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Masato Kubota, [Seiichi Kato](https://orcid.org/0000-0002-6427-5463)

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[Influence of local structures on amorphous alumina exhibiting resistance random-access memory function](https://mdr.nims.go.jp/datasets/fc9ca41d-68d8-427a-8d93-520a348e65c6)

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Influence of local structures on amorphous alumina exhibiting resistance random-access memory functionViewOnlineExportCitationRESEARCH ARTICLE |  JULY 08 2024Influence of local structures on amorphous aluminaexhibiting resistance random-access memory function Masato Kubota   ; Seiichi KatoJ. Appl. Phys. 136, 025102 (2024)https://doi.org/10.1063/5.0208486 19 August 2024 01:28:32https://pubs.aip.org/aip/jap/article/136/2/025102/3302442/Influence-of-local-structures-on-amorphous-aluminahttps://pubs.aip.org/aip/jap/article/136/2/025102/3302442/Influence-of-local-structures-on-amorphous-alumina?pdfCoverIconEvent=citejavascript:;https://orcid.org/0009-0005-0896-903Xjavascript:;https://crossmark.crossref.org/dialog/?doi=10.1063/5.0208486&domain=pdf&date_stamp=2024-07-08https://doi.org/10.1063/5.0208486https://servedbyadbutler.com/redirect.spark?MID=176720&plid=2510968&setID=592934&channelID=0&CID=908656&banID=522064375&PID=0&textadID=0&tc=1&rnd=1824766886&scheduleID=2429165&adSize=1640x440&data_keys=%7B%22%22%3A%22%22%7D&matches=%5B%22inurl%3A%5C%2Fjap%22%5D&mt=1724030912813819&spr=1&referrer=http%3A%2F%2Fpubs.aip.org%2Faip%2Fjap%2Farticle-pdf%2Fdoi%2F10.1063%2F5.0208486%2F20033561%2F025102_1_5.0208486.pdf&hc=0aa23320d2cd665bf6997380c7e22398325a76f3&location=Influence of local structures on amorphousalumina exhibiting resistance random-accessmemory functionCite as: J. Appl. Phys. 136, 025102 (2024); doi: 10.1063/5.0208486View Online Export Citation CrossMarkSubmitted: 27 March 2024 · Accepted: 11 June 2024 ·Published Online: 8 July 2024Masato Kubota1,a) and Seiichi Kato2AFFILIATIONS1Japan Atomic Energy Agency (JAEA), 2-4 Shirakata Tokai-mura, Naka-gun, Ibaraki 319-1195, Japan2International Center for Materials Nanoarchitectonics (MANA), National Institute for Materials Science (NIMS), 1-1 Namiki,Tsukuba, Ibaraki 305-0044, Japana)Author to whom correspondence should be addressed: kubota.masato@jaea.go.jpABSTRACTAmorphous alumina resistance random-access memory is a promising candidate as a next-generation nonvolatile memory. It is intriguingthat the nonvolatile memory function emerges in only amorphous samples, unlike crystalline samples. We studied local structures of amor-phous alumina samples and Al2O3 polycrystalline using atomic pair distribution function measurements. We derived the Al–Al, O–O, andAl–O atomic distances for each sample. By comparing them, we revealed that the subtle difference in the local structure significantly influ-ences the performance of a nonvolatile memory function.© 2024 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license(https://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/5.0208486I. INTRODUCTIONAccording to the evolution of a modern information intensivesociety, the mass consumption of electric power is a pressingissue.1–3 One effective way to resolve this problem is to prevalentlyuse a next-generation high-performance nonvolatile memorysystem. Resistance random-access memory (ReRAM) with resis-tance switching operated by voltage is a promising candidate forthe next-generation nonvolatile memory. In the recent developmentof the ReRAM, many transition metal-based ReRAM materials,such as NiO and Ta2O5, are intensively investigated.4–9 However,there are several conclusively