Optical-helicity-driven magnetization dynamics in metallic ferromagnets

Recent observations of switching of magnetic domains in ferromagnetic metals by circularly polarized light, so-called all-optical helicity dependent switching, has renewed interest in the physics that governs the interactions between the angular momentum of photons and the magnetic order parameter of materials. Here we use time-resolved-vectorial measurements of magnetization dynamics of thin layers of Fe, Ni and Co driven by picosecond duration pulses of circularly polarized light. We decompose the torques that drive the magnetization into field-like and spin-transfer components that we attribute to the inverse Faraday effect and optical spin-transfer torque, respectively. The inverse Faraday effect is approximately the same in Fe, Ni and Co, but the optical spin-transfer torque is strongly enhanced by adding a Pt capping layer. Our work provides quantitative data for testing theories of light–material interactions in metallic ferromagnets and multilayers.

6) Instead of evaluating the DSP responsible for the OSTT, it would be helpful if the authors could reference the spin polarization induced by the circularly polarized light to the spin polarization of the 3d-ferromagnetic metals at the Fermi level. Then, it would be immediately clear how big this effect really is.
Reviewer #2 (Remarks to the Author): The manuscript by G.M. Choi et al. reports on magnetization dynamics triggered by circularly polarized optical laser in thin ferromagnetic layers (Co, Fe and Ni). Experimentally the magnetization dynamics is probed by measuring the polar MOKE signal, from which the authors extract the system coupled dynamic. The dynamic is explained by the combination of two helicitydependent mechanisms; first, the magnetic torque induced by an optomagnetic field created by the circularly polarized laser (inverse Faraday effect, -IFE), and second, the torque induced by spin polarized currents created through laser-induced dipole transition in systems with non-vanishing spin-orbit coupling (optical spin transfer torque, -OSTT). Although both mechanisms relies on the transfer of angular momentum from the light to the material, the IFE induces a torque perpendicular to both, the magnetization direction and the angular momentum of photons, while the torque induced by the OSTT is parallel to the angular momentum of photons. To disentangle the partial contribution of each mechanism the authors use different capping layers (Au, Pt or MgO), where the contribution of the inverse Faraday effect remains constant while the effect of optical spin transfer torque increases significantly, and fit the helicity-dependent data to a damped cosine function. Similar magnetization dynamics is observed for Co, Ni and Fe, with differences only due to the magnitude of the magnetization. A study of the ultrafast linearly polarized laserinduced demagnetization is also carried out.
Despite this work is focused on gaining understanding about the transfer of angular momentum of light to metals, a developing field which might have key implications in the technological development of magnetic recording media, and that the experimental finding are interesting, there are several questions that arise regarding the theoretical interpretation of the results that make it unsatisfactory for publication at the current state.
1) The theoretical interpretation of two helicity-dependent mechanisms triggering two orthogonal torques on the system magnetization is well presented. It is based on the initial assumption that IFE does not require absorption while OSTT is an adsorption-dependent phenomena. This assumption, if correct, would support the experimental findings. However, this is a daring assumption under the current theory development, where as pointed by the authors "rigorous theory for IFE especially in metals is still under development". Thus, for instance, two very recent theoretical papers by different groups, A. Qaiumzadeh et al.
(https://arxiv.org/pdf/1604.01188.pdf), claim that the IFE is not an absorption-free phenomena, but rather that absorption plays a fundamental role to explain the different dynamics in different ferromagnetic metals. As a consequence, and until further theoretical clarification, the interpretation of the results of this manuscript is questionable.
Additionally, the following conclusion made by the authors, "We interpret IFE and OSTT as coming from non-absorbing and absorbing part of light, respectively", involves a false reasoning, since the analysis of the results is precisely made under such assumption, and clearly leaves not space for other possibility.
