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Negative differential friction coefficients of two-dimensional commensurate contacts dominated by electronic phase transition

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Abstract

Friction force (f) usually increases with the normal load (N) macroscopically, according to the classic law of Da Vinci—Amontons (f = μN), with a positive and finite friction coefficient (μ). Herein near-zero and negative differential friction (ZNDF) coefficients are discovered in two-dimensional (2D) van der Waals (vdW) magnetic CrI3 commensurate contacts. It is identified that the ferromagnetic—antiferromagnetic phase transition of the interlayer couplings of the bilayer CrI3 can significantly reduce the interfacial sliding energy barriers and thus contribute to ZNDF. Moreover, phase transition between the in-plane (px and py) and out-of-plane (pz) wave-functions dominates the sliding barrier evolutions, which is attributed to the delicate interplays among the interlayer vdW, electrostatic interactions, and the intralayer deformation of the CrI3 layers under external load. The present findings may motivate a new concept of slide-spintronics and are expected to play an instrumental role in design of novel magnetic solid lubricants applied in various spintronic nano-devices.

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References

  1. Persson, B. N. J. Sliding Friction: Physical Principles and Applications, 2nd ed.; Springer: Berlin, 2000.

    Book  Google Scholar 

  2. Vanossi, A.; Manini, N.; Urbakh, M.; Zapperi, S.; Tosatti, E. Colloquium: Modeling friction: From nanoscale to mesoscale. Rev. Mod. Phys. 2013, 85, 529–552.

    Article  CAS  Google Scholar 

  3. Persson, B. N. J. Theory of rubber friction and contact mechanics. J. Chem. Phys. 2001, 115, 3840–3861.

    Article  CAS  Google Scholar 

  4. Urbakh, M.; Klafter, J.; Gourdon, D.; Israelachvili, J. The nonlinear nature of friction. Nature 2004, 430, 525–528.

    Article  CAS  Google Scholar 

  5. Bormuth, V.; Varga, V.; Howard, J.; Schäffer, E. Protein friction limits diffusive and directed movements of kinesin motors on microtubules. Science 2009, 325, 870–873.

    Article  CAS  Google Scholar 

  6. Holmberg, K.; Andersson, P.; Erdemir, A. Global energy consumption due to friction in passenger cars. Tribology International 2012, 47, 221–234.

    Article  Google Scholar 

  7. Holmberg, K.; Erdemir, A. Influence of tribology on global energy consumption, costs and emissions. Friction 2017, 5, 263–284.

    Article  CAS  Google Scholar 

  8. Tshiprut, Z.; Zelner, S.; Urbakh, M. Temperature-induced enhancement of nanoscale friction. Phys. Rev. Lett. 2009, 102, 136102.

    Article  CAS  Google Scholar 

  9. Guerra, R.; Tartaglino, U.; Vanossi, A.; Tosatti, E. Ballistic nanofriction. Nat. Mater. 2010, 9, 634–637.

    Article  CAS  Google Scholar 

  10. Persson, B. N. J.; Albohr, O.; Tartaglino, U.; Volokitin, A. I.; Tosatti, E. On the nature of surface roughness with application to contact mechanics, sealing, rubber friction and adhesion. J. Phys. Condens. Matter 2005, 17, R1–R62.

    Article  CAS  Google Scholar 

  11. Xie, H. T.; Wang, S. L.; Huang, H. Effects of surface roughness on the kinetic friction of SiC nanowires on SiN substrates. Tribol. Lett. 2018, 66, 15.

    Article  CAS  Google Scholar 

  12. Li, S. Z.; Li, Q. Y.; Carpick, R. W.; Gumbsch, P.; Liu, X. Z.; Ding, X. D.; Sun, J.; Li, J. The evolving quality of frictional contact with graphene. Nature 2016, 539, 541–545.

