SciPost Submission Page
Dynamical Spin-Orbit-Based Spin Transistor
by F. N. Gürsoy, P. Reck, C. Gorini, K. Richter, I. Adagideli
This is not the latest submitted version.
|Authors (as Contributors):||Inanc Adagideli · Fahriye Nur Gursoy|
|Arxiv Link:||https://arxiv.org/abs/2109.10991v1 (pdf)|
|Date submitted:||2021-10-06 21:17|
|Submitted by:||Gursoy, Fahriye Nur|
|Submitted to:||SciPost Physics|
Spin-orbit interaction (SOI) has been a key tool to steer and manipulate spin-dependent transport properties in two-dimensional electron gases. Here we demonstrate how spin currents can be created and efficiently read out in nano- or mesoscale conductors with time-dependent and spatially inhomogenous Rashba SOI. Invoking an underlying non-Abelian SU(2) gauge structure we show how time-periodic spin-orbit fields give rise to spin-motive forces and enable the generation of pure spin currents of the order of several hundred nano-Amperes. In a complementary way, by combining gauge transformations with "hidden" Onsager relations, we exploit spatially inhomogenous Rashba SOI to convert spin currents (back) into charge currents. In combining both concepts, we devise a spin transistor that integrates efficient spin current generation, by employing dynamical SOI, with its experimentally feasible detection via conversion into charge signals. We derive general expressions for the respective spin- and charge conductances, covering large parameter regimes of SOI strength and driving frequencies, far beyond usual adiabatic approaches such as the frozen scattering matrix approximation. We check our analytical expressions and approximations with full numerical spin-dependent transport simulations and demonstrate that the predictions hold true in a wide range from low to high driving frequencies.
Submission & Refereeing History
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- Report 3 submitted on 2022-04-13 07:10 by Anonymous
- Report 2 submitted on 2022-04-07 23:34 by Anonymous
- Report 1 submitted on 2022-02-08 20:32 by Anonymous
Reports on this Submission
Anonymous Report 3 on 2022-4-13 (Invited Report)
1-Comprehensive and unified description of non-Abelian gauge-field approach to calculating spin-dependent transport.
2-Striking comparison of analytical predictions with numerical Floquet simulations.
3-The authors discuss an interesting device-application proposal.
1-Acknowledgement of previous work on spin currents arising from time-varying and spatially inhomogeneous spin-orbit coupling is incomplete.
2-Some crucial aspects of the new formalism are discussed only cursorily.
The authors present an interesting extension of the formalism that views linear-in-momentum spin-orbit coupling as a spin-dependent non-Abelian gauge field. They derive analytical results for spin currents arising from time-varying and/or spatially inhomogeneous spin-orbit-coupling strengths. Numerical results based on the powerful Floquet scattering theory support the applicability of the new theory well beyond the adiabatic limit that has been the focus of previous spin-dependent mesoscopic-transport theories.
The present work constitutes a follow-up on earlier results by some of the authors reported in Ref. . As such, one would expect some more detail in the present manuscript regarding certain basic derivations that had to be omitted in the short letter publication . In particular, Sec. 3.1.2 feels short and at times cryptic, leaving especially unclear the type and level of approximations involved in the derivations. I would suggest the extend the discussion to include more detailes and rigorous statements about validity of the approximations employed.
The new approach utilized by the authors is more generally applicable than previously used scattering-theory formalisms. While it is useful to demonstrate clearly the deviation between the two theories by direct comparison for particular parameters as is done in Fig. 5, it would be even more useful and interesting to the reader to understand better the appropriate limit in which the adiabatic result is contained within the more general approach. The discussion of Sec. 3.2.2 is again quite short in this regard, merely stating the almost obvious fact that corrections are of order Omega. But what is the scale to compare Omega with? The authors may want to clarify this.