disadvantageous matters for the per-formance of the nonvolatile memory. For instance, a large leakagecurrent is a weak point in NiO, whereas a chemical reaction isaccompanied by minor reactions that generate by-products inTa2O5. Deteriorating factors, such as by-products and/or an oxygenion movement in a chemical reaction, reduce the endurance of thetransition metal-based ReRAM device. Furthermore, an additionalforming process is indispensable to generate a preliminary conduct-ing path, which is disadvantageous for the mass production ofmemory devices.We study amorphous alumina-based ReRAM (AlO-ReRAM)without transition metals, which cause the deterioration of the non-volatile memory function. We accomplished the top-class function-ality with high speed (5 ns) and low power consumption (28 μA).10In addition, many advantageous features exist, such as a large On/Off resistance ratio (� 10�9),11 no requirement of an additionalforming process, and the exclusion of rare and noxious elementsfor developing the AlO-ReRAM in the near future.12We propose the oxygen vacancy model for the electrical prop-erty in the AlO-ReRAM.10,12 In this model, it is expected that thecharge/discharge (On/Off) switching of the nonvolatile memoryresults from the changes of electron cloud overlap/isolationbetween oxygen vacancy clusters, where a conducting path can beformed. Consequently, injecting external electrons around anoxygen vacancy form the energy subband in a metallic state,whereas extracting electrons diminish the subband in an insulatingstate. This model has several fingerprints for verification. Wedetected a change in the electronic structure between high and lowresistance states and demonstrated that AlO-ReRAM shows nochemical reaction or by-products in the x-ray absorption spectra.12A subpeak for the charging of electrons into oxygen vacancies wasJournal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 136, 025102 (2024); doi: 10.1063/5.0208486 136, 025102-1© Author(s) 2024 19 August 2024 01:28:32https://doi.org/10.1063/5.0208486https://doi.org/10.1063/5.0208486https://pubs.aip.org/action/showCitFormats?type=show&doi=10.1063/5.0208486http://crossmark.crossref.org/dialog/?doi=10.1063/5.0208486&domain=pdf&date_stamp=2024-07-08https://orcid.org/0009-0005-0896-903Xmailto:kubota.masato@jaea.go.jphttps://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/https://doi.org/10.1063/5.0208486https://pubs.aip.org/aip/japobserved between the valence and conduction bands. It is also rec-ognized that the energy potential for the electron around theoxygen vacancy is stable, revealed by the first-principlescalculation.13We clarified that only amorphous alumina shows a nonvolatilememory function, unlike polycrystalline alumina.10,11 The first-principles calculation exhibits that the energy level of the subband(midgap) changes depending on the electronic states in amorphousalumina, whereas the energy level in polycrystalline alumina isrobust.13 The calculation also shows that the change in the elec-tronic states is accompanied by subtle structural relaxation due tothe change in the local structure in amorphous alumina. Based onthese theoretical suggestions, we expect that the local structure inthe Off state essentially affects the presence or absence of the non-volatile memory function and the superiority or inferiority of thefunction.Considering these things, to experimentally reveal the relation-ship between the local structure in the Off state and the feature ofthe nonvolatile memory function, we perform atomic pair distribu-tion function (PDF) measurements on two types of amorphoussamples with good/less switching performance of the