2) Despite the extensive literature of optical orientation in semiconductors, and more recently in magnetic semiconductors (leading to optical spin transfer torque), to the best of my knowledge this is the fist time it is used to explain magnetization dynamics in ferromagnetic metals. The carriers spin polarization generated by the optical orientation is determined by the selection rules of the material related to the crystal symmetry and depend ultimately on an interplay between angular momentum conservation and spin-orbit interactions. Thus, in a material with vanishing spin-orbit coupling there is not spin polarization of the carries due to optical orientation (Optical Orientation, edited by F. Meier and B. P. Zakharchenya (North Holland, New York, 1984)). Hence, crystal symmetry and spin-orbit coupling play an essential role to generate spin currents due to optical orientation, which subsequently induce spin transfer torque in magnetic materials. However, from literature it is not clear which is the influence of the strength of the spin-orbit coupling in the degree of spin polarization in metals (in atoms the polarization does not depend on the strength of the spin-orbit interaction -see for instance Chapter 7 in "Optical Orientation" cited above). Therefore, it is oversimplifying to consider that "the degree of spin polarization for Pt is 25 times larger than for Co due to the stronger spin-orbit coupling" as the authors claim. In addition, and under the author's conclusion that a stronger spin-orbit coupling leads to a larger spin polarization, (and being the spin orbit strength in Au of the same magnitude than in Pt), it would be expected a spin polarization in Au about 30 times smaller than in Pt (30 times smaller energy absorption). According to the results provided by the authors, this would unambiguously lead to a negligible spin polarization in Co, but not in Au (the spin polarization in Au should be 1.2x10^-3 and 0.2x10^-4 for Au and Co, respectively). These results would definitely be of very strong interest if first, they were well interpreted with a further support/justification of the interpretation, and second, an analysis of the influence of the crystal structures were made.
3) The authors wrongly assume that reference [33] provides a theory to IFE in terms of an interaction Hamiltonian coupling angular momentum of light with the material. Actually, the theory developed in reference [33] contributes to the IFE as a part of it, but not providing the whole effect, whose theory can be found for instance in reference [32]. In fact, one of the conclusion of reference [33] is that the proposed interaction mechanism has a very small effect on the magnetization, which would support the small optomagnetic field obtained with the use of that theory in this manuscript. Here it is important to remark again that this is just a very small contribution to the total IFE. 4) Another source of misunderstanding is the use of the optomagnetic field induced by the IFE as an effective Zeeman field, and its subsequent use in the Landau-Lifshitz-Gilbert equation. This leads to a wrong description of the magnetization dynamics. Contrarily, the IFE has to be treated as an induced magnetization rather than as an effective optomagnetic field, due to the fact that the laser induces different spin and orbital magnetization dynamics (https://arxiv.org/pdf/1604.01188.pdf). 5) As long as the IFE effect is an absorption free phenomena (assumption made by the authors in the manuscript), IFE can be related to Faraday effect, and the theoretical description made in the manuscript is valid. However, if assuming that the IFE is not an absorption free phenomena, the clear relation between both mechanisms is lost, and a new theoretical description would be needed (see point (1) above). 6) In my understanding it is not clear why the M_y component changes when changing the capping layer and its thicknesses (IFE is effectively independent to them). I would expect that as long as the IFE is effectively applying a torque into the system a M_y component should be present. This does not seem to occur for the Co/NM systems, where the M_y component goes from -2x10^-4 to zero. Could you clarify these results? 7) In reference [40] Choi et al. justify the generation of spin currents due to the formation of a thermal gradient inside of a ferromagnetic material. It would also be expected to find such thermal gradient under the conditions of the experiments carried out in this work. Thus, it is clear that the thermal gradient-induced spin currents does not exert any torque in the magnetization of the system as long as both have the same orientation. However, when introducing a capping layer. these currents can travel through it and, upon reflection, come back to the ferromagnetic material having a different orientation than the system magnetization. This is due to the fact that the system magnetization has been under the effect of the torque induced by IFE or OSTT. Therefore, this effect should be mention and analyzed to have a complete description of the magnetization dynamics.
8) The authors also report the magnetization dynamics of the different systems with linearly polarized pump-probe experiments. The authors justify the demagnetization due to magnon heating, without considering other possible demagnetization mechanisms. Even though I am not certain how this analysis contributes to the problem studied in this work, if the authors still consider important to mention the demagnetization dynamics, they would have to justify the choice of the mechanism and argue why other possible demagnetization mechanisms can be neglected.
