Electric-field control of field-free spin-orbit torque switching via laterally modulated Rashba effect in Pt/Co/AlOx structures

Spin-orbit coupling effect in structures with broken inversion symmetry, known as the Rashba effect, facilitates spin-orbit torques (SOTs) in heavy metal/ferromagnet/oxide structures, along with the spin Hall effect. Electric-field control of the Rashba effect is established for semiconductor interfaces, but it is challenging in structures involving metals owing to the screening effect. Here, we report that the Rashba effect in Pt/Co/AlOx structures is laterally modulated by electric voltages, generating out-of-plane SOTs. This enables field-free switching of the perpendicular magnetization and electrical control of the switching polarity. Changing the gate oxide reverses the sign of out-of-plane SOT while maintaining the same sign of voltage-controlled magnetic anisotropy, which confirms the Rashba effect at the Co/oxide interface is a key ingredient of the electric-field modulation. The electrical control of SOT switching polarity in a reversible and non-volatile manner can be utilized for programmable logic operations in spintronic logic-in-memory devices.

Reviewer #2: Remarks to the Author: I think this work has several important findings attracting the attentions of specialists in this field; for example (i) ferromagnet/oxide interface has sizable contribution to the magnetization dynamics induced by SOT and (ii) lateral modulation of the gate state generates SOT along the film normal direction (z-SOT), resulting in field-free magnetization switching. Therefore, I think this manuscript in principle warrant publication in Nature Communications. However, before the acceptance, the following three issues should be addressed.
(1) Contribution of bulk Pt, Pt/Co interface, and Co/AlOx interface for SOT should be clarified. It is likely from the presented results that Co/AlOx plays a crucial role for z-SOT; however, it is not clear how the bulk Pt, Pt/Co interface, and Co/AlOx interface contribute to the conventional inplane SOT. In addition, I think the authors should consider the effect reported in PRB 94, 140414(R) (2016), in which fieldlike torque generated through a spin scattering at FM/oxide interface is reported. I am wondering if this kind of effect can also explain the present results even without considering the Rashba effect.
(2) While the authors state that the z-SOT and associated switching polarity are controllable by gate voltage in a reversible and "non-volatile" manner, but the "non-volatile" control is not fully supported in the present manuscript. How long does the state of oxide (TiO2 or ZrO2) last? The authors should either show evidence of "non-volatility" or tone down this claim.
(3) The results shown in Fig. 4 clearly indicates that TiO2 and ZrO2 have different properties with each other, resulting in an opposite switching polarity shown in Fig. 1d,e and Fig. 3b,c, and the authors attribute this result to different transport mechanism of the two oxides (ion migration/charge trap) in lines 184-186. However, I think the actual picture happening in the oxide in their side-gate device is not clear to the readers and should be schematically shown in Fig.  4 or SI. Do the authors speculate that the electric charges with lateral gradient remain after turning off the side-gate voltage, and the direction of gradient differs between TiO2 and ZrO2? Such illustration should aid in the understanding of potential readers.
Reviewer #3: Remarks to the Author: The authors have given further quantitate estimates on the oxygen gradients which was one of my concerns, albeit still far from what is observed in the measured devices. They however argue that any gradient, how small what so-ever, will lead to field free switching. Which in essence for the physics symmetry breaking might be true. However, in real devices and in the atomic world where gradients will be discrete this is not true. Hence, as the authors claim real-life applications should give a lower bound on dependence of the 'probability' of field-free switching when a small gradient is present. In a sense saying that it will always work, is weakening the claim of the paper, as the observed result just as well be explained due to a minor tilt of the sample during e.g. sputtering or processing or wherever.
The scaling claim in SPICE is still not sufficiently accompanied by a warning. Give a clear limit at which the effect here has been shown, and indicate that if, and only if, the scaling holds SPICE can be used accordingly, preferably even add a lower limit with an argument. Again, too many scaling problems are created by uninformed engineers scaling down such effects to 10x10 nm^2 and claiming it will work as a charm.
Overall I am still in favor of publishing this work. The limits are clear, time effects are beyond the scope but addressed.
The authors have addressed most of the concerns raised by the referees. Although I still have my doubts regarding the possibility of scaling this device architecture down to nano size, the authors have shown its potential. I believe that the present manuscript will be a good fit for Nature Communications.

Response)
We appreciate the reviewer's recommendation for publication of our manuscript in Nature Communications.

Reviewer #2 (Remarks to the Author)
I think this work has several important findings attracting the attentions of specialists in this field; for example (i) ferromagnet/oxide interface has sizable contribution to the magnetization dynamics induced by SOT and (ii) lateral modulation of the gate state generates SOT along the film normal direction (z-SOT), resulting in field-free magnetization switching. Therefore, I think this manuscript in principle warrant publication in Nature Communications. However, before the acceptance, the following three issues should be addressed.

Response)
We appreciate the reviewer's comment that "this work has several important findings attracting the attentions of specialists in this field; I think this manuscript in principle warrant publication in Nature Communications." We respond to the reviewer's additional comments below, which hopefully alleviates the reviewer's concerns and the revised manuscript is now acceptable for publication. (

In addition, I think the authors should consider the effect reported in PRB 94, 140414(R) (2016), in
which field-like torque generated through a spin scattering at FM/oxide interface is reported. I am wondering if this kind of effect can also explain the present results even without considering the Rashba effect.