nonvolatilememory function. For comparison, PDF measurement is also per-formed for Al2O3 polycrystalline, which exhibits no effect of non-volatile memory.II. EXPERIMENTTwo amorphous alumina samples were prepared using anodicoxidation. Alumina material (4N) was oxidized in 0.3 M oxalic acidat 40 V (sample A), and 0.3 M phosphoric acid at 130 V (sampleB), in the same sample preparation noted in Ref. 14. In current–voltage measurements, sample A with a thickness of approximately5 μm shows switching performance of nonvolatile memory byapplying an electric voltage of 60 V, whereas sample B exhibits noperformance, even by applying up to 70 V. We separated anodizedalumina from a raw aluminum material using the voltage reversaltechnique. The only anodized alumina is grinded into powder forthe PDF measurements. The Al2O3 polycrystalline powder (4 N) isalso measured as a reference sample.The high energy x-ray PDF measurements were performed onthe amorphous samples and the polycrystalline at the BL04B2beamline at the SPring-8 synchrotron radiation facility.15,16 Theincident x-ray energy was 61.36 keV with the energy resolution ΔE/E of approximately 5� 10�3. We meticulously addressed to reducetruncation effects and related errors by the measurements with thelow statistical noise and the extended Q-range, as noted in Ref. 17Notably, the dedicated diffractometer of BL04B2 yields high-qualitydata through step-scan measurements, where the background noiseis extremely small. The measuring time is so long that the magni-tude of the statistical noise is less than 0.2% of that of the signal forthe total structure factor in the whole Q-range. In addition, it isgenerally recognized that the scan Q-range up to 28 Å�1 (Qmax) inthis study is wide enough to analyze the accurate PDF data.The diffractometer features three Ge detectors (GL-0515R,Cambella, USA) accompanied with an automated liquid nitrogenfilling system and four CdTe detectors (X-123CdTe, Amptek,USA).15 The supersensitivity of a Ge detector is advantageous forthe measurements in the high-diffraction-angle region, because thediffraction intensity is weak in the high-diffraction-angle regiondue to the decay of Q-dependent atomic form factors. Conversely,the smallness of a CdTe detector is advantageous for covering alow-diffraction-angle region in a limited space. Additionally, thesemiconductor detectors provide high energy resolution to discrim-inate the fluorescence from the sample and the signal of the higherharmonic reflection of the monochromator crystal, which areessential for obtaining accurate PDF data. Furthermore, the limitedflight path with a double-slit system is employed for minimizingthe background scattering from the experimental surroundings.Consequently, our observed data are sufficiently reliable for theanalyses.The samples were transferred into quartz capillaries, with thediameter of 2 mm. The sample changer combined with a fully auto-mated alignment system is utilized to exchange the quartz capillar-ies containing the samples, which causes no difference of eachsample position for an x-ray beam without experimental ambiguity.We used the reliable software package of “BL04B2anaGUI” forPDF data extraction, which is widely utilized by many researchersat beamline BL04B2 in SPring-8.16,18–21 The raw data were cor-rected for polarization, absorption, and background, and the con-tribution of Compton scattering was subtracted.III. RESULTS AND DISCUSSIONFigure 1(a) compares the x-ray total structure factors of S(Q)Afor sample A and S(Q)B for sample B. The profiles in the amor-phous samples are broad and weak. As similar features in S(Q)Aand S(Q)B, two local maxima appear