Optical spin-orbit torque in heavy metal-ferromagnet heterostructures

Spin current generation through the spin-orbit interaction in non-magnetic materials lies at the heart of spintronics. When the generated spin current is injected to a ferromagnet, it produces spin-orbit torque and manipulates magnetization efficiently. Optically generated spin currents are expected to be superior to their electrical counterparts in terms of the manipulation speed. Here we report optical spin-orbit torques in heavy metal/ferromagnet heterostructures. The strong spin-orbit coupling of heavy metals induces photo-excited carriers to be spin-polarized, and their transport from heavy metals to ferromagnets induces a torque on magnetization. Our results demonstrate that heavy metals can generate spin-orbit torque not only electrically but also optically.


1)
, which reports their key experimental results, is not as clear as it should be. The axis labels on (a) (b) and (c) appear to be messed up, as well as some labels on other figures. Importantly, they don't show their longitudinal MOKE data. Instead, they just show their "conversion" of those signals into M_y in Fig. 2b. They should show the signals they are measuring, because the difference in polar and longitudinal signals is central to their claims.
2) It's not clear how the authors went from experimental signals to Mz and My in Fig. 2b. They include a supplemental note about this, but it describes it in very broad terms. No equations are provided that would enable someone trying to repeat the conversion on their own. For longitudinal MOKE , the polarization rotation will depend on the angle of incidence of 20 degrees. They should provide details, i.e. the relevant magneto-optical equations, that relate what is measured (voltage propor tional to polarization rotation) to magneto-optical constants to Mz and My.
It looks more detail about the longitudinal MO effect was requested in the prior referee report, but the au thors seemed to misunderstand the comment. They added a supplemental note about the polarization of the probe beam in polar MOKE. This is irrelevant because p and s polarization are equivalent in a polar configuration. They did not discuss how the angle of incidence effects signals in the l ongitudinal MOKE configuration, or how they account for it to get Fig. 2b.
3) Figure 2c is referred to as "amount of measured optical spin-orbit torque" but has units of Amps, not torque. They say the dashed lines are fitting with light absorption in Pt and Co. It's not clear w hat they mean by "with light absorption in Pt and Co." 4) On lines 145-151 they explain Fig. 2c. They say they find the "pump absorption in Pt exhibits the exactly same d_Co dependence as /deltaM*d_Co. It would be helpful to show how the pump absorption in Pt depends on d_Co. The amount of light absorbed by the top Pt layer shouldn't really care how thick the Co layer once it's thicker than the optical penetration depth. In other words, since the Pt is on top, once no "reflection" occurs from interfaces below the Cobalt layer, the number of photons absorbed in Pt should stay constant. But the authors report /deltaM*d_Co steadil y decreasing with Cobalt thickness. So, the conclusion that the "pump absorption in Pt exhibits exactly" the same dependence needs to be clarified.
5) The authors invoke "built-in potential" at the interface as a possible explanation for the spincurrent from Pt to Co. Both prior referee reports pointed out this is a more questionable argument to ma ke for metal-metal junctions. The authors ignored the prior request to discuss relevant literature and cite prior work on this topic. Instead, they cite a semiconductor device physics text book. A re the authors the first people to ever propose an optically induced charge current at a metal-metal interface? If not, why is there no discussion of the literature on this topic?
6) The authors describe a "charge" current that results from optical excitation. The time-scale for charge current to relax in a metal under an open circuit condition should be much shorter than their experimental time-scales, i.e. tau = epsilon/sigma ~ 1e-18 seconds [PRB 95 014402 (2017)]. Here epsilon is the permittivity and sigma is the conductivity. So their conclusion that the pump pulse generates a 1.1 ps charge current that can traverse 25 nm is hard to understand. They don't provide enough details to understand what exactly their "charge transport simulation" is. They just say they used a "SPICE simulation. This is another example where the manuscript doesn't contain all elements necessary to replicate the results.
Reviewer #2 (Remarks to the Author): The submitted paper reports on the helicity-dependent optical spin-injection experiments in structures containing heavy metal (HM) on cobalt. I have reviewed the closely related manuscript in 2017, when the authors submitted it to Nature Nanotechnology. At this time, I had severalrather serious -doubts/questions about the physical mechanisms that were proposed as explanations of the performed experiments. In the current version of the manuscript, the authors have addressed all my previous experimental and theoretical concerns. The resulting paper is, at least in my eyes, very interesting and I have no doubts that it will attract a considerable attention of scientific community after its publication. At present, I have only one request, which is detailed below, that I would like the authors to address in the paper (or in the modified Supplementary information). After this, I recommend the publication of the paper in Nature Communication.
It is a very interesting and non-trivial result that the optical spin-injection efficiency has the same sign for different HMs, which have different work functions -see Fig. 5(c). However, as there are several experimental inputs that could affect the determined sign, I would find it very useful if the authors could provide also the "raw" experimental data from which this figure was derived. In particular, it would be nice to see the time-resolved magneto-optical data [analogous to Fig. 2  In Fig. 2 (b), we show the normalized Kerr rotation to emphasize the difference of dynamics between M z and M y components. The process to measure M y dynamics will be discussed in our response to the reviewer's next comment. To avoid confusion with axis in It looks more detail about the longitudinal MO effect was requested in the prior referee report, but the authors seemed to misunderstand the comment. They added a supplemental note about the polarization of the probe beam in polar MOKE. This is irrelevant because p and s polarization are equivalent in a polar configuration. They did not discuss how the angle of incidence effects signals in the longitudinal MOKE configuration, or how they account for it to get Fig. 2b.
