to much higher

signal-to-noise ratio the measurement time is reduced to 0.5 s. We observe that the





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negative pulse switches 𝐦𝐦 more than 50% (red curve), whereas the positive pulse has no

effect on 𝐦𝐦 (blue curve). This result is opposite to what was found for TmIG/Pt and

compatible with the SHE-induced switching scenario since Pt position with respect to the

magnetic layer is opposite in these two cases.

S7. Estimation of Joule heating due to current injection

Figure S7 | Estimated temperature rise (ΔT) of Pt layer due to current injection.

In order to estimate the temperature rise due to Joule heating we placed a device on a

heating plate and measured the resistance by systematically increasing the plate

temperature. By assuming that the heating plate and the sample are in thermal

equilibrium we obtained the relation resistance versus temperature. By using the

resistance versus current density data, measured independently, we obtained the direct

relation between the temperature rise (ΔT) and j (see Fig. S7). We note that the

temperature rise is significant (negligible) above (below) j=1x1011 A/m2, indicating that

the Joule heating might play an important role to facilitate switching for relatively high





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current densities. We also note that the estimation of Joule heating is likely to be an

overestimation since current spread towards the Hall branches would decrease the net

current density in the central region of the Hall cross hence creating lower Joule heating

in the active area of the device.

References

1. Botdorf & McCarthy. XRD on TmIG. (1971).

2. Chen, Y. T. et al. Theory of spin Hall magnetoresistance. Phys. Rev. B 87, 144411

(2013).

3. Vélez, S. et al. Hanle Magnetoresistance in Thin Metal Films with Strong

Spin-Orbit Coupling. Phys. Rev. Lett. 116, 016603 (2016).

4. Avci, C. O. et al. Interplay of spin-orbit torque and thermoelectric effects in

ferromagnet/normal-metal bilayers. Phys. Rev. B - Condens. Matter Mater. Phys.

90, 1–11 (2014).

5. Avci, C. O. et al. Unidirectional spin Hall magnetoresistance in

ferromagnet/normal metal bilayers. Nat Phys 11, 570–575 (2015).

6. Vlietstra, N. et al. Simultaneous detection of the spin-Hall magnetoresistance and

the spin-Seebeck effect in platinum and tantalum on yttrium iron garnet. Phys. Rev.

B - Condens. Matter Mater. Phys. 90, 1–8 (2014).

7. Miron, I. M. et al. Perpendicular switching of a single ferromagnetic layer induced

by in-plane current injection. Nature 476, 189–193 (2011).

8. Liu, L. Q., Lee, O. J., Gudmundsen, T. J., Ralph, D. C. & Buhrman, R. A.

Current-Induced Switching of Perpendicularly Magnetized Magnetic Layers Using

Spin Torque from the Spin Hall Effect. Phys. Rev. Lett. 109, 96602 (2012).





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