around Q ¼ 2:2Å�1and 2.9Å�1(first and second peaks). The center positions of the profilesfor sample A around Q � 4:4Å�1(third peak) and � 7:6Å�1(fourth peak) are located lower than those for sample B (dashedarrows), respectively, whereas the center position of the profilearound Q � 11:2Å�1(fifth peak) for sample A is similar to thatfor sample B. For sample B, a shoulder in the profile can beobserved around Q ¼ 6:7Å�1. Figure 1(b) shows the total structurefactor S(Q)Al2O3for Al2O3 polycrystalline, where sharp and strongprofiles corresponding to Bragg reflections are observed in contrastwith S(Q)A and S(Q)B.It is well-known that the first sharp diffraction peak (FSDP) isobserved in a total structure factor of typical glass-forming materi-als, such as SiO2, originating from successive small structuralcages reproduced by voids.22–24 However, the profiles aroundQ ¼ 2:2 Å�1 in S(Q)A and S(Q)B are extremely broad, meaningthat FSDPs are absent in both amorphous alumina samples. Thisresult reflects that the cages of oxide polyhedra reproduced byoxygen void and surrounding Al and O atoms (oxygen vacancycluster) are significantly disordered, and the correlation of theoxygen vacancy clusters remains short-ranged in both samples.We obtain corresponding real space information, such asatomic distances, using the reduced PDF G(r), which is defined asG(r) ¼ 2πðQmaxQminQ[S(Q)� 1]sin(Qr)dQ,where r is the distance in real space. Qmin and Qmax in this studyJournal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 136, 025102 (2024); doi: 10.1063/5.0208486 136, 025102-2© Author(s) 2024 19 August 2024 01:28:32https://pubs.aip.org/aip/japare 0.2 and 28, respectively. In the calculation of G(r), the Lorchwindow function is used.16,25Figure 2 shows the reduced PDFs G(r) for sample A, sampleB, and Al2O3 polycrystalline. For the polycrystalline, clear profilesare observed at 1.91(1) and 2.73(2) Å. These center positions of theprofiles correspond to the Al–O and O–O atomic distances, respec-tively, whereas the shoulder around 3.23(3) Å corresponds to theAl–Al atomic distance, based on the assigned profiles as referencedin Refs. 19 and 26 In a similar way, for sample A, the center posi-tion of the profile at 1.81(1) Å is assigned to the Al–O atomic dis-tance. From the local maximum and the center position of theprofile, it is revealed that the O–O atomic distance is around 2.73(4), and the Al–Al atomic distance is approximately 3.15(4) Å. Forsample B, the Al–O, O–O, and Al–Al atomic distances are 1.81(1),2.83(4), and 3.18(2) Å, respectively.In Al2O3 polycrystalline, the coordination number of oxygenaround aluminum is six. However, aluminum with the coordina-tion number of four and five also exist within the amorphoussamples, including six, by NMR measurements.14 We evaluated theAl–O coordination number through the observed data for theamorphous samples. The evaluated Al–O coordination number is5.0(2). This value is consistent with the coordination number ofapproximately 4.9 revealed by NMR in the amorphous samples,14which were prepared in the same way as this study.A typical glass-forming material, SiO2, forms successive smallcages with the network of regular SiO4 tetrahedra with sharedoxygen atoms at the corners, where the periodicity of the boundar-ies of the cages is clear. The coordination number of SiO2 polyhe-dra is four.20 However, it is well-known that the periodicity of theboundaries in the liquid-Al2O3 cluster is unclear due to the largecontribution of AlO5 polyhedra.20 Considering these things, it canbe safely said that the boundary of the oxygen vacancy clusters isdisturbed in the amorphous sample because the Al0O coordinationnumber