 We check the probe polarization dependence in polar MOKE geometry to confirm that a quadratic Kerr rotation, which can have the M y information even at normal incidence angle, is not significant in our samples. To measure the M y dynamics, we inject the probe beam to the sample with an oblique angle, , in the y-z plane (Fig. S3 of Supplementary Note). In this geometry, the measured Kerr rotation is a mixture of the polar Kerr rotation ( ), which is due to M z dynamics, and the longitudinal Kerr rotation ( ), which is due to M y dynamics.
When the sample consists of a single magnetic layer whose thickness is much thicker than the optical penetration depth, the ratio between the and has a simple relationship of 5) The authors invoke "built-in potential" at the interface as a possible explanation for the spin-current from Pt to Co. Both prior referee reports pointed out this is a more questionable argument to make for metal-metal junctions. The authors ignored the prior request to discuss relevant literature and cite prior work on this topic. Instead, they cite a semiconductor device physics text book. Are the authors the first people to ever propose an optically induced charge current at a metal-metal interface? If not, why is there no discussion of the literature on this topic?
 We argue that the existence of built-in potential (or E-field) at interfaces is general regardless of the band structure of materials as charge transfer occurs at the interface between materials with different work functions. We quote a theoretical paper that shows the built-in potential of composite metallic interfaces of a few tens of meV [J. Phys. Chem. Lett. 3, 818 (2012)]. We also quote three papers about Rashba spin splitting at metallic interfaces, for which an E-field at the interfaces is a key requirement [Phys. Rev. Lett. 77, 3419-3422 (1996), Phys. Rev. B 90, 235422 (2014), and Phys. Rev. B 93, 174421 (2016]. However, we admit that the magnitude of the built-in potential in a metallic junction would be much smaller than that of a semiconductor junction. Especially, the E-field should be strong enough to induce photocurrent. We explicitly stated this assumption for the photocurrent in line 267~272 and moved the detailed analysis for the charge transport to Supplementary Note 7. We remove the word "built-in potential" as it is rarely used for metallic junctions. Instead we use the word "E-field" as it is often used to describe the Rashba effect. 6) The authors describe a "charge" current that results from optical excitation.  (2017)]. Here epsilon is the permittivity and sigma is the conductivity. So their conclusion that the pump pulse generates a 1.1 ps charge current that can traverse 25 nm is hard to understand. They don't provide enough details to understand what exactly their "charge transport simulation" is. They just say they used a "SPICE simulation. This is another example where the manuscript doesn't contain all elements necessary to replicate the results.
 Assuming that the E-field at the Pt/Cu interface is strong enough, we calculate the photoinduced charge transport in the Pt(5)/Cu(x)/Co (3)  with an exponential length scale of 20~30 nm (Fig. S7 (b)). We also calculate the charge accumulation on Co with a relative ratio of the electronic capacitance of Co and Cu. When we ignore the resistance effect and assume no backward current, charge accumulation Co (Q Co ) will be determined by where Q 0 is the time integration of J c . When d Co is fixed, Q Co decrease with increasing d Cu , and the calculated length scale of the decaying is 20~30 nm, which is the same as the SPICE simulation ( Fig. S7 (b)).
where is the charge density and is the charge current density. One then combines this equation with the Ohm's law = and the Gauss law ∇ • = / to obtain the approximate equation, The solution of this approximate equation is given by ( , ) = ( , = 0)exp (− / ), which implies that the initial charge density at = 0 decays exponentially fast in time with the characteristic time scale . We are now ready to discuss the length scale. For concreteness, one considers a metallic thin film (shown below) and assumes ( , = 0) to be spatially homogeneous within the film, ( , = 0) = (this assumption is not crucial, however).
For this film geometry, one then uses the Gauss law to calculate the electric field from the above solution ( , ) to obtain ( , ) = ̂ exp − + . Together with the Ohm's law, one obtains where is the coordinate along the thickness direction and ̂ is the unit vector along the direction. Note that ( , ) does grow in space (proportional to ), implying that the characteristic length scale is long-ranged. This long-rangedness persists even for spatially localized ( , = 0), say, ( , = 0) = ( ). For this initial condition, one obtains where sgn( ) is the Heaviside step function. Note that ( , ) for this choice of The resulting paper is, at least in my eyes, very interesting and I have no doubts that it will attract a considerable attention of scientific community after its publication. At present, I have only one request, which is detailed below, that I would like the authors to address in the paper (or in the modified Supplementary information). After this, I recommend the publication of the paper in Nature Communication.
It is a very interesting and non-trivial result that the optical spin-injection efficiency has the same sign for different HMs, which have different work functions -see Fig. 5(c). However, as there are several experimental inputs that could affect the determined sign, I would find it very useful if the authors could provide also the "raw" experimental data from which this  Supplementary Table S1.