Smaller remarks: 9) Along the reading of the manuscript one of the main experimental findings is repeated, namely, that using Pt layer significantly enhances OSTT against Au or Mg, even before the results have been shown, and with not citation to those. This leaves the sentences unjustified and out of context, and could be interpreted as an assumption or as a known fact. Therefore it should be reformulated in a different way. 10) At the end of the manuscript the authors write that in reference [11] it has been proposed that, IFE or OSTT can lead to AO-HDS. I would like to remark that in such reference there is not mention of OSTT. 11) From the figures is very difficult to extract the details given in the manuscript. Clearer figures with, for instance, a guide line for the eye would be very helpful. Especially a vertical line at zero time, from which the delay phase could be more easily seen.

Reviewer #3 (Remarks to the Author):
This is potentially a very important work that identifies out-of-plane and in-plane torque components generated by circularly polarized laser pulses in ferromagnetic transition metal films. By a combination of experimental and theoretical analysis the authors associate the torque oriented in the plane of the film with the inverse Faraday effect in a convincing way. The torque oriented out of the plane shows a much stronger sensitivity to the capping layers which provides an additional indication that it is of a different microscopic physics origin. The authors ascribe the out-of-plane torque to the optical spin transfer torque mechanism recently discovered in a ferromagnetic semiconductor GaMnAs. As the authors of the present paper emphasize, this mechanism is a combination of the optical spin orientation effect and of the spin transfer torque effect. Optical spin orientation is a well established field in semiconductors. In the present manuscript the authors consider optical spin polarization in Co and also in Pt. They also argue that a larger degree of optical spin polarization in Pt than in Au is due to the larger spin-orbit coupling in Pt. From the text it is however not clear what the authors assume is the microscopic physics of the optical orientation in the considered transition metal films. While the optical spin transfer torque interpretation is certainly appealing, a reference or at least a qualitative explanation of the optical orientation process in the transition metals would be desirable for making the whole story of the paper fully convincing and for increasing the impact of this interesting work. With (at least) a qualitative explanation of this the paper would be suitable for publication in Nature Communications.
We thank the three referees for their positive and constructive comments. We believe our manuscript is substantially improved as a result. Below, we summarize the major changes and 5. Reviewer 2 asks us to justify our description of OSTT by considering the dependence on crystal structure and spin-orbit coupling effects. This request requires full calculation of band structure, which depends on crystal structure, and energy splitting in multiple bands by spin-orbit coupling. However, the focus of our work is experimental and a full theoretical calculation is beyond the scope of our work. Instead, as our response to this comment of reviewer 1, we discuss recent theoretical papers that are relevant to OSTT in metals.
6. Reviewer 3 asks us to cite references that are relevant to OSTT in metals. This is the same comment of Reviewer 1 above. 7. Reviewer 3 asks us to clarify our assumptions for determining the degree of spin polarization (DSP) for OSTT. We describe our assumptions for the determination of DSP and supporting arguments on the first and second paragraphs on page eleven of the revised manuscript.

Reviewers' comments:
Reviewer #1 (Remarks to the Author): The manuscript "Optical-helicity-driven magnetization dynamics in metallic ferromagnets" by 1) The authors introduce two main helicity-dependent mechanisms that will influence the magnetization dynamics: the optical spin transfer torque (OSTT) and the inverse Faraday effect (IFE).
The OSTT has been discussed up to now mainly for inorganic semiconductors. In these systems it is a very well-known fact that circularly polarized light generates a transient spin-polarization (due to the optical selection rules and the presence of spin-orbit coupling). In contrast, in a 3dferromagnet optical excitation will basically excite hot-electrons above the Fermi energy. These electrons will possess a spin-polarization that is in general aligned with the magnetization of the sample, in this case the x-direction (according to the reference frame defined in Fig. 1). The additional spin polarization generated by the circularity of the light in the z-direction due to the optical selection rules, will probably be negligible (if at all different than zero!) compared to the spin polarization of the optically excited carriers along the x-direction.