    Article  CAS  Google Scholar 

  13. Lee, C.; Li, Q. Y.; Kalb, W.; Liu, X. Z.; Berger, H.; Carpick, R. W.; Hone, J. Frictional characteristics of atomically thin sheets. Science 2010, 328, 76–80.

    Article  CAS  Google Scholar 

  14. Filleter, T.; McChesney, J. L.; Bostwick, A.; Rotenberg, E.; Emtsev, K. V.; Seyller, T.; Horn, K.; Bennewitz, R. Friction and dissipation in epitaxial graphene films. Phys. Rev. Lett. 2009, 102, 086102.

    Article  CAS  Google Scholar 

  15. Gnecco, E.; Bennewitz, R.; Gyalog, T.; Loppacher, C.; Bammerlin, M.; Meyer, E.; Güntherodt, H. J. Velocity dependence of atomic friction. Phys. Rev. Lett. 2000, 84, 1172–1175.

    Article  CAS  Google Scholar 

  16. Thorén, P. A.; de Wijn, A. S.; Borgani, R.; Forchheimer, D.; Haviland, D. B. Imaging high-speed friction at the nanometer scale. Nat. Commun. 2016, 7, 13836.

    Article  CAS  Google Scholar 

  17. Dayo, A.; Alnasrallah, W.; Krim, J. Superconductivity-dependent sliding friction. Phys. Rev. Lett. 1998, 80, 1690–1693.

    Article  CAS  Google Scholar 

  18. Park, J. Y.; Ogletree, D. F.; Thiel, P. A.; Salmeron, M. Electronic control of friction in silicon pn junctions. Science 2006, 313, 186.

    Article  CAS  Google Scholar 

  19. Kisiel, M.; Gnecco, E.; Gysin, U.; Marot, L.; Rast, S.; Meyer, E. Suppression of electronic friction on Nb films in the superconducting state. Nat. Mater. 2011, 10, 119–122.

    Article  CAS  Google Scholar 

  20. Kaiser, U.; Schwarz, A.; Wiesendanger, R. Magnetic exchange force microscopy with atomic resolution. Nature 2007, 446, 522–525.

    Article  CAS  Google Scholar 

  21. Androulidakis, C.; Koukaras, E. N.; Paterakis, G.; Trakakis, G.; Galiotis, C. Tunable macroscale structural superlubricity in two-layer graphene via strain engineering. Nat. Commun. 2020, 11, 1595.

    Article  CAS  Google Scholar 

  22. Luo, J. B.; Liu, M.; Ma, L. R. Origin of friction and the new frictionless technology—Superlubricity: Advancements and future outlook. Nano Energy 2021, 86, 106092.

    Article  CAS  Google Scholar 

  23. Andersson, D.; de Wijn, A. S. Understanding the friction of atomically thin layered materials. Nat. Commun. 2020, 11, 420.

    Article  CAS  Google Scholar 

  24. Zhang, Y. N.; Hanke, F.; Bortolani, V.; Persson, M.; Wu, R. Q. Why sliding friction of Ne and Kr monolayers is so different on the Pb(111) surface. Phys. Rev. Lett. 2011, 106, 236103.

    Article  CAS  Google Scholar 

  25. Gao, W.; Tkatchenko, A. Sliding mechanisms in multilayered hexagonal boron nitride and graphene: The effects of directionality, thickness, and sliding constraints. Phys. Rev. Lett. 2015, 114, 096101.

    Article  CAS  Google Scholar 

  26. Vazirisereshk, M. R.; Ye, H.; Ye, Z. J.; Otero-de-la-Roza, A.; Zhao, M. Q.; Gao, Z. L.; Johnson, A. T. C.; Johnson, E. R.; Carpick, R. W.; Martini, A. Origin of nanoscale friction contrast between supported graphene, MoS2, and a graphene/MoS2 heterostructure. Nano Lett. 2019, 19, 5496–5505.

