The ultrafast Einstein–de Haas effect

Abstract

The Einstein-de Haas effect was originally observed in a landmark experiment1 demonstrating that the angular momentum associated with aligned electron spins in a ferromagnet can be converted to mechanical angular momentum by reversing the direction of magnetization using an external magnetic field. A related problem concerns the timescale of this angular momentum transfer. Experiments have established that intense photoexcitation in several metallic ferromagnets leads to a drop in magnetization on a timescale shorter than 100 femtoseconds—a phenomenon called ultrafast demagnetization2,3,4. Although the microscopic mechanism for this process has been hotly debated, the key question of where the angular momentum goes on these femtosecond timescales remains unanswered. Here we use femtosecond time-resolved X-ray diffraction to show that most of the angular momentum lost from the spin system upon laser-induced demagnetization of ferromagnetic iron is transferred to the lattice on sub-picosecond timescales, launching a transverse strain wave that propagates from the surface into the bulk. By fitting a simple model of the X-ray data to simulations and optical data, we estimate that the angular momentum transfer occurs on a timescale of 200 femtoseconds and corresponds to 80 per cent of the angular momentum that is lost from the spin system. Our results show that interaction with the lattice has an essential role in the process of ultrafast demagnetization in this system.

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Fig. 1: Overview of the experiment and its implementation.
Fig. 2: Time-resolved X-ray diffraction signal, measured and simulated at different values of the out-of-plane momentum transfer qz.
Fig. 3: Frequency of modulations observed in the X-ray diffraction signal as a function of the out-of-plane momentum transfer qz.

Data availability

Raw data were generated at the LCLS large-scale facility, and intermediate datasets were generated during analysis. The raw and intermediate datasets are available from the corresponding author on reasonable request.

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Acknowledgements

Time-resolved X-ray diffraction measurements were carried out at the XPP endstation at LCLS. Use of the Linac Coherent Light Source (LCLS), SLAC National Accelerator Laboratory, is supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences under contract number DE-AC02-76SF00515. Preparatory static diffraction measurements were performed at the X04SA beamline of the Swiss Light Source. We acknowledge financial support by the NCCR Molecular Ultrafast Science and Technology (NCCR MUST), a research instrument of the Swiss National Science Foundation (SNSF). E.A. acknowledges support from the ETH Zurich Postdoctoral Fellowship Program and from the Marie Curie Actions for People COFUND programme. E.M.B. acknowledges funding from the European Commission’s Seventh Framework Programme (FP7/2007-2013) under grant agreement number 290605 (PSI-FELLOW/COFUND). M.P. acknowledges support from NCCR MARVEL, funded by the SNSF.

Reviewer information

Nature thanks P. G. Evans, M. Münzenberg and S. Sharma for their contribution to the peer review of this work.

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Authors

Contributions

C.D. and S.L.J. conceived and designed the experiment. C.A.F.V. performed the sample fabrication. C.D., M.S., M.K., M.J.N., E.A., L.H., E.M.B., M.P., V.E., L.R. and Y.W.W. performed synchrotron measurements to characterize the sample and prior sample candidates. M.B. and C.D. built the electromagnet. Y.A. built and programmed the pulser for the magnet. A.A. assisted C.D. in analysing X-ray reflectivity measurements of sample candidates. M.S., C.A.F.V., L.H., E.A., G.L., H.L., M.B., P.B. and U.S. gave input to C.D. and S.L.J. on the experimental design and during data analysis. C.D., Y.A., M.S., M.K., H.L., E.M.B., M.P., U.S. and S.L.J. performed the experiment with the help of D.Z., S.S. and J.M.G., the LCLS beamline staff. C.D. and S.L.J. wrote the manuscript and all authors contributed to its final version.

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Correspondence to C. Dornes or S. L. Johnson.

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Extended data figures and tables

Extended Data Fig. 1 Optical pump–probe measurements of the sample magnetization at varying incident fluence.

The individual traces have been offset for clarity. These results were taken by recreating the geometric conditions of the X-ray experiment, that is, the laser spot size and angle of incidence were identical. At the highest fluence, laser damage was evident, and the static MOKE signal of the damaged area was permanently lower afterwards.

Extended Data Fig. 2 Maximum relative demagnetization as a function of fluence.

From the traces in Extended Data Fig. 1, the magnitudes of demagnetization just after the coherent artefact (0.4–0.7 ps) were extracted. A linear fit (excluding the highest fluence where damage was evident) captures the observed behaviour well. The fluence in the X-ray experiment was 8.0 ± 0.3 mJ cm−2, corresponding to a demagnetization of 10%.

Extended Data Fig. 3 Goodness of fit, assessed by χ2, for different combinations of angular momentum transfer time and magnitude.

The left panel has a coarse logarithmic axis for the transfer time, whereas the right panel has a linear scale for a more precise determination of the optimum. The optima are indicated by the red crosses; for the coarse scale, the best χ2 of 628.9 is reached for the simulation with 100 fs transfer time and 7% magnitude. For the fine scale, the best values are 200 fs and 8%, with a χ2 of 618.8. The traces in Fig. 2 were generated using the latter parameters.

Extended Data Fig. 4 Snapshots of simulated velocity, displacement and strain in the transverse and longitudinal direction at different times.

The iron film is indicated by grey shading; to the left are the Al and MgO capping layers and to the right is the MgAl2O4 substrate.

Extended Data Fig. 5 Magnetic difference signal plots and two ‘virtual’ control measurements with the same magnetization sign.

The three vertical panels of each set show the three qz ranges centred at 0.0737, 0.0482 and 0.0236 reciprocal lattice units, as in Fig. 2. We constructed the ‘M+’ virtual control dataset by taking only the M > 0 data from each of the 158 scans. Data analysis was then performed by taking the difference of all even and all odd scan numbers. The ‘M−’ control dataset was created in the same manner by using only the M < 0 shots. We note that the uncertainties on both control sets are larger than for the actual magnetic difference data, because each control set uses only half of the total data. These control measurements are also more strongly influenced by longer-term drifts in the alignment of the free electron laser (there were about 4 min between consecutive scans), leading to some noise correlations. Nevertheless, all control sets are consistent with no signal.

Extended Data Table 1 Force-constant matrices for bcc metals in the five-shell Born–von Kármán model
Extended Data Table 2 Force-constant contributions for a chain of layers along z

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Dornes, C., Acremann, Y., Savoini, M. et al. The ultrafast Einstein–de Haas effect. Nature 565, 209–212 (2019). https://doi.org/10.1038/s41586-018-0822-7

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