I am not sure about how such a small fraction of spin-polarized carriers could lead to any measurable effect: in comparison, the spin-polarization that can be generated by optical orientation in GaAs is as big as 50%.
 Response: In our experiments, we align magnetization and light propagation directions orthogonal to each other. When magnetization and light propagation directions are parallel, spinpolarization from spin-dependent DOS probably dominates, and spin polarization from optical helicity will be overwhelmed. However, when magnetization and light propagation directions are orthogonal, spin polarization from optical helicity can be distinguished from spin polarization that results from spin-dependent DOS. We included this explanation in Supplementary Note 4.
We are indeed measuring a small quantity. We are able to measure such a small effect because we suppress noise level using synchronous detection using a high modulation frequency (10 MHz) combined with balanced detection. In our set-up, the noise level for polar MOKE detection is on the order of 0.1 μrad per root Hz which corresponds to a fractional change of magnetization of about 10 -5 for Co when measured on a 1 sec time scale. We can further reduce noise by averaging multiple measurements. We included this explanation in the method section of the revised manuscript.
From our analysis for OSTT, we found that degree of spin polarization of Pt is 0.03, which is about one order of magnitude smaller than that of GaAs. It is small but not negligible. (In the revised manuscript, we changed our estimate of the DSP of Pt from 0.036 to 0.03. DSP of 0.036 was obtained assuming that all M z tilting of Co(10)/Pt(4) sample is due to spin polarization of Pt.
DSP of 0.03 was obtained assuming that difference of M z tilting between Co(10)/Pt(4) and Co(10)/Au(2) is due to spin polarization of Pt.) We included the comparison of DSP between Pt and GaAs on the first paragraph on page ten of the revised manuscript.
2) Let's now assume that a small spin polarization (denoted with mz by the authors) can be generated in the z-direction (the direction of light propagation in Fig. 1) using circularly polarized light.
The authors explain that while the spin polarization mz should cause a torque on the sample magnetization in the z-direction, the IFE field (called Bz, and also directed along the z-direction!) will cause a torque along the y direction. I do not really understand this point. As far as I understand, in both equations describing the precession of the magnetization due to either the IFE or the OSTT, dM/dt is proportional to the cross product of M with either mz or Bz.  Response: When magnetization is tilted from the equilibrium position by optical pulse, its dynamics after the optical pulse is governed by the effective B-field (determined by shape anisotropy, crystalline anisotropy, and external magnetic field) along the equilibrium position.
Since the effective B-field is along the x-direction, the magnetization dynamics is the precessional motion in the y-z plane with the center axis of the x-direction. Because of the shape anisotropy of ferromagnets, the precessional motion is elliptical not circular in the y-z plane.
After many precessional motion, the magnetization settles to the equilibrium direction (xdirection) by damping. We included this explanation on the first paragraph on page five of the revised manuscript.  respectively, and discuss their results on the second paragraph on page ten of the revised manuscript.
Reviewer #2 (Remarks to the Author): The 1) The theoretical interpretation of two helicity-dependent mechanisms triggering two orthogonal torques on the system magnetization is well presented. It is based on the initial assumption that Additionally, the following conclusion made by the authors, "We interpret IFE and OSTT as coming from non-absorbing and absorbing part of light, respectively", involves a false reasoning, since the analysis of the results is precisely made under such assumption, and clearly leaves not space for other possibility. Hence, crystal symmetry and spin-orbit coupling play an essential role to generate spin currents due to optical orientation, which subsequently induce spin transfer torque in magnetic materials.
However, from literature it is not clear which is the influence of the strength of the spin-orbit coupling in the degree of spin polarization in metals (in atoms the polarization does not depend on the strength of the spin-orbit interaction -see for instance Chapter 7 in "Optical Orientation" cited above). Therefore, it is oversimplifying to consider that "the degree of spin polarization for Pt is 25 times larger than for Co due to the stronger spin-orbit coupling" as the authors claim. In addition, and under the author's conclusion that a stronger spin-orbit coupling leads to a larger spin polarization, (and being the spin orbit strength in Au of the same magnitude than in Pt), it would be expected a spin polarization in Au about 30 times smaller than in Pt (30 times smaller energy absorption). According to the results provided by the authors, this would unambiguously lead to a negligible spin polarization in Co, but not in Au (the spin polarization in Au should be 1.2x10^-3 and 0.2x10^-4 for Au and Co, respectively). These results would definitely be of very strong interest if first, they were well interpreted with a further support/justification of the interpretation, and second, an analysis of the influence of the crystal structures were made.
