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# Giant modulation of optical nonlinearity by Floquet engineering

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A Publisher Correction to this article was published on 12 January 2022

## Abstract

Strong periodic driving with light offers the potential to coherently manipulate the properties of quantum materials on ultrafast timescales. Recently, strategies have emerged to drastically alter electronic and magnetic properties by optically inducing non-trivial band topologies1,2,3,4,5,6, emergent spin interactions7,8,9,10,11 and even superconductivity12. However, the prospects and methods of coherently engineering optical properties on demand are far less understood13. Here we demonstrate coherent control and giant modulation of optical nonlinearity in a van der Waals layered magnetic insulator, manganese phosphorus trisulfide (MnPS3). By driving far off-resonance from the lowest on-site manganese dd transition, we observe a coherent on–off switching of its optical second harmonic generation efficiency on the timescale of 100 femtoseconds with no measurable dissipation. At driving electric fields of the order of 109 volts per metre, the on–off ratio exceeds 10, which is limited only by the sample damage threshold. Floquet theory calculations14 based on a single-ion model of MnPS3 are able to reproduce the measured driving field amplitude and polarization dependence of the effect. Our approach can be applied to a broad range of insulating materials and could lead to dynamically designed nonlinear optical elements.

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eLight Open Access 19 May 2022

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## Data availability

All other data that support the findings of this study are available from the corresponding author on reasonable request. Source data are provided with this paper.

## References

1. Oka, T. & Aoki, H. Photovoltaic Hall effect in graphene. Phys. Rev. B 79, 081406 (2009).

2. Kitagawa, T., Oka, T., Brataas, A., Fu, L. & Demler, E. Transport properties of nonequilibrium systems under the application of light: photoinduced quantum Hall insulators without Landau levels. Phys. Rev. B 84, 235108 (2011).

3. Rudner, M. S. & Lindner, N. H. Band structure engineering and non-equilibrium dynamics in Floquet topological insulators. Nat. Rev. Phys. 2, 229–244 (2020).

4. Hübener, H., Sentef, M. A., De Giovannini, U., Kemper, A. F. & Rubio, A. Creating stable Floquet–Weyl semimetals by laser-driving of 3D Dirac materials. Nat. Commun. 8, 13940 (2017).

5. McIver, J. W. et al. Light-induced anomalous Hall effect in graphene. Nat. Phys. 16, 38–41 (2020).

6. Wang, Y. H., Steinberg, H., Jarillo-Herrero, P. & Gedik, N. Observation of Floquet–Bloch states on the surface of a topological insulator. Science 342, 453–457 (2013).

7. Mentink, J. H., Balzer, K. & Eckstein. M. Ultrafast and reversible control of the exchange interaction in Mott insulators. Nat. Commun. 6, 6708 (2015).

8. Claassen, M., Jiang, H. C., Moritz, B. & Devereaux, T. P. Dynamical time-reversal symmetry breaking and photo-induced chiral spin liquids in frustrated Mott insulators. Nat. Commun. 8, 1192 (2017).

9. Liu, J., Hejazi, K. & Balents, L. Floquet engineering of multiorbital Mott insulators: applications to orthorhombic titanates. Phys. Rev. Lett. 121, 107201 (2018).

10. Mikhaylovskiy, R. V. et al. Ultrafast optical modification of exchange interactions in iron oxides. Nat. Commun. 6, 8190 (2015).

11. Chaudhary, S., Hsieh, D. & Refael, G. Orbital Floquet engineering of exchange interactions in magnetic materials. Phys. Rev. B 100, 220403 (2019).

12. Mitrano, M. et al. Possible light-induced superconductivity in K3C60 at high temperature. Nature 530, 461–464 (2016).

13. Gu, B. & Franco, I. Optical absorption properties of laser-driven matter. Phys. Rev. A 98, 063412 (2018).

14. Shirley, J. H. Solution of the Schrödinger equation with a Hamiltonian periodic in time. Phys. Rev. 138, B979–B987 (1965).

15. Bayarjargal, L. & Winkler, B. Pressure-induced magnetic phase transition in Cr2O3 determined by second harmonic generation measurements. Appl. Phys. Lett. 102, 182403 (2013).

16. Terhune, R. W., Maker, P. D. & Savage, C. M. Optical harmonic generation in calcite. Phys. Rev. Lett. 8, 404–406 (1962).

17. An, Y. Q., Nelson, F., Lee, J. U. & Diebold, A. C. Enhanced optical second-harmonic generation from the current-biased graphene/SiO2/Si(001) structure. Nano Lett. 13, 2104–2109 (2013).