    Article  CAS  Google Scholar 

  27. Müser, M. H. Structural lubricity: Role of dimension and symmetry. Eur. Lett. 2004, 66, 97–103.

    Article  CAS  Google Scholar 

  28. Shinjo, K.; Hirano, M. Dynamics of friction: Superlubric state. Surf. Sci. 1993, 283, 473–478.

    Article  CAS  Google Scholar 

  29. Peyrard, M.; Aubry, S. Critical behaviour at the transition by breaking of analyticity in the discrete Frenkel-Kontorova model. J. Phys. C Solid State Phys. 1983, 16, 1593–1608.

    Article  CAS  Google Scholar 

  30. Hirano, M.; Shinjo, K.; Kaneko, R.; Murata, Y. Anisotropy of frictional forces in muscovite mica. Phys. Rev. Lett. 1991, 67, 2642–2645.

    Article  CAS  Google Scholar 

  31. Berman, D.; Deshmukh, S. A.; Sankaranarayanan, S. R. S.; Erdemir, A.; Sumant, A. V. Macroscale superlubricity enabled by graphene nanoscroll formation. Science 2015, 348, 1118–1122.

    Article  CAS  Google Scholar 

  32. Song, Y. M.; Mandelli, D.; Hod, O.; Urbakh, M.; Ma, M.; Zheng, Q. S. Robust microscale superlubricity in graphite/hexagonal boron nitride layered heterojunctions. Nat. Mater. 2018, 17, 894–899.

    Article  CAS  Google Scholar 

  33. Deng, Z.; Smolyanitsky, A.; Li, Q. Y.; Feng, X. Q.; Cannara, R. J. Adhesion-dependent negative friction coefficient on chemically modified graphite at the nanoscale. Nat. Mater. 2012, 11, 1032–1037.

    Article  CAS  Google Scholar 

  34. Liu, B. T.; Wang, J.; Zhao, S. J.; Qu, C. Y.; Liu, Y.; Ma, L. R.; Zhang, Z. H.; Liu, K. H.; Zheng, Q. S.; Ma, M. Negative friction coefficient in microscale graphite/mica layered heterojunctions. Sci. Adv. 2020, 6, eaaz6787.

    Article  CAS  Google Scholar 

  35. Mandelli, D.; Ouyang, W. G.; Hod, O.; Urbakh, M. Negative friction coefficients in superlubric graphite-hexagonal boron nitride heterojunctions. Phys. Rev. Lett. 2019, 122, 076102.

    Article  CAS  Google Scholar 

  36. Sun, J. H.; Lu, Y. Y.; Feng, Y. Q.; Lu, Z. B.; Zhang, G. A.; Yuan, Y. P.; Qian, L. M.; Xue, Q. J. Friction-load relationship in the adhesive regime revealing potential incapability of AFM investigations. Tribol. Lett. 2020, 68, 18.

    Article  CAS  Google Scholar 

  37. Sun, J. H.; Zhang, Y. N.; Lu, Z. B.; Li, Q. Y.; Xue, Q. J.; Du, S. Y.; Pu, J. B.; Wang, L. P. Superlubricity enabled by pressure-induced friction collapse. J. Phys. Chem. Lett. 2018, 9, 2554–2559.

    Article  CAS  Google Scholar 

  38. Yang, C. B.; Xiao, S. Y.; Yang, J. C.; Lu, X. M.; Chu, Y. H.; Zhou, M.; Huang, F. Z.; Zhu, J. S. Dry lubrication of friction on ferroelectric BiFeO3 film. Appl. Surf. Sci. 2018, 457, 797–803.

    Article  CAS  Google Scholar 

  39. Sun, J. G.; Zhang, L. L.; Pang, R.; Zhao, X. J.; Cheng, J. T.; Zhang, Y. M.; Xue, X. L.; Ren, X. Y.; Zhu, W. G.; Li, S. F. et al. Negative differential friction predicted in two-dimensional ferroelectric In2Se3 commensurate contacts. Adv. Sci. 2022, 9, 2103443.