Finally, I think it would be justified to acknowledge a few key earlier contributions to the understanding of spin-orbit coupling acting like a gauge field, and its time dependence generating spin-dependent electric fields. In addition to current Ref. , the paper by Governale, Taddei and Fazio [PRB 68, 155324 (2003)] was seminal. Also, Avishai, Cohen and Nagaosa [PRL 104, 196601 (2010)] made an important contribution. Potentially there are more relevant citations, especially from the spin-pumping literature, that would be appropriately included in the paper's reference list. In addition to merely giving the references, it would also be useful to state more explicitly (maybe in the conclusions?) which qualitatively new effects and additional transport regimes the current manuscript's formalism allows to explore compared to the earlier types of scattering formalism. Furthermore, clarifying briefly also in the part discussing the "gauging away" of constant spin-orbit coupling [paragraph below Eq. (5)] which types of transport effects still occur at order k_so^2 (weak antilocalization!?) would be helpful to better embed the current approach to prior ones.
See my report.
Anonymous Report 2 on 2022-4-7 (Invited Report)
The paper deals with important topics in Spintronics, that is all electrical generation of spin currents and the design of a robust and experimentally realisable spin transistor.
1) The paper is well written and sufficiently self-contained that an expert in the field can follow all derivations without the need to peruse other material.
2) The physics at play is clearly explained.
3) The results from the analytical theoretical treatments are validated by a full numerical approach. The results are plausible and in my opinion correct.
1. The main weakness of this manuscript is that it is not easy to distinguish which ideas or results are novel.
2. The paper proposes a design for a spin transistor. However, no result is shown for the transistor operation, that is the on/off switching of the current.
The authors present a detailed study of a mesoscopic spin transistor realised in a two-dimensional electron gas exploiting the tunability of the Rashba spin-orbit interaction (SOI). The device functionality relies on the generation of a spin current by a time-dependent Rashba SOI and by its transformation into a charge current in a region with spatially inhomogeneous SOI in a three-terminal geometry. The authors exploit the fact that the SOI can be written as a non-Abelian gauge field to derive analytical expressions for the charge and spin currents. These expressions are then compared with a full numerical calculation.
Below, I outline my main comments on the paper:
1. In my opinion, in this paper it is difficult for the reader to distinguish which results are new and what is already known in the literature. For example, the idea of exploiting a time-dependent SOI to generate a spin current was presented in PRB 68, 154324 (2003) and PRB 68, 233307 (2003). In the first of these two papers the spin-current generation is also described in terms of a spin-dependent electric field. The fact that there are previous works in the literature, is not at all clear in Sections 4 and 2.2 . Similarly, the idea of exploiting an inhomogeneous SOI to transform spin currents into charge currents has already been presented in Ref.  and it would be useful for the reader to have this clearly stated at the beginning of Section 5.
2. In Section 5, the authors describe a system that combines the generation of a time-dependent spin current and its detection.
2.(a) It is not clear to me why the authors consider a Aharonov-Bohm ring geometry in the detection part of the setup. This would be understandable if they were using a magnetic field to break time reversal symmetry and achieve spin detection. Without magnetic field the ring seems only an unnecessary complication.
2(b) Since the author emphasise that the device is a "dynamical spin-orbit based spin transistor", they need to show that the system indeed works as a transistor. In particular, they state "controlling the symmetry properties of the system, we can obtain on/off states of this dynamical spin transistor." The authors need to provide a figure where this on/off switching is shown as a function of some external parameter (perhaps, a tunnel coupling to lead 2).
3) In the captions of Figs 3,4, 5 and 7 . The author should state that the current is plotted as a function of the Fermi Energy.
1) Add citations and if relevant modify the text to make it easier to distinguish new results from results already known, as detailed in point 1 of the report.
2) Introduce a figure in Section 5 , showing the on/off switching of the device.
3) Improve the figure captions (see, point 3 in the report).
Anonymous Report 1 on 2022-2-8 (Invited Report)
The manuscript meets "4. Provide a novel and synergetic link between different research areas." acceptance criterion. See also my Report.
See my Report.