18. Ruzicka, B. A. et al. Second-harmonic generation induced by electric currents in GaAs. Phys. Rev. Lett. 108, 077403 (2012).

19. Seyler, K. L. et al. Electrical control of second-harmonic generation in a WSe2 monolayer transistor. Nat. Nanotechnol. 10, 407–411 (2015).

20. Soavi, G. et al. Broad-band, electrically tunable third-harmonic generation in graphene. Nat. Nanotechnol. 13, 583–588 (2018).

21. Satoh, T., Van Aken, B. B., Duong, N. P., Lottermoser, T. & Fiebig, M. Ultrafast spin and lattice dynamics in antiferromagnetic Cr2O3. Phys. Rev. B 75, 155406 (2007).

22. Zhang, M. Y. et al. Light-induced subpicosecond lattice symmetry switch in MoTe2. Phys. Rev. X 9,021036 (2019).

23. Sartorello, G. et al. Ultrafast optical modulation of second- and third-harmonic generation from cut-disk-based metasurfaces. ACS Photon. 3, 1517–1522 (2016).

24. Piryatinskaya, V. G., Kachur, I. S., Slavin, V. V., Yeremenko, A. V. & Vysochanskii, Y. M. Temperature behavior of the fundamental optical absorption band in quasi-two-dimensional crystalline MnPS3. Low Temp. Phys. 38, 870–873 (2012).

25. Chu, H. et al. Linear magnetoelectric phase in ultrathin MnPS3 probed by optical second harmonic generation. Phys. Rev. Lett. 124, 027601 (2020).

26. Vaclavkova, D. et al. Magnetoelastic interaction in the two-dimensional magnetic material MnPS3 studied by first principles calculations and Raman experiments. 2D Mater. 7, 035030 (2020).

27. Kurosawa, K., Saito, S. & Yamaguchi, Y. Neutron diffraction study on MnPS3 and FePS3. J. Phys. Soc. Jpn 52, 3919–3926 (1983).

28. Grasso, V., Neri, F., Perillo, P., Silipigni, L. & Piacentini, M. Optical-absorption spectra of crystal-field transitions in MnPS3 at low temperatures. Phys. Rev. B 44, 11060–11066 (1991).

29. Fiebig, M., PavlovV. V. & Pisarev, R. V. Second-harmonic generation as a tool for studying electronic and magnetic structures of crystals: review. J. Opt. Soc. Am. B 22, 96–118 (2005).

30. Boyd, R. W. Nonlinear Optics (Academic Press, 2003).

31. Muthukumar, V. N., Valentí, R. & Gros, C. Microscopic model of nonreciprocal optical effects in Cr2O3. Phys. Rev. Lett. 75, 2766–2769 (1995).

32. Harter, J. W., Niu, L., Woss, A. J. & Hsieh, D. High-speed measurement of rotational anisotropy nonlinear optical harmonic generation using position-sensitive detection. Opt. Lett. 40, 4671–4674 (2015).

33. Wildes, A. R., Rønnow, H. M., Roessli, B., Harris, M. J. & Godfrey, K. W. Static and dynamic critical properties of the quasi-two-dimensional antiferromagnet MnPS3. Phys. Rev. B 74, 094422 (2006).

34. Autler, S. H. & Townes, C. H. Stark effect in rapidly varying fields. Phys. Rev. 100, 703–722 (1955).

35. Sie, E. J. et al. Valley-selective optical Stark effect in monolayer WS2. Nat. Mater. 14, 290–294 (2015).

36. Bloch, F. & Siegert, A. Magnetic resonance for nonrotating fields. Phys. Rev. 57, 522–527 (1940).

37. Sentef, M. A., Li, J., Künzel, F. & Eckstein, M. Quantum to classical crossover of Floquet engineering in correlated quantum systems. Phys. Rev. Res. 2, 033033 (2020).

38. Long, G. et al. Isolation and characterization of few-layer manganese thiophosphite. ACS Nano 11, 11330–11336 (2017).

39. Yang, J., Zhou, Y., Guo, Q., Dedkov, Y. & Voloshina, E. Electronic, magnetic and optical properties of MnPX3 (X = S, Se) monolayers with and without chalcogen defects: a first-principles study. RSC Adv. 10, 851–864 (2020).

40. Shklovskii, B. I. & Efros, A. L. Electronic Properties of Doped Semiconductors (Springer-Verlag, 1984).

41. Bloembergen, N. & Pershan, P. S. Light waves at the boundary of nonlinear media. Phys. Rev. 128, 606–622 (1962).

42. Dang, W., Chen, Y., Gong, M. & Chen, X. Competition between SFG and two SHGs in broadband type-I QPM. Appl. Phys. B 110, 477–482 (2013).