REVIEWERS' COMMENTS:
Reviewer #1 (Remarks to the Author): The manuscript contains interesting and novel experimental results regarding the response of magnetic order in ferromagnetic orders to circularly polarized light. The results will be of interest to a broad audience. The authors have done a thorough job responding to my comments by adding significant detail describing how the experiments and analysis was conducted. I recommend for publication in Nature Communications.
Reviewer #2 (Remarks to the Author): In my eyes, the authors addressed reasonably well all the questions/comments of the referees. Therefore, I recommend the publication of the paper in Nature Communication.

Response letter to Referee's comments
"Optical spin-orbit torque in heavy metal-ferromagnet heterostructures" by G. M. Choi et al.
We thank both referees for their constructive comments. Since both reviewers do not ask any further work, we do not change the main contents of the manuscript.

Reviewers' comments:
Reviewer #1 (Remarks to the Author): The manuscript contains interesting and novel experimental results regarding the response of magnetic order in ferromagnetic orders to circularly polarized light. The results will be of interest to a broad audience. The authors have done a thorough job responding to my comments by adding significant detail describing how the experiments and analysis was conducted. I recommend for publication in Nature Communications.
Reviewer #2 (Remarks to the Author): In my eyes, the authors addressed reasonably well all the questions/comments of the referees.
Therefore, I recommend the publication of the paper in Nature Communication.