The manuscript combines two decades of studies in spintronics, focused on 2D electron systems with the Rashba spin-orbit coupling, with pumping by time-dependent potentials (in the manuscript case, this is time-dependent Rashba spin-orbit coupling controlled by AC gate voltage) to propose interesting new type of spin transistor. This is interesting result, and in my opinion manuscript satifies "4. Provide a novel and synergetic link between different research areas." as the criterion of acceptance in SciPost Physics.
However, I see the need to improve current presentation as follows:
1. Spin current generation by time-dependent Rashba coupling has already been discussed long ago in cited Ref. 8. Thus, a paragraph is needed to describe how the present manuscript offers something new in terms of physics and theoretical treatment. For example, the authors usage of Floquet scattering matrix for this problem is certainly far more sophisticated than what was done in Ref. 8, and this methodology is also more general than adiabatic scattering matrix approach (also employed in the manuscript, with limitations clearly explained) which is the dominant approach for other types of spin pumping problems in spintronics,
2. Equation 34 is written without any citation, which gives impression that the authors have derived it in the present manuscript. However, this seems to be just usage of Equations from Sec. 3.3.1 of Moskalets' book, cited as Ref. 23, so the authors should add appropriate citations here and in Appendices.
3. The authors evalute Eq. 34 using just one harmonic. However, very recent studies:
A. High-harmonic generation in spin-orbit coupled systems
Phys. Rev. B 102, 081121(R) – Published 26 August 2020
B. High-harmonic generation in spin and charge current pumping at ferromagnetic or antiferromagnetic resonance in the presence of spin-orbit coupling
point out that time-dependent Rashba systems invariably generate higher than one harmonic in pumped spin and/or charge currents. Thus, this is my MAIN suggestion which could CONNECT paper with this contemporry direction -> try to compute higher harmonics in pumped current. Also, as discussed in B. above, once the device is left-right asymmetric [see also Fig. 4 in J. Phys.: Mater. 2, 025004 (2019) or Phys. Rev. B 72, 245339 (2005) for detailed discussion about symmetry breaking requirements], one should observe DC charge current without any second "2DEG converted" in Fig. 1. I am wondering if the authors have checked that by simply computing Eq. 34 for charge current.
4. The definition of adiabatic limit, "If the frequency is much smaller than the inverse of the time of
fight, ..., the scattering process is considered to be in the adiabatic limit.", does not take into account the relationship between frequency and Fermi energy. That is, one can see immediately from Eq. 34 that integration is not needed, which is adiabatic, if frequency is much smaller than the Fermi energy. Some comment on the connection between these definitions would be useful.
5. In Fig. 9 it will look puzzling to experts in general theory of Floquet systems that the results are NOT very sensitive to the driving frequency (left versus right panels). Usually it is the combination of both the driving frequency and amplitude which sets the regime.
6. The authors repeatedly use term "spin-motive force", including in abstract and conclusion:
"For the time-dependent Rashba SOI, the U(1) elds correspond to spin-dependent voltages
with opposite associated electrical elds for spin-up and -down electrons, respectively. Then
the total spin-dependent voltage becomes Vup-Vdown to linear order in the Rashba SOI strehgth.
Thus the action of the time-dependent Rashba SOI can be considered as a spin-motive force,
that enables to generate a pure AC spin current in the absence of an applied bias voltage."
However, this term is widely accepted to denote CHARGE pumping by dynamical noncollinear and noncoplanar magnetic textures (such as domain walls), see, e.g., theory of:
Equation-of-motion approach of spin-motive force
Journal of Applied Physics 109, 07C735 (2011); https://doi.org/10.1063/1.3565398
and references therein, or experiments such as:
Time-Domain Observation of the Spin-motive Force in Permalloy Nanowires
Phys. Rev. Lett. 108, 147202 – Published 5 April 2012
So, to avoid confusion, they should change this terminology.
7. Current manuscript has many typos: under Eq. 52 "prediction demostrating"; "Figure 7: Dyanmical spin transistor", ... Please run spell checker.
See my Report.