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## Creator

F. Sun, S. Mishra, P. H. McGuinness, Z. H. Filipiak, I. Markovic, D. A. Sokolov, [N. Kikugawa](https://orcid.org/0000-0003-3975-4478), J. W. Orenstein, S. A. Hartnoll, A. P. Mackenzie, V. Sunko

## Rights

This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in F. Sun et al., Rev. Sci. Instrum. 95, 047102 (2024) and may be found at https://doi.org/10.1063/5.0195810.[In Copyright](http://rightsstatements.org/vocab/InC/1.0/)

## Other metadata

[Response to the Comment on “A spatially resolved optical method to measure thermal diffusivity"](https://mdr.nims.go.jp/datasets/1c72aa59-9f7e-432e-93a7-b103b998befc)

## Fulltext

Response to “Comment on ‘A spatially resolved optical method to measure thermal diffusivity’” [Rev. Sci. Instrum. 95, 047101 (2024)]ViewOnlineExportCitationREPLY |  APRIL 16 2024Response to “Comment on ‘A spatially resolved opticalmethod to measure thermal diffusivity’” [Rev. Sci. Instrum.95, 047101 (2024)] F. Sun  ; S. Mishra  ; P. H. McGuinness  ; Z. H. Filipiak  ; I. Marković  ; D. A. Sokolov; N. Kikugawa  ;J. W. Orenstein  ; S. A. Hartnoll  ; A. P. Mackenzie  ; V. Sunko  Rev. Sci. Instrum. 95, 047102 (2024)https://doi.org/10.1063/5.0195810 16 April 2024 21:39:09https://pubs.aip.org/aip/rsi/article/95/4/047102/3283014/Response-to-Comment-on-A-spatially-resolvedhttps://pubs.aip.org/aip/rsi/article/95/4/047102/3283014/Response-to-Comment-on-A-spatially-resolved?pdfCoverIconEvent=citejavascript:;https://orcid.org/0000-0001-7940-9607javascript:;https://orcid.org/0000-0002-5948-8835javascript:;https://orcid.org/0000-0001-5938-6452javascript:;https://orcid.org/0000-0003-3497-5837javascript:;https://orcid.org/0000-0002-1631-9556javascript:;javascript:;https://orcid.org/0000-0003-3975-4478javascript:;https://orcid.org/0000-0003-3741-6707javascript:;https://orcid.org/0000-0002-9952-9566javascript:;https://orcid.org/0000-0001-8000-4949javascript:;https://orcid.org/0000-0003-2724-3523https://crossmark.crossref.org/dialog/?doi=10.1063/5.0195810&domain=pdf&date_stamp=2024-04-16https://doi.org/10.1063/5.0195810https://servedbyadbutler.com/redirect.spark?MID=176720&plid=2372062&setID=592934&channelID=0&CID=872265&banID=521836443&PID=0&textadID=0&tc=1&scheduleID=2290747&adSize=1640x440&data_keys=%7B%22%22%3A%22%22%7D&matches=%5B%22inurl%3A%5C%2Frsi%22%5D&mt=1713303549790592&spr=1&referrer=http%3A%2F%2Fpubs.aip.org%2Faip%2Frsi%2Farticle-pdf%2Fdoi%2F10.1063%2F5.0195810%2F19884984%2F047102_1_5.0195810.pdf&hc=c6cfafc14f712603b6bb7f3bc326aa3156b428e6&location=Review ofScientific InstrumentsRESPONSE pubs.aip.org/aip/rsiResponse to “Comment on ‘A spatially resolvedoptical method to measure thermal diffusivity’”[Rev. Sci. Instrum. 95, 047101 (2024)]Cite as: Rev. Sci. Instrum. 95, 047102 (2024); doi: 10.1063/5.0195810Submitted: 4 January 2024 • Accepted: 3 March 2024 •Published Online: 16 April 2024F. Sun,1 S. Mishra,1 P. H. McGuinness,1 Z. H. Filipiak,1 I. Marković,1 D. A. Sokolov,1 N. Kikugawa,2J. W. Orenstein,3 ,4 S. A. Hartnoll,5 A. P. Mackenzie,1 ,6 and V. Sunko1 ,3,a)AFFILIATIONS1 Max Planck Institute for Chemical Physics of Solids, 01187 Dresden, Germany2National Institute for Materials Science, Ibaraki 305-0003, Japan3Department of Physics, University of California, Berkeley, California 94720, USA4Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA5Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, United Kingdom6School of Physics and Astronomy, University of St Andrews, St Andrews KY16 9SS, United Kingdoma)Author to whom correspondence should be addressed: vsunko@berkeley.eduhttps://doi.org/10.1063/5.0195810We thank Salazar et al. for pointing out the error in Eq. (6) ofour manuscript1 and for offering the correct expression. While fullyacknowledging the importance of their correction,2 we emphasizethat Eq. (6) was not used for any of our data interpretation or analy-sis, which therefore remains valid. We address those points in moredetail below.(1) In Eqs. (6) and (A23) of our paper, we repeat the claim ofRef. 13 of our original paper3 that the diffusivity D along anarbitrary direction in an anisotropic material is given by1Dθ=cos2 θDx+sin2 θDy,where Dx and Dy are the values of diffusivity along two prin-cipal axis directions and θ is the angle between the measureddirection and the x axis. The difference between the claim ofRef. 