- Letter
- Open Access
Resonant inelastic x-ray scattering from electronic excitations in nanolayers
Phys. Rev. B 108, L041406 – Published 27 July, 2023
DOI: https://doi.org/10.1103/PhysRevB.108.L041406
Abstract
We present Ru -edge resonant inelastic x-ray scattering (RIXS) measurements of spin-orbit and excitations in exfoliated nanolayers of the Kitaev spin-liquid candidate . Whereas the spin-orbit excitations are independent of thickness, we observe a pronounced redshift and broadening of the excitations in layers with thicknesses below nm. Aided by model calculations, we attribute these effects to distortions of the octahedra near the surface. Our study paves the way towards RIXS investigations of electronic excitations in various other two-dimensional materials and heterostructures.
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References (54)
- K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 666 (2004).
- K. S. Novoselov, D. Jiang, F. Schedin, T. J. Booth, V. V. Khotkevich, S. V. Morozov, and A. K. Geim, Proc. Natl. Acad. Sci. USA 102, 10451 (2005).
- Y. Liu, N. O. Weiss, X. Duan, H.-C. Cheng, Y. Huang, and X. Duan, Nat. Rev. Mater. 1, 16042 (2016).
- K. S. Novoselov, A. Mishchenko, A. Carvalho, and A. H. C. Neto, Science 353, aac9439 (2016).
- S. Manzeli, D. Ovchinnikov, D. Pasquier, O. V. Yazyev, and A. Kis, Nat. Rev. Mater. 2, 17033 (2017).
- Y. Cao, V. Fatemi, S. Fang, K. Watanabe, T. Taniguchi, E. Kaxiras, and P. Jarillo-Herrero, Nature (London) 556, 43 (2018).
- A. Kotani and S. Shin, Rev. Mod. Phys. 73, 203 (2001).
- L. J. P. Ament, M. van Veenendaal, T. P. Devereaux, J. P. Hill, and J. van den Brink, Rev. Mod. Phys. 83, 705 (2011).
- M. Minola, D. Di Castro, L. Braicovich, N. B. Brookes, D. Innocenti, M. Moretti Sala, A. Tebano, G. Balestrino, and G. Ghiringhelli, Phys. Rev. B 85, 235138 (2012).
- H. Suzuki, H. Gretarsson, H. Ishikawa, K. Ueda, Z. Yang, H. Liu, H. Kim, D. Kukusta, A. Yaresko, M. Minola, J. A. Sears, S. Francoual, H.-C. Wille, J. Nuss, H. Takagi, B. J. Kim, G. Khaliullin, H. Yavaş, and B. Keimer, Nat. Mater. 18, 563 (2019).
- Y. Lu, D. Betto, K. Fürsich, H. Suzuki, H.-H. Kim, G. Cristiani, G. Logvenov, N. B. Brookes, E. Benckiser, M. W. Haverkort, G. Khaliullin, M. Le Tacon, M. Minola, and B. Keimer, Phys. Rev. X 8, 031014 (2018).
- J. Pelliciari, S. Lee, K. Gilmore, J. Li, Y. Gu, A. Barbour, I. Jarrige, C. H. Ahn, F. J. Walker, and V. Bisogni, Nat. Mater. 20, 188 (2021).
- A. Kitaev, Ann. Phys. 321, 2 (2006).
- L. Balents, Nature (London) 464, 199 (2010).
- G. Jackeli and G. Khaliullin, Phys. Rev. Lett. 102, 017205 (2009).
- L. J. Sandilands, Y. Tian, K. W. Plumb, Y.-J. Kim, and K. S. Burch, Phys. Rev. Lett. 114, 147201 (2015).
- A. Banerjee, C. A. Bridges, J.-Q. Yan, A. A. Aczel, L. Li, M. B. Stone, G. E. Granroth, M. D. Lumsden, Y. Yiu, J. Knolle, S. Bhattacharjee, D. L. Kovrizhin, R. Moessner, D. A. Tennant, D. G. Mandrus, and S. E. Nagler, Nat. Mater. 15, 733 (2016).
- I. A. Leahy, C. A. Pocs, P. E. Siegfried, D. Graf, S.-H. Do, K.-Y. Choi, B. Normand, and M. Lee, Phys. Rev. Lett. 118, 187203 (2017).