Response)
We appreciate the reviewer's comment that the contributions of bulk Pt, Pt/Co interface, and Co/AlOx interface to in-plane spin-orbit torques (SOTs) should be examined. In this study, we   (2018)]. Therefore, the interfacial spin scattering quoted by the reviewer and the Rashba effect in our manuscript are not mutually exclusive but rather closely related each other.
In the revised manuscript on page 10, we added the following sentences regarding the above  [PRB 103, 134405 (2021)]." (2) While the authors state that the z-SOT and associated switching polarity are controllable by gate voltage in a reversible and "nonvolatile" manner, but the "nonvolatile" control is not fully supported in the present manuscript. How long does the state of oxide (TiO2 or ZrO2) last? The authors should either show evidence of "non-volatility" or tone down this claim.

Response)
We appreciate the reviewer's comments on the non-volatility of the electric-field effect. To demonstrate the nonvolatile behavior of our device, we examined how long the voltage-controlled magnetic anisotropy (VCMA) effect persists in a Pt (5 nm)/Co (1.4 nm)/AlO x (2 nm)/TiO 2 (40 nm) structure, which is the same sample used in Fig. 1 of the main text. Figure R1a shows the VCMA effect of the sample; coercivity (B c ) is reduced when a V G of +8V (equivalent to 2.5 MV/cm) is applied. To demonstrate the retention of the VCMA effect, we repeatedly measured the B c over a week, where the measurement was performed every hour on the first day and once a day thereafter. Figure   R1b shows that the reduced B c remains almost the same over the measurement time, demonstrating the VCMA effect remains nearly the same for more than 6×10 5 seconds, corresponding to seven days.
We included the results of the nonvolatile VCMA effect in Supplementary Note 2. between the TiO 2 and ZrO 2 samples. We include a schematic of the lateral variation in barrier height (φ) as the inset of Fig. 4 in the revised manuscript, which is shown in Fig. R2, where the black or red line indicates the potential barrier height of the oxide layer. We believe that the opposite electric field effect may be due to the different transport mechanisms of the oxides; oxygen ion migration (charge trap) is the dominant mechanism in TiO 2 (ZrO 2 ). However, further investigation is required to clarify the gate oxide dependence of the electric field effect.

Reviewer #3 (Remarks to the Author)
The authors have given further quantitate estimates on the oxygen gradients which was one of my concerns, albeit still far from what is observed in the measured devices. They however argue that any gradient, how small what so-ever, will lead to field free switching. Which in essence for the physics symmetry breaking might be true. However, in real devices and in the atomic world where gradients will be discrete this is not true. Hence, as the authors claim real-life applications should give a lower bound on dependence of the 'probability' of field-free switching when a small gradient is present. In a sense saying that it will always work, is weakening the claim of the paper, as the observed result just as well be explained due to a minor tilt of the sample during e.g. sputtering or processing or wherever.

Response)
We appreciate the reviewer's comment. As the reviewer pointed out, real samples may have a gradient that arises during fabrication. However, this gradient is randomly distributed so that it cannot cause a well-defined net gradient along the y-direction transverse to the current direction, which is required for the generation of z-SOT and associated field-free switching. In our experiment, field-free switching is realized when an asymmetric gate voltage (ΔV G ) is larger than 8 V, which is a critical ΔV G that overcomes unintended non-uniformities to create a net gradient.
In the revised manuscript on page 5, we added the following sentence describing a critical asymmetric gate voltage for field-free switching, "Note that field-free switching is achieved when the ΔV G is greater than 8 V, which is a critical ΔV G to create a net lateral asymmetry." The scaling claim in SPICE is still not sufficiently accompanied by a warning.

Response)
We appreciate the reviewer's acknowledgment, "Overall, I am still in favor of publishing this work." We have responded to the reviewer's additional comments above, which hopefully convinces her/him to support the publication of our manuscript.

Reviewers' Comments:
Reviewer #2: Remarks to the Author: In the previous round, I made three comments, to which the authors have addressed in this revision. I think the first comment on the origin of spin-orbit torque and the second comment on the nonvolatility have been satisfactorily addressed. On the other hand, the authors' action to my third comment is different from what I intended. While the authors added a lateral variation in potential barrier in Fig. 4, I thought that what is actually happening inside the gate oxide should been illustrated, for example, by drawing a possible spatial variation of oxygen owing to the difference in the transport mechanism, because this is the most important ingredient achieving the field-free spin-orbit torque switching in this work. However, if the authors want to keep it vague, I do understand. Apart from that, I found one typo in line 279; a square after "125" should read degree Celsius. Once the above issues are addressed, I would be happy to recommend the acceptance of this manuscript.

Reviewer #2 (Remarks to the Author)
In

Response)
We thank the reviewer for carefully reading our responses. We are happy to hear that "Once the above issues are addressed, I would be happy to recommend the acceptance of this manuscript." Following the reviewer's suggestions, we revised the manuscript as described below.
First of all, we apologize for misunderstanding the reviewer's comment about the illustration of actual happening inside the gate oxide. We note that the microscopic origin of field-free switching is the lateral variation of the potential barrier and associated Rashba effect at the Co/oxide interface. We, therefore, added corresponding schematics in Figure 4 of the revised manuscript. The reviewer wanted us to explain the different field-free switching polarities between the samples with TiO 2 and ZrO 2 gate oxides based on the transport mechanism of the oxide. In the original manuscript, we speculated that the opposite electric field effect might be due to the different transport mechanisms of the oxides, but this has not been confirmed by experimental or theoretical studies. Further investigation of the oxygen distribution along the thickness direction is required to address this conclusively. Therefore, we think it would be better not to include schematic drawings in the current manuscript, which may mislead the readers.
Furthermore, we revised the typo in line 279 as "125 C".