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Persistent magnetic coherence in magnets

Nature Materials (2024)Cite this article

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Abstract

When excited, the magnetization in a magnet precesses around the field in an anticlockwise manner on a timescale governed by viscous magnetization damping, after which any information carried by the initial actuation seems to be lost. This damping appears to be a fundamental bottleneck for the use of magnets in information processing. However, here we demonstrate the recall of the magnetization-precession phase after times that exceed the damping timescale by two orders of magnitude using dedicated two-colour microwave pump–probe experiments for a Y3Fe5O12 microstructured film. Time-resolved magnetization state tomography confirms the persistent magnetic coherence by revealing a double-exponential decay of magnetization correlation. We attribute persistent magnetic coherence to a feedback effect, that is, coherent coupling of the uniform precession with long-lived excitations at the minima of the spin-wave dispersion relation. Our finding liberates magnetic systems from the strong damping in nanostructures that has limited their use in coherent information storage and processing.

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Fig. 1: Two-colour pump–probe microwave spectroscopy.
Fig. 2: Observation of PMC.
Fig. 3: Damping of magnetization precession and time-resolved state tomography experiment.
Fig. 4: Magnetic-field dependence under subharmonic conditions.

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Data availability

The data that support the findings in this study are available from the corresponding author upon reasonable request.

Code availability

The codes used in the theoretical simulations and calculations are available from the corresponding author upon reasonable request.

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Acknowledgements

We thank T. Kikkawa and S. Daimon for fruitful discussions. This work was partially supported by JST CREST (JPMJCR20C1 and JPMJCR20T2), JST ERATO (JPMJER1402), JST PRESTO (JPMJPR20LB), JSPS KAKENHI (JP26103005, JP19H00645, JP19H05600, JP20K15160, JP21K13847, JP21K13886, JP22K14584, JP22H04965 and JP22H05114), Advanced Technology Institute Research Grants, Institute for AI and Beyond of the University of Tokyo, and IBM–UTokyo Lab. B.H. and A.A.S. acknowledge funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) via TRR 173/2–268565370 Spin+X.

Author information

Author notes

  1. These authors contributed equally: T. Makiuchi, T. Hioki, H. Shimizu.

Authors and Affiliations

  1. Department of Applied Physics, University of Tokyo, Tokyo, Japan

    T. Makiuchi, T. Hioki, H. Shimizu, K. Hoshi, N. Yokoi & E. Saitoh

  2. Quantum-Phase Electronics Center, University of Tokyo, Tokyo, Japan

    T. Makiuchi & E. Saitoh

  3. WPI Advanced Institute for Materials Research, Tohoku University, Sendai, Japan

    T. Hioki, M. Elyasi, G. E. W. Bauer & E. Saitoh

  4. Institute for AI and Beyond, University of Tokyo, Tokyo, Japan

    K. Hoshi, N. Yokoi & E. Saitoh

  5. Advanced Science Research Center, Japan Atomic Energy Agency, Tokai, Japan

    K. Yamamoto & E. Saitoh

  6. Department of Physics and Research Center OPTIMAS, RPTU Kaiserslautern-Landau, Kaiserslautern, Germany

    A. A. Serga & B. Hillebrands

  7. Kavli Institute for Theoretical Sciences, University of the Chinese Academy of Sciences, Beijing, China

    G. E. W. Bauer

  8. RIKEN Center for Emergent Matter Science, Wako, Japan

    E. Saitoh

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Contributions

T.M., T.H., H.S. and E.S. designed the experiments. T.M. and T.H. prepared the sample. T.M. performed the pump–probe experiments and analysed the data. T.H. and H.S. performed the time-resolved state tomography experiments and analysed the data. K.H. executed the numerical simulations and K.H., T.H. and T.M. analysed the data. M.E., G.E.W.B., K.Y. and E.S. developed the theory. T.M., T.H., H.S., K.H., M.E., K.Y., N.Y., A.A.S., B.H., G.E.W.B. and E.S. discussed the interpretation. E.S. supervised the project. E.S., T.M., T.H., M.E. and G.E.W.B. wrote the paper with input from all authors. All authors discussed the results and contents of the paper.

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Correspondence to E. Saitoh.