- Y. Kasahara, T. Ohnishi, Y. Mizukami, O. Tanaka, S. Ma, K. Sugii, N. Kurita, H. Tanaka, J. Nasu, Y. Motome, T. Shibauchi, and Y. Matsuda, Nature (London) 559, 227 (2018).
- T. Yokoi, S. Ma, Y. Kasahara, S. Kasahara, T. Shibauchi, N. Kurita, H. Tanaka, J. Nasu, Y. Motome, C. Hickey, S. Trebst, and Y. Matsuda, Science 373, 568 (2021).
- P. Czajka, T. Gao, M. Hirschberger, P. Lampen-Kelley, A. Banerjee, J. Yan, D. G. Mandrus, S. E. Nagler, and N. P. Ong, Nat. Phys. 17, 915 (2021).
- B. Zhou, Y. Wang, G. B. Osterhoudt, P. Lampen-Kelley, D. Mandrus, R. He, K. S. Burch, and E. A. Henriksen, J. Phys. Chem. Solids 128, 291 (2019).
- L. Du, Y. Huang, Y. Wang, Q. Wang, R. Yang, J. Tang, M. Liao, D. Shi, Y. Shi, X. Zhou, Q. Zhang, and G. Zhang, 2D Mater. 6, 015014 (2018).
- D. Lin, K. Ran, H. Zheng, J. Xu, L. Gao, J. Wen, S.-L. Yu, J.-X. Li, and X. Xi, Phys. Rev. B 101, 045419 (2020).
- S. Mashhadi, D. Weber, L. M. Schoop, A. Schulz, B. V. Lotsch, M. Burghard, and K. Kern, Nano Lett. 18, 3203 (2018).
- J.-H. Lee, Y. Choi, S.-H. Do, B. H. Kim, M.-J. Seong, and K.-Y. Choi, npj Quantum Mater. 6, 43 (2021).
- S. Biswas, Y. Li, S. M. Winter, J. Knolle, and R. Valentí, Phys. Rev. Lett. 123, 237201 (2019).
- B. Zhou, J. Balgley, P. Lampen-Kelley, J.-Q. Yan, D. G. Mandrus, and E. A. Henriksen, Phys. Rev. B 100, 165426 (2019).
- S. Mashhadi, Y. Kim, J. Kim, D. Weber, T. Taniguchi, K. Watanabe, N. Park, B. Lotsch, J. H. Smet, M. Burghard, and K. Kern, Nano Lett. 19, 4659 (2019).
- Y. Wang, J. Balgley, E. Gerber, M. Gray, N. Kumar, X. Lu, J.-Q. Yan, A. Fereidouni, R. Basnet, S. J. Yun, D. Suri, H. Kitadai, T. Taniguchi, K. Watanabe, X. Ling, J. Moodera, Y. H. Lee, H. O. H. Churchill, J. Hu, L. Yang et al., Nano Lett. 20, 8446 (2020).
- C. Balz, P. Lampen-Kelley, A. Banerjee, J. Yan, Z. Lu, X. Hu, S. M. Yadav, Y. Takano, Y. Liu, D. A. Tennant, M. D. Lumsden, D. Mandrus, and S. E. Nagler, Phys. Rev. B 100, 060405(R) (2019).
- L. Janssen, S. Koch, and M. Vojta, Phys. Rev. B 101, 174444 (2020).
- D. Aasen, R. S. K. Mong, B. M. Hunt, D. Mandrus, and J. Alicea, Phys. Rev. X 10, 031014 (2020).
- G. Kishony and E. Berg, Phys. Rev. B 104, 235118 (2021).
- S.-Q. Jia, L.-J. Zou, Y.-M. Quan, X.-L. Yu, and H.-Q. Lin, Phys. Rev. Res. 4, 023251 (2022).
- R. Mazzilli, A. Levchenko, and E. J. König, arXiv:2211.08421.
- H. Suzuki, H. Liu, J. Bertinshaw, K. Ueda, H. Kim, S. Laha, D. Weber, Z. Yang, L. Wang, H. Takahashi, K. Fürsich, M. Minola, B. V. Lotsch, B. J. Kim, H. Yavaş, M. Daghofer, J. Chaloupka, G. Khaliullin, H. Gretarsson, and B. Keimer, Nat. Commun. 12, 4512 (2021).