 Response: We are working toward developing the capability to predict OSTT of metals based on density functional theory but those calculations are not yet reliable or adequately validated.
The focus of our work is experimental. As stated above, we regret that we over-interpreted the data in our original submission and we have extensively revised our manuscript to be more guarded in the conclusions we draw from the data concerning microscopic mechanisms.
In the revised manuscript, we cite and discuss Berritta's paper (Berrita et al.  in Au would be ~20 times smaller than in Pt because the amount of light absorption in Au is ~20 times smaller. In original submission, we erroneously concluded that the degree of spin polarization from Co is larger than that of Au in Co(10)/Au(2) because M z dynamics is similar with Co(10)/Au(2) and Co(10)/MgO(5). However, given the uncertainty of small M z tilitng of Co(10)/Au(2) and Co(10)/MgO(5), we cannot reliable determine the contribution of the Au layer to OSTT. Therefore, we focus on DSP of Pt and have removed the analysis of DSP of the ferromagnet layer in the revised manuscript.
3) The authors wrongly assume that reference [33] provides a theory to IFE in terms of an interaction Hamiltonian coupling angular momentum of light with the material. Actually, the theory developed in reference [33] contributes to the IFE as a part of it, but not providing the whole effect, whose theory can be found for instance in reference [32]. In fact, one of the conclusion of reference [33] is that the proposed interaction mechanism has a very small effect on the magnetization, which would support the small optomagnetic field obtained with the use of that theory in this manuscript. Here it is important to remark again that this is just a very small contribution to the total IFE. However, we admit that when IFE can lead to equilibrium magnetization at times of pulse duration we cannot distinguish whether light-induced magnetization is coming from IFE or OSTT. We also discuss this possibility on the first paragraph on page eleven of the revised manuscript. layer. these currents can travel through it and, upon reflection, come back to the ferromagnetic material having a different orientation than the system magnetization. This is due to the fact that the system magnetization has been under the effect of the torque induced by IFE or OSTT.

5) As long as the
Therefore, this effect should be mention and analyzed to have a complete description of the magnetization dynamics.
 Response: We agree that a large spin current should be generated in the x-direction, travel through the capping layer, and come back to ferromagnet. If there is any helicity-dependent effect on this process, this spin current should lead to helicity-dependent torque in the x-direction.
However, we do not see any helicity dependence in M x dynamics. We include data of M x dynamics in Supplementary Note 4. Smaller remarks: 9) Along the reading of the manuscript one of the main experimental findings is repeated, namely, that using Pt layer significantly enhances OSTT against Au or Mg, even before the results have been shown, and with not citation to those. This leaves the sentences unjustified and out of context, and could be interpreted as an assumption or as a known fact. Therefore it should be reformulated in a different way.   We also discuss results of recent theories (Freimuth et al. arXiv 1608.02656v1 and Berritta et al. arXiv 1604.01188) that are relevant to OSTT in metals. This is the same as the response to reviewer 1's final comment.

Reviewers' comments:
Reviewer #1 (Remarks to the Author): I think that the authors did a good job in replying to the quite tough questions of the three referees, especially considering that the microscopic mechanisms mediating the transfer of angular momentum between light and magnetic materials are far by being fully understood. I am sure that the present manuscript will generate strong interest in the femtosecond magnetism community and stimulate further theoretical efforts to shed more light on the physics behind the optical spin transfer torque and inverse faraday effect.
To my opinion the revised version of the manuscript should thus now be published without any further revision.
