Abstract
Magnons are quantized collective spin-wave excitations in magnetically ordered materials. Revealing the interactions among these collective modes is crucial for the understanding of fundamental many-body effects in such systems and the development of high-speed information transport and processing devices based on them. Nevertheless, identifying couplings between individual magnon modes remains a long-standing challenge. Here we demonstrate spectroscopic fingerprints of anharmonic coupling between distinct magnon modes in an antiferromagnet, as evidenced by coherent photon emission at the sum and difference frequencies of the two modes. This discovery is enabled by driving two magnon modes coherently with a pair of tailored terahertz fields and then disentangling a mixture of nonlinear responses with different origins. Our approach provides a route for generating nonlinear magnon–magnon mixing.
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Data availability
Source data are provided with this paper. All other data that support the findings of this study are available from the corresponding authors on reasonable request.
Code availability
The codes used to perform the simulations and to analyse the data in this work are available from the corresponding authors upon request.
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Acknowledgements
Z.Z., Z.-J.L., M.T.W. and K.A.N. acknowledge support from the US Department of Energy, Office of Basic Energy Sciences, under award no. DE-SC0019126. Work at UT Austin was primarily supported by the Robert A. Welch Foundation (F-2092-20220331) (to F.Y.G. for data taking and analysis) and the United States Army Research Office (W911NF-23-1-0394) (to E.B. for data interpretation, manuscript writing and supervision). Y.-C.C. acknowledges direct funding from the MIT UROP. A.v.H. gratefully acknowledges funding by the Humboldt Foundation. J.C. and P.N. were supported by the Quantum Science Center (QSC), a National Quantum Information Science Research Center of the US Department of Energy (DOE). P.N. acknowledges support as a Moore Inventor Fellow through grant no. GBMF8048 from the Gordon and Betty Moore Foundation and from the John Simon Guggenheim Memorial Foundation (Guggenheim Fellowship). T.K. acknowledges support from JSPS KAKENHI (21K14550, 20K22478).
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Z.Z. and F.Y.G. conceived the study and designed the research. Z.Z. and F.Y.G. performed the experiments and analysed the data, assisted by Z.-J.L. and Y.-C.C. Z.Z., F.Y.G., J.B.C., Y.-C.C. and M.T.W. performed theoretical analysis and simulated the LLG dynamics. T.K. and T.S. provided the sample. Z.Z., F.Y.G., J.B.C., A.v.H., P.N., E.B. and K.A.N. interpreted the data. Z.Z., F.Y.G., E.B. and K.A.N. wrote the manuscript. K.A.N. and E.B. supervised the project.
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Extended data
Extended Data Fig. 1 Simulated 2D THz spectra of YFeO3.
Theoretical 2D THz spectra obtained from LLG simulations of b-cut YFeO3 using the same THz magnetic field orientations shown in Fig. 2: a, HTHz || a axis, b, HTHz || c axis, and c, HTHz || ac bisector. Nonlinear mixing signals: SFG and DFG appear only upon simultaneous excitation of both qFM and qAFM modes when HTHz || ac bisector, in agreement with our experimental observations.
Extended Data Fig. 2 Simulated polarimetry patterns.
(left) Theoretical anisotropic SFG and DFG signal amplitudes are shown as a function of azimuthal angle θ for both parallel- (\({{{{\rm{H}}}}}_{{{{\rm{THz}}}}}| | {{{{\rm{H}}}}}_{\det }\)) and cross-polarized (\({{{{\rm{H}}}}}_{{{{\rm{THz}}}}}\perp {{{{\rm{H}}}}}_{\det }\)) detection configurations along with the (right) corresponding decompositions into excitation and detection terms. For each \({{\chi }_{{{{\rm{m}}}}}}^{(2)}\) magnon mixing signal, the generation mechanism is the result of the simultaneous excitation of qFM (\(\cos \theta\)) and qAFM (sin θ) modes, while nonlinear emission occurs along the crystallographic a-axis leading to separate symmetry terms for parallel- (\(\cos \theta\)) and cross-polarized (\(\sin \theta\)) signals.
Supplementary information
Supplementary Information
Supplementary Notes 1–5, Figs. 1–8 and Tables 1 and 2.
Source data
Source Data Fig. 1
1D time-domain THz waveforms, associated frequency domain THz waveforms, 1D THz polarimetry signal.
Source Data Fig. 2
Experimental 2D THz spectra.
Source Data Fig. 3
Field-dependent nonlinear THz signal, nonlinear 2D THz polarimetry.
Source Data Fig. 4
Simulated nonlinear spin dynamics.
Source Data Extended Data Fig. 1
Simulated 2D THz Spectra.
Source Data Extended Data Fig. 2
Theoretical nonlinear polarimetry signals.
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Zhang, Z., Gao, F.Y., Curtis, J.B. et al. Terahertz field-induced nonlinear coupling of two magnon modes in an antiferromagnet. Nat. Phys. (2024). https://doi.org/10.1038/s41567-024-02386-3
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DOI: https://doi.org/10.1038/s41567-024-02386-3
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