- H. Gretarsson, H. Suzuki, H. Kim, K. Ueda, M. Krautloher, B. J. Kim, H. Yavaş, G. Khaliullin, and B. Keimer, Phys. Rev. B 100, 045123 (2019).
- H. Gretarsson, D. Ketenoglu, M. Harder, S. Mayer, F.-U. Dill, M. Spiwek, H. Schulte-Schrepping, M. Tischer, H.-C. Wille, B. Keimer, and H. Yavaş, J. Synchrotron Radiat. 27, 538 (2020).
- J. Bertinshaw, M. Krautloher, H. Suzuki, H. Takahashi, A. Ivanov, H. Yavaş, B. J. Kim, H. Gretarsson, and B. Keimer, Phys. Rev. B 103, 085108 (2021).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevB.108.L041406 for details of sample preparation, model calculation Hamiltonian and results, fitting and decomposition method, and HRM with counting time of the spectra shown in the main text, which includes Refs. [37, 47, 48, 49, 50, 51, 52, 53, 54].
- Notice that given our resolution above 50 meV we cannot exclude energy shifts an order of magnitude smaller. Indeed, a recent Raman study [26] reports a shift of about 10 meV below 7 nm thickness, albeit based on a delicate spectral decomposition where no error bars are given.
- H. Takahashi, H. Suzuki, J. Bertinshaw, S. Bette, C. Mühle, J. Nuss, R. Dinnebier, A. Yaresko, G. Khaliullin, H. Gretarsson, T. Takayama, H. Takagi, and B. Keimer, Phys. Rev. Lett. 127, 227201 (2021).
- M. Ziatdinov, A. Banerjee, A. Maksov, T. Berlijn, W. Zhou, H. B. Cao, J.-Q. Yan, C. A. Bridges, D. G. Mandrus, S. E. Nagler, A. P. Baddorf, and S. V. Kalinin, Nat. Commun. 7, 13774 (2016).
- Z. Dai, J.-X. Yu, B. Zhou, S. A. Tenney, P. Lampen-Kelley, J. Yan, D. Mandrus, E. A. Henriksen, J. Zang, K. Pohl, and J. T. Sadowski, 2D Mater. 7, 035004 (2020).
- K. L. Seyler, D. Zhong, D. R. Klein, S. Gao, X. Zhang, B. Huang, E. Navarro-Moratalla, L. Yang, D. H. Cobden, M. A. McGuire, W. Yao, D. Xiao, P. Jarillo-Herrero, and X. Xu, Nat. Phys. 14, 277 (2018).
- D. Weber, L. M. Schoop, V. Duppel, J. M. Lippmann, J. Nuss, and B. V. Lotsch, Nano Lett. 16, 3578 (2016).
- L. Wang, I. Meric, P. Y. Huang, Q. Gao, Y. Gao, H. Tran, T. Taniguchi, K. Watanabe, L. M. Campos, D. A. Muller, J. Guo, P. Kim, J. Hone, K. L. Shepard, and C. R. Dean, Science 342, 614 (2013).
- S. Sugano, Y. Tanabe, and H. Kamimura, Multiplets of Transition-Metal Ions in Crystals, Pure and Applied Physics Vol. 33 (Elsevier, Amsterdam, 1970), Chap. II, pp. 38–65.
- A. Georges, L. de' Medici, and J. Mravlje, Annu. Rev. Condens. Matter Phys. 4, 137 (2013).
- Y. Tanabe and S. Sugano, J. Phys. Soc. Jpn. 9, 766 (1954).
- Y. Lu, M. Höppner, O. Gunnarsson, and M. W. Haverkort, Phys. Rev. B 90, 085102 (2014).
- M. W. Haverkort, G. Sangiovanni, P. Hansmann, A. Toschi, Y. Lu, and S. Macke, Europhys. Lett. 108, 57004 (2014).
- M. W. Haverkort, M. Zwierzycki, and O. K. Andersen, Phys. Rev. B 85, 165113 (2012).