is approximately five, as mentioned above. This result isconsistent with the suppression of the FSDP in the amorphoussamples [Fig. 1(a)].FIG. 1. (a) Comparison of the x-ray total structure factor S(Q) for samples A [S(Q)A] and B [S(Q)B]. The solid (dashed) arrows show the center positions of the profiles forsample A (sample B). The inset shows S(Q)A and S(Q)B in a whole Q range. (b) Total structure factor S(Q)Al2O3for Al2O3 polycrystalline.FIG. 2. Comparison of reduced PDFs G(r ) for samples A [G(r )A], B [G(r )B],and Al2O3 polycrystalline [G(r )Al2O3].Journal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 136, 025102 (2024); doi: 10.1063/5.0208486 136, 025102-3© Author(s) 2024 19 August 2024 01:28:32https://pubs.aip.org/aip/japFigure 3 compares the atomic distances for Al–Al, O–O, andAl–O in the three samples. First, we compare the features of theatomic distances between the polycrystalline and sample A. TheAl–Al atomic distance in sample A is 2.5% shorter than that inthe polycrystalline, and the Al–O atomic distance in the former is5.2% shorter than that in the latter. The O–O atomic distance ofsample A is similar to that of the polycrystalline. Oxygen is defi-cient in the amorphous samples, unlike the polycrystalline sample.In a simple viewpoint, the oxygen deficiency elongates the O–Oatomic distance. Since the oxygen in sample A is deficient, it isexpected that the O–O atomic distance in sample A is longer thanthat in the polycrystalline. However, the O–O atomic distances forboth samples are surprisingly similar in Fig. 3. This result effec-tively means that the distance of the O–O atomic distance withinan oxygen vacancy cluster in sample A further shortens, comparedwith that in the polycrystalline.Successively, to reveal the role of the atomic distances inamorphous alumina accompanied with the nonvolatile memoryfunction, we compare the features of the atomic distancesbetween samples A and B. Oxygen vacancies exist in the amor-phous samples. The amount of oxygen vacancies in sample B islarger than that in sample A, as noted in Ref. 14. The mostnoticeable point is that the O–O atomic distance in sample B isapproximately 3.7% elongated against the polycrystalline, in con-trast with that in sample A. The Al–Al and Al–O atomic dis-tance in sample B are shortened against the polycrystalline. Inmore detail, the Al–Al atomic distance in sample B is approxi-mately 1% longer than that in sample A. The Al–O atomic dis-tance in sample B is similar to that in sample A, indicating thatthe different amorphization has little influence on the Al–Oatomic distance.The relationship between the nonvolatile memory functionand the local structure is theoretically examined by focusing on thechange in the size of the oxygen vacancy cluster, which necessarilycauses the change in the atomic distances.13 Considering that anonvolatile memory function never emerges in a polycrystallinesample, appropriate requirements for the atomic distances in theOff state below a specific value are likely to produce the switchingperformance in an amorphous sample. An amorphous aluminasample is more suitable for a ReRAM material than a polycrystal-line sample because the energy levels and local structures in theformer sample are more sensitive to the change in the electronicstate than those in the latter sample.13By comparison, the Al–Al atomic distance in sample A is0.03 Å shorter than that in sample B, whereas the O–O atomic dis-tance in sample A is 0.1 Å shorter than that in sample B (Fig. 3).Sample A shows better switching performance of nonvolatilememory than sample B. Therefore, it is likely that short Al–Al andO–O atomic distances are