Reviewer #2 (Remarks to the Author): I thank the authors for addressing and giving response to the comments raised by me and the other two referees, and I also acknowledge that in its new version the manuscript is considerably improved. However, I still cannot recommend its publication in Nature Communications. My major concern remains regarding the theoretical interpretation. Despite the authors explicitly specify that the focus of the work is experimental, they still assume that two different mechanisms for optical helicity-driven magnetization dynamics, namely inverse Faraday effect (IFE) and optical spin transfer torque (OSTT), provide orthogonal torques, and concentrate in measuring such perpendicular torques. Nonetheless, as far as I understand, this essential assumption is not yet clear and, as pointed out by the authors, it is possible that IFE can generate magnetization on the time scale of the pulse duration (1 ps) that could provide a torque in the same direction than that induced by OSTT. If that was the case, the interpretation of the results would be different, and would invalidate the conclusions drawn in the manuscript.
In addition I would like to mention that the paragraph in page 3 indicating the key differences between IFE and OSTT is not clear and does not help to understanding both mechanisms. More specifically, I do not understand the following statement: "while OSTT-induced magnetization is a transient quantity calculated from the transition probability and therefore proportional to the square of the density matrix". In my understanding, the density matrix includes the transition amplitudes and I do not see why it should be proportional to the square of the density matrix (when the density matrix is modified it carries information for both the IFE and the transient torque coming form OSTT).
Reviewer #3 (Remarks to the Author): The authors have properly addressed my comments and I recommend the paper for publication.
Below, we summarize the point-by-point responses to the second referee's comments. The corresponding corrections are incorporated in the revised manuscript. All changes are highlighted with blue color in the revised manuscript.

Point-by-point responses
Reviewers' comments: Reviewer #2 (Remarks to the Author): I thank the authors for addressing and giving response to the comments raised by me and the other two referees, and I also acknowledge that in its new version the manuscript is considerably improved. However, I still cannot recommend its publication in Nature Communications. My major concern remains regarding the theoretical interpretation. Despite the authors explicitly specify that the focus of the work is experimental, they still assume that two different mechanisms for optical helicity-driven magnetization dynamics, namely inverse Faraday effect (IFE) and optical spin transfer torque (OSTT), provide orthogonal torques, and concentrate in measuring such perpendicular torques. Nonetheless, as far as I understand, this essential assumption is not yet clear and, as pointed out by the authors, it is possible that IFE can generate magnetization on the time scale of the pulse duration (1 ps) that could provide a torque in the same direction than that induced by OSTT. If that was the case, the interpretation of the results would be different, and would invalidate the conclusions drawn in the manuscript.
 Response: For IFE-driven magnetization by short optical pulse, we must consider dynamic behavior. For example, the alignment of magnetization along the B-field will take a few nanoseconds for Co as magnetization undergoes a damped precessional motion to approach the equilibrium position. However, if the alignment of magnetization occurs during the pulse duration, we can treat IFE as a magnetization rather than a B-field. In our analysis, we assume that the timescale for IFE to induce magnetization is much longer than the pulse duration, and treat IFE as a transient B-field created by the optical pulse and solve the torque equation. We include this discussion on the paragraph that starts at the bottom on page three of the revised manuscript.
To consider the possible contribution of IFE to spin-transfer torque along the z-direction, we compare the initial M z with theoretical IFE-induced magnetization (m IFE ) in Pt assuming the timescale for m IFE in Pt is shorter than the pulse duration. At I 0 = 10 13 W m -2 , and ħω = 1.58 eV, We also included the statement of "Despite our interpretation, it is possible that IFE causes a similar effect on Pt as OSTT does when the timescale for IFE-induced magnetization is shorter than the pulse duration" in the discussion section that starts at the bottom of page thirteen of the revised manuscript.
2) In addition I would like to mention that the paragraph in page 3 indicating the key differences between IFE and OSTT is not clear and does not help to understanding both mechanisms. More specifically, I do not understand the following statement: "while OSTT-induced magnetization is a transient quantity calculated from the transition probability and therefore proportional to the square of the density matrix". In my understanding, the density matrix includes the transition amplitudes and I do not see why it should be proportional to the square of the density matrix (when the density matrix is modified it carries information for both the IFE and the transient torque coming form OSTT).