    Article  CAS  Google Scholar 

  40. Monceau, P.; Richard, J.; Renard, M. Charge-density-wave motion in NbSe3. I. Studies of the differential resistance \({{{\rm{d}}V} \over {{\rm{d}}I}}\). Phys. Rev. B 1982, 25, 931–947.

    Article  CAS  Google Scholar 

  41. Chen, L.; Hu, Z. P.; Zhao, A. D.; Wang, B.; Luo, Y.; Yang, J. L.; Hou, J. G. Mechanism for negative differential resistance in molecular electronic devices: Local orbital symmetry matching. Phys. Rev. Lett. 2007, 99, 146803.

    Article  CAS  Google Scholar 

  42. Íñiguez, J.; Zubko, P.; Luk’yanchuk, I.; Cano, A. Ferroelectric negative capacitance. Nat. Rev. Mater. 2019, 4, 243–256.

    Article  Google Scholar 

  43. Huang, B.; Clark, G.; Navarro-Moratalla, E.; Klein, D. R.; Cheng, R.; Seyler, K. L.; Zhong, D.; Schmidgall, E.; McGuire, M. A.; Cobden, D. H. et al. Layer-dependent ferromagnetism in a van der Waals crystal down to the monolayer limit. Nature 2017, 546, 270–273.

    Article  CAS  Google Scholar 

  44. Sivadas, N.; Okamoto, S.; Xu, X. D.; Fennie, C. J.; Xiao, D. Stacking-dependent magnetism in bilayer CrI3. Nano Lett. 2018, 18, 7658–7664.

    Article  CAS  Google Scholar 

  45. Jiang, P. H.; Wang, C.; Chen, D. C.; Zhong, Z. C.; Yuan, Z.; Lu, Z. Y.; Ji, W. Stacking tunable interlayer magnetism in bilayer CrI3. Phys. Rev. B 2019, 99, 144401.

    Article  CAS  Google Scholar 

  46. Soriano, D.; Cardoso, C.; Fernández-Rossier, J. Interplay between interlayer exchange and stacking in CrI3 bilayers. Solid State Commun. 2019, 299, 113662.

    Article  CAS  Google Scholar 

  47. Chen, W. O.; Sun, Z. Y.; Wang, Z. J.; Gu, L. H.; Xu, X. D.; Wu, S. W.; Gao, C. L. Direct observation of van der Waals stacking-dependent interlayer magnetism. Science 2019, 366, 983–987.

    Article  CAS  Google Scholar 

  48. Huang, B.; Clark, G.; Klein, D. R.; MacNeill, D.; Navarro-Moratalla, E.; Seyler, K. L.; Wilson, N.; McGuire, M. A.; Cobden, D. H.; Xiao, D. et al. Electrical control of 2D magnetism in bilayer CrI3. Nat. Nanotechnol. 2018, 13, 544–548.

    Article  CAS  Google Scholar 

  49. Song, T.; Fei, Z.; Yankowitz, M.; Lin, Z.; Jiang, Q.; Hwangbo, K.; Zhang, Q.; Sun, B.; Taniguchi, T.; Watanabe, K. et al. Switching 2D magnetic states via pressure tuning of layer stacking. Nat. Mater. 2019, 18, 1298–1302.

    Article  CAS  Google Scholar 

  50. Li, T.; Jiang, S.; Sivadas, N.; Wang, Z.; Xu, Y.; Weber, D.; Goldberger, J. E.; Watanabe, K.; Taniguchi, T.; Fennie, C. J. et al. Pressure-controlled interlayer magnetism in atomically thin CrI3. Nat. Mater. 2019, 18, 1303–1308.

    Article  CAS  Google Scholar 

  51. Soriano, D.; Katsnelson, M. I. Magnetic polaron and antiferromagnetic-ferromagnetic transition in doped bilayer CrI3. Phys. Rev. B 2020, 101, 041402.