43. Choge, D. K., Chen, H., Guo, L., Li, G. & Liang, W. Simultaneous second-harmonic, sum-frequency generation and stimulated Raman scattering in MgO:PPLN. Materials 11, 2266 (2018).

44. Takano, Y. et al. Magnetic properties and specific heat of MPS3 (M=Mn, Fe, Zn). J. Magn. Magn. Mater. 272–276, E593–E595 (2004).

45. Gnatchenko, S. L., Kachur, I. S., Piryatinskaya, V. G., Vysochanskii, Y. M. & Gurzan, M. I. Exciton-magnon structure of the optical absorption spectrum of antiferromagnetic MnPS3. Low Temp. Phys. 37, 144–148 (2011).

46. Kargar, F. et al. Phonon and thermal properties of quasi-two-dimensional FePS3 and MnPS3 antiferromagnetic semiconductors. ACS Nano 14, 2424–2435 (2020).

47. Villars, P. Pauling file. Inorganic Solid Phases, SpringerMaterials (Springer, 2016); https://materials.springer.com/isp/crystallographic/docs/sd_0558101

## Acknowledgements

We acknowledge discussions with X. Li, S. Chaudhary and G. Refael. This work was supported by ARO MURI grant number W911NF-16-1-0361. D.H. also acknowledges support for instrumentation from the David and Lucile Packard Foundation and from the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center (PHY-1733907). M.Y. acknowledges support by the Gordon and Betty Moore Foundation through grant GBMF8690 to UCSB and by the National Science Foundation under grant number NSF PHY-1748958. J.-G.P. was supported by the Leading Researcher Program of the National Research Foundation of Korea (grant number 2020R1A3B2079375).

## Author information

Authors

### Contributions

S.L. and J.-G.P. synthesized and characterized the MnPS3 crystals. J.-Y.S. and H.C. performed the optical measurements. M.Y., J.-Y.S. and L.B. performed the single-ion model based static and Floquet dynamical calculations. J.-Y.S., M.Y. and D.H. wrote the paper with input from all authors.

### Corresponding author

Correspondence to D. Hsieh.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature thanks thanks Liang Wu and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

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## Extended data figures and tables

### Extended Data Fig. 1 EDX measurements.

The EDX spectrum and the calculated atomic percentage measured at three different spots.

### Extended Data Fig. 2 Magnetic susceptibility measurements.

The magnetic susceptibility measured with the magnetic field parallel to the ab plane and to the c* axis, which is the out-of-plane direction.

### Extended Data Fig. 3 Optical absorption data.

The relationship between (KE)2 and E is plotted (green circles) to facilitate the linear fit (black curve). Inset shows the DOS of in-gap impurity states.

### Extended Data Fig. 4 Linear coupling between SHG susceptibility and AFM order parameter.

The log-log plot of the critical behavior of $${\chi }_{{ijk}}^{{\rm{ED}}({\rm{c}})}$$ (squares). Linear fits within two different temperature ranges are overlaid (lines).

### Extended Data Fig. 5 Linear reflectivity transients.

ΔR/R with 1.55 eV probe and ħΩ = 0.66 eV taken at various driving a, amplitudes and b, polarizations.

### Extended Data Fig. 6 Ruling out competition between SHG and SFG as the source of SHG suppression.

Driving field amplitude dependence of SFG intensity at various probe fluences.

### Extended Data Fig. 7 SHG transients at higher temperatures.

Time-resolved SHG measured at a, 70 K and b, 90 K with ħΩ = 0.66 eV driving. $${E}_{{\rm{\max }}}^{{\rm{pu}}}$$ = 109 V/m, θ = 90˚ and φ = 60˚.

### Extended Data Fig. 8 Comparisons between RA patterns induced by resonant driving and static RA patterns at higher temperatures.

Upper panels show the time-resolved RA patterns taken at 10 K, and lower panels show the static RA patterns taken at higher temperatures. Identical fits to the crystal point group for each column are overlaid (black lines).

### Extended Data Fig. 9 Drive amplitude dependence of long time SHG suppression.

The calculated (black) and experimental (blue) driving amplitude (ħΩ = 2.07 eV) dependence of ∆Imag/Imag plateau values. Experimental data are taken at t = 200 ps.

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Shan, JY., Ye, M., Chu, H. et al. Giant modulation of optical nonlinearity by Floquet engineering. Nature 600, 235–239 (2021). https://doi.org/10.1038/s41586-021-04051-8

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• DOI: https://doi.org/10.1038/s41586-021-04051-8

• ### Floquet metamaterials

• Shixiong Yin
• Emanuele Galiffi
• Andrea Alù

eLight (2022)