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Extended data

Extended Data Fig. 1 Pump-probe measurement procedure.

a, Microwave circuit. The microwave pulses were made by using signal generators (SGs), radio frequency switches (2 ns rise time) and pulse generators (PGs). The 2f pump and probe pulses were combined, amplified (+35 dB) and filtered (–80 dB at 1f) to eliminate parasitic subharmonic waves at 1f (less than –60 dB). The microwave pulses were injected to the main CPW. The a.c. signal generated from the YIG|Pt disk (grey coloured) was filtered (–80 dB at 2f) to reject crosstalk at 2f, amplified (+35 dB) and combined with an auxiliary microwave to detect the 0/π phase of the a.c. voltage. The 0/π phase measurement by using a signal analyser (SA) was synchronised with the probe pulse. The measurement cycles were repeated a hundred times for each t and θ. We adjusted the input and output microwave phases by using a 100 GS/s real-time oscilloscope. All the microwave instruments (SGs, PGs, SA and oscilloscope) were synchronised with a rubidium frequency standard. For generating FMR pump pulses, the SG in the middle raw (2f, pump) was turned off and the SG in the top raw (1f, bias) was used. b, Pulse sequence generated by the input circuit. c, AC voltage measured with the output circuit.

Extended Data Fig. 2 Microwave circuit for time-resolved tomography measurement.

The microwave pulses for exciting magnetization dynamics were made by using two signal generators (SGs), two radio frequency switches (2 ns rise time), and a pulse generator (PG). The pump pulses were amplified (+35 dB) and filtered (4–8 GHz bandwidth, –80 dB at 1f) to eliminate parasitic subharmonic waves at 1f (less than –60 dB). The pump pulse was combined with a bias pulse at a combiner and injected into the main CPW with the sample, YIG|Pt disk (grey coloured). The a.c. signal generated from the sample was filtered (2.11–2.17 GHz bandwidth, –80 dB at 2f) to reject crosstalk at 2f, and amplified (+35 dB) by using a low-noise HEMT amplifier (LNA). A radio-frequency switch was used to extract the signal within 25 ns. The frequency of the signal was down-converted to δf by using a mixer, and measured using a lock-in amplifier (LIA). We used a 100 GS/s oscilloscope to confirm the measurement circuit function. All the SGs, PG, and LIA were synchronized with a rubidium frequency standard. For the time-resolved state tomography for FMR driving field, we used a boxcar averager function of the LIA.

Extended Data Fig. 3 Persistent coherence in the magnetization dynamics based on the Suhl instability.

Breakdown of different stages of the magnon number \({|{\alpha }_{0(\pm {\mathscr{K}})}|}^{2}\) dynamics for the valley magnons. The dotted vertical lines are characteristic times, viz. tsuhl (Suhl instability kicks in), tsw (parametric excitation is turned off), and td (first stage of the Kittel mode relaxation ends). The dashed-dotted lines indicate single exponential decay at different rates. Here, T = 1 K, P0 = 0.6, Hext = 14 mT, \({\xi }_{\pm\;{\overrightarrow{\,{\mathscr{K}}}}}\) = 0.2 MHz and ξ0 = 2 MHz. The three-magnon confluence exhibits minimal impact on the overall decay rate of the valley magnons (\({|{\alpha }_{\pm {\mathscr{K}}^{\prime} }|}^{2}\)).

Extended Data Fig. 4 Different persistent coherence mechanisms.

a, Examples of \({|{\alpha }_{0}|}^{2}\) dynamics for three main mechanisms of persistent coherence. b, Θ(t) of the condensate based mechanism for several time evolutions from random initial conditions. c, \({\mathscr{P}}(t)\) corresponding to (b).

Extended Data Fig. 5 Persistent coherence with a BEC model.

a, Statistical average of condensate pair phase, \(\langle \text{arg}({c}_{\overrightarrow{{\mathscr{K}}}}{c}_{-\overrightarrow{{\mathscr{K}}}})\rangle\) with and without inclusion of the three-magnon scattering (3MS) with the Kittel mode. b, Θ(t) of the BEC based mechanism for several time evolutions from random initial conditions.

Extended Data Fig. 6 Estimation of lifetime t* from numerical calculation.

a, Temporal evolution of magnetization precession amplitudes calculated from a stochastic Landau–Lifshitz–Gilbert equation. t = 0 is set as the time when the a.c. pumping microwave is turned off. b, A magnified view of a. c, Magnetic field dependence of the magnon decay rate defined as the slope of the calculated precession amplitudes shown in b. The points represent the mean and the error bars indicate the standard deviation obtained from 100 data samples. d, Magnetic field dependence of the magnon lifetime t*. Here, t* is defined as the time at which the precession amplitude decayed to the noise level (Mz/Ms ~ 10–5). The points represent the mean and the error bars indicate the standard deviation obtained from 100 data samples.

Supplementary information

Supplementary Information

Supplementary Sections 1 and 2.

Supplementary Video 1

Temporal evolution of the observed Wigner function during the relaxation process.

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Makiuchi, T., Hioki, T., Shimizu, H. et al. Persistent magnetic coherence in magnets. Nat. Mater. (2024). https://doi.org/10.1038/s41563-024-01798-z

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