advantageous for the emergence of theswitching performance. It could be that the good switching perfor-mance of the nonvolatile memory function occurs in sample Asince the short atomic distances can easily cause electron clouds tobe overlapped between oxygen vacancy clusters. This is consistentwith the theoretical suggestion of the local structure.13It is experimentally revealed that even the subtle difference inthe local structure in the Off state is crucial for the nonvolatilememory function of amorphous alumina, mentioned above.Combined with the first-principles calculation,13 it is suggestivethat AlO-ReRAM works based on the oxygen vacancy model,which shows possible high endurance. This suggestion is in con-trast with the fact that chemical reactions accompanied withby-products and/or an oxygen ion movement deteriorate transitionmetal-based ReRAM. In addition, high speed and low power con-sumption are realized, and no by-product exists inAlO-ReRAM.10–12 We believe that the knowledge obtained in thisstudy is vital for the development of high-performanceAlO-ReRAM.IV. CONCLUSIONSIn conclusion, we performed PDF measurements on amor-phous alumina samples and Al2O3 polycrystalline to reveal theirlocal structures. We obtained the Al–Al, O–O, and Al–O atomicdistances for each sample. By comparing these atomic distances, werevealed their conditions in the Off state for showing the nonvola-tile memory function. We clarified that even the subtle differencein the local structure in the Off state influences the performance ofthe nonvolatile memory function in amorphous alumina.ACKNOWLEDGMENTSWe gratefully thank Dr. H. Yamada, Dr. J. Tseng, Dr. S.Nigo, and Dr. K. Kodama for their technical support and fruitfuldiscussions. The x-ray experiment was performed under approvalof the SPring-8 Proposal Review Committee (Proposal Nos.2023A1275 and 2024A1413).FIG. 3. Comparison of the atomic distances of Al–Al, O–O, and Al–O forsamples A, B, and Al2O3 polycrystalline. The horizontal broken line is a guideto the eyes for the comparison.Journal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 136, 025102 (2024); doi: 10.1063/5.0208486 136, 025102-4© Author(s) 2024 19 August 2024 01:28:32https://pubs.aip.org/aip/japAUTHOR DECLARATIONSConflict of InterestThe authors have no conflicts to disclose.Author ContributionsMasato Kubota: Conceptualization (lead); Data curation (lead);Formal analysis (lead); Investigation (equal); Methodology (lead);Supervision (equal); Writing – original draft (lead); Writing –review & editing (equal). Seiichi Kato: Investigation (equal);Supervision (equal); Writing – original draft (supporting);Writing – review & editing (equal).DATA AVAILABILITYThe data that support the findings of this study are availablefrom the corresponding author upon reasonable request.REFERENCES1L. Belkhir and A. Elmeligi, J. Clean. Prod. 177, 448 (2018).2A. S. G. Andrae and T. Edler, Challenges 6, 117 (2015).3T. Bawdy, “Global warming: Data centres to consume three times as muchenergy in next decade, experts warn,” The Independent, 23 January 2016.4J. F. Gibbons and W. E. Beadle, Solid-State Electron. 7, 785 (1964).5I. G. Baek, M. S. Lee, S. Seo, M. J. Lee, D. H. Seo, D.-S. Suh, J. C. Park,S. O. Park, H. S. Kim, I. K. Yoo, U.