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# Polarized phonons carry angular momentum in ultrafast demagnetization

## Abstract

Magnetic phenomena are ubiquitous in nature and indispensable for modern science and technology, but it is notoriously difficult to change the magnetic order of a material in a rapid way. However, if a thin nickel film is subjected to ultrashort laser pulses, it loses its magnetic order almost completely within femtosecond timescales1. This phenomenon is widespread2,3,4,5,6,7 and offers opportunities for rapid information processing8,9,10,11 or ultrafast spintronics at frequencies approaching those of light8,9,12. Consequently, the physics of ultrafast demagnetization is central to modern materials research1,2,3,4,5,6,7,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28, but a crucial question has remained elusive: if a material loses its magnetization within mere femtoseconds, where is the missing angular momentum in such a short time? Here we use ultrafast electron diffraction to reveal in nickel an almost instantaneous, long-lasting, non-equilibrium population of anisotropic high-frequency phonons that appear within 150–750 fs. The anisotropy plane is perpendicular to the direction of the initial magnetization and the atomic oscillation amplitude is 2 pm. We explain these observations by means of circularly polarized phonons that quickly absorb the angular momentum of the spin system before macroscopic sample rotation. The time that is needed for demagnetization is related to the time it takes to accelerate the atoms. These results provide an atomistic picture of the Einstein–de Haas effect and signify the general importance of polarized phonons for non-equilibrium dynamics and phase transitions.

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## Data availability

The data supporting the findings of this study are available from the corresponding author upon request.

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## Acknowledgements

We thank I. Wimmer for magnetic hysteresis data, B.-H. Chen for help with the optics, S. Geprägs for access to his X-ray diffractometer and F. Krausz for laboratory infrastructure. This research was supported by the European Union’s Horizon 2020 research and innovation program via CoG 647771 and by the German Research Foundation (DFG) via SFB 1432.

## Author information

Authors

### Contributions

P.B. and U.N. conceived the experiment. S.T., M.V. and D.E. performed the diffraction experiments and analyzed the data. A.B. and S.T. produced the specimen under supervision of W.K. A.B. and W.K. characterized the epitaxial growth. D.K. performed the ultrafast optical measurements and thermal simulations. U.N. conceived the theory and M.E., H.L. and A.D. performed the simulations. P.B., U.N. and S.T. wrote the manuscript with help of all co-authors.

### Corresponding author

Correspondence to P. Baum.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

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Nature thanks Georg Woltersdorf 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 X-ray characterization of the nickel thin-film structure.

a, X-ray reflectivity data and fit of the sample using a four-layer model with the scattering length density profile shown in the inset. The dashed lines in the inset indicate the slab model of the corresponding layers. The best fit parameters obtained by fitting the XRR intensities are shown in the table. The errors are estimated by a 5% increase over the optimum logarithmic figure of merit. b, Out-of-plane XRD scan in the angular regime of 40° ≤ 2θ ≤60°. The observed intensities at 2θ ≈ 50.53° and 2θ ≈ 52.13° correspond to Cu(002) and Ni(002). The lack of any Cu(111) and Ni(111) intensities shows the epitaxial growth. The inset graph shows the rocking-scans over the Cu(002) and Ni(002) peak positions. c, In-plane XRD scan at an inclination angle Δχ = 54.51°. The intensities at 2θ ≈ 43.41° and 2θ ≈ 44.47° correspond to the Cu(111) and Ni(111) reflections, respectively. d, ϕ scans for the Ni(111), Cu(111) and Si(111) ip peaks, obtained at an inclination angle of Δχ = 54.74°. A clear fourfold symmetry of the Cu(111) and Ni(111) ip reflections is observed with an offset angle of 45° to the Si(111) substrate reflections. For reasons of clarity, the scans are shifted in intensity by a factor of two each. e, ϕ scans for the Cu(111) and Ni(111) reflections, obtained at inclination angles of Δχ = 15.80°, Δχ = 54.74° and Δχ = 79.00°. For clarity, the scans are shifted in intensity by 0.1 each. Cu(111) intensities are shown in the angular regime of 0° ≤ ϕ ≤180°, while the Ni(111) intensities are shown for 180° ≤ ϕ ≤360°.