    Article  CAS  Google Scholar 

  52. Webster, L.; Yan, J. A. Strain-tunable magnetic anisotropy in monolayer CrCl3, CrBr3, and CrI3. Phys. Rev. B 2018, 98, 144411.

    Article  CAS  Google Scholar 

  53. Wang, Z.; Gutiérrez-Lezama, I.; Ubrig, N.; Kroner, M.; Gibertini, M.; Taniguchi, T.; Watanabe, K.; Imamoğlu, A.; Giannini, E.; Morpurgo, A. F. Very large tunneling magnetoresistance in layered magnetic semiconductor CrI3. Nat. Commun. 2018, 9, 2516.

    Article  CAS  Google Scholar 

  54. Jiang, S. W.; Xie, H. C.; Shan, J.; Mak, K. F. Exchange magnetostriction in two-dimensional antiferromagnets. Nat. Mater. 2020, 19, 1295–1299.

    Article  CAS  Google Scholar 

  55. Cantos-Prieto, F.; Falin, A.; Alliati, M.; Qian, D.; Zhang, R.; Tao, T.; Barnett, M. R.; Santos, E. J. G.; Li, L. H.; Navarro-Moratalla, E. Layer-dependent mechanical properties and enhanced plasticity in the van der Waals chromium trihalide magnets. Nano Lett. 2021, 21, 3379–3385.

    Article  CAS  Google Scholar 

  56. Stern, M. V.; Waschitz, Y.; Cao, W.; Nevo, I.; Watanabe, K.; Taniguchi, T.; Sela, E.; Urbakh, M.; Hod, O.; Ben Shalom, M. Interfacial ferroelectricity by van der Waals sliding. Science 2021, 372, 1462–1466.

    Article  CAS  Google Scholar 

  57. Yasuda, K.; Wang, X. R.; Watanabe, K.; Taniguchi, T.; Jarillo-Herrero, P. Stacking-engineered ferroelectricity in bilayer boron nitride. Science 2021, 372, 1458–1462.

    Article  CAS  Google Scholar 

  58. Zheng, Z. R.; Ma, Q.; Bi, Z.; de la Barrera, S.; Liu, M. H.; Mao, N. N.; Zhang, Y.; Kiper, N.; Watanabe, K.; Taniguchi, T. et al. Unconventional ferroelectricity in moiré heterostructures. Nature 2020, 588, 71–76.

    Article  CAS  Google Scholar 

  59. Constantinescu, G.; Kuc, A.; Heine, T. Stacking in bulk and bilayer hexagonal boron nitride. Phys. Rev. Lett. 2013, 111, 036104.

    Article  CAS  Google Scholar 

  60. Kresse, G.; Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 1996, 54, 11169–11186.

    Article  CAS  Google Scholar 

  61. Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 1994, 50, 17953–17979.

    Article  Google Scholar 

  62. Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 1996, 77, 3865–3868.

    Article  CAS  Google Scholar 

  63. McGuire, M. A.; Dixit, H.; Cooper, V. R.; Sales, B. C. Coupling of crystal structure and magnetism in the layered, ferromagnetic insulator CrI3. Chem. Mater. 2015, 27, 612–620.

    Article  CAS  Google Scholar 

  64. Klimeš, J.; Bowler, D. R.; Michaelides, A. Van der Waals density functionals applied to solids. Phys. Rev. B 2011, 83, 195131.

    Article  CAS  Google Scholar 

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Nos. 12074345, 12174349, 11674289, 11804306, 11634011 and U2030120), and Henan Provincial Key Science and Technology Research Projects (No. 212102210130).

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Correspondence to Chongxin Shan, Hongjie Liu or Shunfang Li.

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Negative differential friction coefficients of two-dimensional commensurate contacts dominated by electronic phase transition

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Liu, K., Cheng, J., Zhao, X. et al. Negative differential friction coefficients of two-dimensional commensurate contacts dominated by electronic phase transition. Nano Res. 15, 5758–5766 (2022). https://doi.org/10.1007/s12274-022-4316-4

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