3 and the older literature was brought to our attentionin the review process, but we made an error while evaluatingthe two expressions, leading us to the incorrect conclusionthat Eq. (6) is valid. As Salazar et al. convincingly argue intheir comment,2 the correct expression for Dθ, defined as theratio of thermal conductivity and heat capacity, isDθ = Dx cos2 θ +Dy sin2 θ.(2) We emphasize that all the data analysis and ensuing con-clusions of our work1 remain valid since Eq. (6) was usedonly for illustrative purposes. The data are analyzed throughthe calculated relationships between the measured phase dif-ference ϕ and the principal axis diffusivities Dx and Dy[Eqs. (A14) and (A20) for the overlapped and separatedconfiguration, respectively]. Those relationships are not con-troversial: indeed, Eq. (A20) is reproduced in the commentby Salazar et al. [Eqs. (10) and (11) of Ref. 2 are equiva-lent to our Eq. (A20) in Ref. 1]. The quantities of interest inour measurements were the diffusivities along the two prin-cipal directions, and we never discussed diffusivity measuredalong an arbitrary direction. This approach is most promi-nent in Fig. 3(d): we plot the directly measured difference inphase lag between two domains as a function of orientationθ, without relying on any calculation for Dθ. We also notethat, far from being a paper “devoted to the measurement ofthe in-plane thermal diffusivity of anisotropic materials,” thelarge majority of our paper is about other topics since thecase of anisotropic diffusivity appeared to be covered in theearlier literature. Indeed, as discussed in the introduction toour paper, the advances it reports are systematic methods toretain instrument focus over wide ranges of temperature anda technique involving overlapping pump and probe beams,Rev. Sci. Instrum. 95, 047102 (2024); doi: 10.1063/5.0195810 95, 047102-1Published under an exclusive license by AIP Publishing 16 April 2024 21:39:09https://pubs.aip.org/aip/rsihttps://doi.org/10.1063/5.0195810https://pubs.aip.org/action/showCitFormats?type=show&doi=10.1063/5.0195810https://crossmark.crossref.org/dialog/?doi=10.1063/5.0195810&domain=pdf&date_stamp=2024-April-16https://doi.org/10.1063/5.0195810https://orcid.org/0000-0001-7940-9607https://orcid.org/0000-0002-5948-8835https://orcid.org/0000-0001-5938-6452https://orcid.org/0000-0003-3497-5837https://orcid.org/0000-0002-1631-9556https://orcid.org/0000-0003-3975-4478https://orcid.org/0000-0003-3741-6707https://orcid.org/0000-0002-9952-9566https://orcid.org/0000-0001-8000-4949https://orcid.org/0000-0003-2724-3523mailto:vsunko@berkeley.eduhttps://doi.org/10.1063/5.0195810Review ofScientific InstrumentsRESPONSE pubs.aip.org/aip/rsiwhich enhances spatial resolution over techniques relying onseparated pump and probe beams.(3) Salazar et al. refer to “two mistakes” made in our work:Eq. (6) and the claim that the diffusivity along an arbitrarydirection can be deduced from the measured phase lag. How-ever, that is actually the same mistake. Our incorrect Eq. (6)implies that the phase difference ϕ measured at an angle θ isproportional to the diffusivity along the direction defined byθ, whereas the correct one pointed out by Salazar et al. showsthat this is not the case away from the principal axes. How-ever, we never utilize that relationship in our analysis (point2 above).To conclude, we regret that we propagated a misunderstand-ing in the field, and we are grateful to Salazar et al. for clarify-ing it. We hope that our work, and this exchange, helps bringthis technique into new experimental regimes, studying smallinhomogeneous samples, both isotropic and anisotropic, over abroad range of temperatures.AUTHOR DECLARATIONSConflict of InterestThe authors have no conflicts to disclose.REFERENCES1F. Sun, S. Mishra, P. H. McGuinness, Z. H. Filipiak, I. Marković, D. A. Sokolov,N. Kikugawa, J. W. Orenstein, S. A. Hartnoll, A. P. Mackenzie, and V. Sunko, Rev.Sci. Instrum. 94, 043003 (2023).2A. Salazar, A. Mendioroz, A. Bedoya, and E. Marín, Rev. Sci. Instrum. 95, 047101(2024).3J. Zhang, E. M. Levenson-Falk, B. J. Ramshaw, D. A. Bonn, R. Liang, W. N. Hardy,S. A. Hartnoll, and A. Kapitulnik, Proc. Natl. Acad. Sci. U. S. A. 114, 5378 (2017).Rev. Sci. Instrum. 95, 047102 (2024); doi: 10.1063/5.0195810 95, 047102-2Published under an exclusive license by AIP Publishing 16 April 2024 21:39:09https://pubs.aip.org/aip/rsihttps://doi.org/10.1063/5.0098800https://doi.org/10.1063/5.0098800https://doi.org/10.1063/5.0190267https://doi.org/10.1073/pnas.1703416114