### Extended Data Fig. 2 Rocking curve, magnetic hysteresis and optical penetration depth.

a, Rocking scan data obtained with the femtosecond electron beam. Shown is the Ni(200) peak when rotating the specimen around the [010] axis. b, Magnetic hysteresis curve of our nickel specimen, obtained by an in-plane SQUID measurement. c, Simulated optical energy disposition as a function of penetration depth. Upper panel: solid line, normalized electric field amplitude; dotted line, real part of the refractive index; dashed line, imaginary part of the refractive index. The laser comes from the left. Lower panel: absorption as a function of depth. The green, red, blue and grey areas denote nickel, copper, silicon and NiOx, respectively.

### Extended Data Fig. 3 Second-harmonic-generation FROG measurements of the optical pulses after compression.

a, Measured FROG trace. b, Retrieved FROG trace at 0.3% FROG error. c, Evaluated spectrum (blue) and spectral phase (green). d, Retrieved pulse shape (blue) with temporal phase (green). The pulse duration is 93 fs.

### Extended Data Fig. 4 Numerical simulation of heat flow.

a, Temperature profile at 20 ps after laser excitation. Drawing is not to scale. b, Radial profile of the temperature increase ΔT due to quasi-static heat accumulation. c, Cooling dynamics of the front surface at r = 0.

### Extended Data Fig. 5 Magneto-optical Faraday effect and fluence dependency of the electron diffraction results.

a, Magnetic hysteresis curves for a negative (black) and slightly positive pump–probe delay (blue). b, Magnetization as a function of delay time. c, Debye–Waller effect as a function of the applied laser excitation fluence. d, Bragg spot anisotropy as a function of the applied laser excitation fluence. e, Simulated anisotropy as function of the degree of demagnetization.

### Extended Data Fig. 6 Changes of Bragg spots angles as a function of pump–probe delay.

Dots, changes Δαx along the x axis; squares, changes Δαy along the y axis (see Fig. 1d).

### Extended Data Fig. 7 Absence of beam deflection effects.

a, Two time-delayed electron beams on the screen. b, Intensity changes in the reference pulse (black) and probe pulse (blue), showing a Debye–Waller effect in the probe beam only. c, Differences of the beam positions before and after laser excitation as a function of the pump–probe delay, converted to angle changes at the specimen. All changes remain below 5 µrad.

### Extended Data Fig. 8 Control experiment.

Analysis of the anisotropy of the silicon and copper spots as function of the pump–probe delay. a, isotropic Debye–Waller effect of Ni. b, Anisotropy of Si and Cu as a function of time.

### Extended Data Fig. 9 Monte Carlo analysis of the time constants.

a, Distribution of the fitted response times for the Bragg spot asymmetry (blue) and the Debye–Waller effect (black). b, Correlation plot of the asymmetry fit parameters.

### Extended Data Fig. 10 Additional molecular dynamics simulations results.

a, Finite-size effects of the anisotropy of crystallographically equivalent peaks comparing open boundary conditions (OBC) with periodic ones (PBC). For OBC a finite-size effect is observed: the relaxation time of the contrast increases with system size. PBC do not show this effect. b, Long-time evolution for N = 50 testing the three cases (OBC, PBC, and global rotation according to the Einstein–de Hass effect (EdH)) (blue, solid lines). Also shown is the anisotropy of the mean-squared velocities $$2{v}_{y}^{2}/({v}_{x}^{2}+{v}_{z}^{2})$$ (green, dotted lines). c, Temperature dependence; anisotropy of crystallographically equivalent peaks for the same angular momentum L0 (same demagnetization) but different energy transfers to the lattice, leading to a temperature increase of ΔT = 15 K and 60 K, respectively.

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Tauchert, S.R., Volkov, M., Ehberger, D. et al. Polarized phonons carry angular momentum in ultrafast demagnetization. Nature 602, 73–77 (2022). https://doi.org/10.1038/s41586-021-04306-4

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• DOI: https://doi.org/10.1038/s41586-021-04306-4