-I. Chung, and J. T. Moon, in InternationalElectron Devices Meeting. IEDM Technical Digest (IEEE, 2004), p. 587.6C. Yoshida, K. Kinoshita, T. Yamasaki, and Y. Sugiyama, Appl. Phys. Lett. 93,042106 (2008).7Z. Wei, Y. Kanzawa, K. Arita, Y. Katoh, K. Kawai, S. Muraoka, S. Mitani, S. Fujii,K. Katayama, M. Iijima, T. Mikawa, T. Ninomiya, R. Miyanaga, Y. Kawashima,K. Tsuji, A. Himeno, T. Okada, R. Azuma, K. Shimakawa, H. Sugaya, T. Takagi,R. Yasuhara, K. Horiba, H. Kumigashira, and M. Oshima, in InternationalElectron Devices Meeting. IEDM Technical Digest (IEEE, 2008), p. 293.8Y. Sakotsubo, M. Terai, S. Kotsuji, T. Sakamoto, and M. Hada, Jpn. J. Appl.Phys. 49, 04DD19 (2010).9B. Y. Kim, W. G. Kim, H. J. Kim, K. H. Jung, W. Y. Park, B. M. Seo, M. S. Joo,K. J. Lee, K. Hong, and S. K. Park, Jpn. J. Appl. Phys. 52, 04CD05 (2013).10S. Nigo, M. Kubota, Y. Harada, T. Hirayama, S. Kato, H. Kitazawa, andG. Kido, J. Appl. Phys. 112, 033711 (2012).11S. Kato, S. Nigo, Y. Uno, T. Onisi, and G. Kido, J. Phys. Conf. Ser. 38, 148 (2006).12M. Kubota, S. Nigo, S. Kato, and K. Amemiya, AIP Adv. 9, 095050 (2019).13H. Momida, S. Nigo, G. Kido, and T. Ohno, Appl. Phys. Lett. 98, 042102 (2011).14T. Iijima, S. Kato, R. Ikeda, S. Ohki, and G. Kido, Chem. Lett. 34, 1286(2005).15H. Yamada, K. Nakada, M. Takemoto, and K. Ohara, J. Synchrotron Radiat.29, 549 (2022).16K. Ohara, S. Tominaka, H. Yamada, M. Takahashi, H. Yamaguchi, F. Utsuno,T. Umeki, A. Yao, K. Nakada, M. Takemoto, S. Hiroi, N. Tsuji, and T. Wakihara,J. Synchrotron Radiat. 25, 1627 (2018).17L. B. Skinner, S. C. Huang, D. Schlesinger, L. G. M. Pettersson, A. Nilsson,and C. J. Benmore, J. Chem. Phys. 138, 074506 (2013).18L. C. Gallington, S. K. Wilke, S. Kohara, and C. J. Benmore, Quantum BeamSci. 7, 20 (2023).19K. Ohara, Y. Onodera, M. Murakami, and S. Kohara, J. Phys.: Condens.Matter 33, 383001 (2021).20S. Kohara, J. Akola, L. Patrikeev, M. Ropo, K. Ohara, M. Itou, A. Fujiwara,J. Yahiro, J. T. Okada, T. Ishikawa, A. Mizuno, A. Masuno, Y. Watanabe, andT. Usuki, Nat. Commun. 5, 5892 (2014).21K. Kojima, N. Katayama, Y. Matsuda, M. Shiomi, R. Ishii, and H. Sawa, Phys.Rev. B 107, L020101 (2023).22D. L. Price, S. C. Moss, R. Reijers, M. L. Saboungi, and S. Susman, J. Phys. C:Solid State Phys. 21, L1069 (1988).23T. Uchino, J. D. Harrop, S. N. Taraskin, and S. R. Elliott, Phys. Rev. B 71,014202 (2005).24P. H. Gaskell and D. J. Wallis, Phys. Rev. Lett. 76, 66 (1996).25E. Lorch, J. Phys. C: Solid State Phys. 2, 229 (1969).26L. B. Skinner, A. C. Barnes, P. S. Salmon, L. Hennet, H. E. Fischer,C. J. Benmore, S. Kohara, J. K. R. Weber, A. Bytchkov, M. C. Wilding,J. B. Parise, T. O. Farmer, I. Pozdnyakova, S. K. Tumber, and K. Ohara, Phys.Rev. B 87, 024201 (2013).Journal ofApplied PhysicsARTICLE pubs.aip.org/aip/japJ. Appl. Phys. 136, 025102 (2024); doi: 10.1063/5.0208486 136, 025102-5© Author(s) 2024 19 August 2024 01:28:32https://doi.org/10.1016/j.jclepro.2017.12.239https://doi.org/10.3390/challe6010117https://doi.org/10.1016/0038-1101(64)90131-5https://doi.org/10.1016/0038-1101(64)90131-5https://doi.org/10.1063/1.2966141https://doi.org/10.1143/JJAP.49.04DD19https://doi.org/10.1143/JJAP.49.04DD19https://doi.org/10.7567/JJAP.52.04CD05https://doi.org/10.1063/1.4745048https://doi.org/10.1088/1742-6596/38/1/036https://doi.org/10.1063/1.5086212https://doi.org/10.1063/1.3548549https://doi.org/10.1246/cl.2005.1286https://doi.org/10.1107/S1600577521013527https://doi.org/10.1107/S1600577518011232https://doi.org/10.1063/1.4790861https://doi.org/10.3390/qubs7020020https://doi.org/10.3390/qubs7020020https://doi.org/10.1088/1361-648X/ac0193https://doi.org/10.1088/1361-648X/ac0193https://doi.org/10.1038/ncomms6892https://doi.org/10.1103/PhysRevB.107.L020101https://doi.org/10.1103/PhysRevB.107.L020101https://doi.org/10.1088/0022-3719/21/32/001https://doi.org/10.1088/0022-3719/21/32/001https://doi.org/10.1103/PhysRevB.71.014202https://doi.org/10.1103/PhysRevLett.76.66https://doi.org/10.1088/0022-3719/2/2/305https://doi.org/10.1103/PhysRevB.87.024201https://doi.org/10.1103/PhysRevB.87.024201https://pubs.aip.org/aip/jap