Temporal and spectral fingerprints of ultrafast all-coherent spin switching

Abstract

Future information technology demands ever-faster, low-loss quantum control. Intense light fields have facilitated milestones along this way, including the induction of novel states of matter1,2,3, ballistic acceleration of electrons4,5,6,7 and coherent flipping of the valley pseudospin8. These dynamics leave unique ‘fingerprints’, such as characteristic bandgaps or high-order harmonic radiation. The fastest and least dissipative way of switching the technologically most important quantum attribute—the spin—between two states separated by a potential barrier is to trigger an all-coherent precession. Experimental and theoretical studies with picosecond electric and magnetic fields have suggested this possibility9,10,11, yet observing the actual spin dynamics has remained out of reach. Here we show that terahertz electromagnetic pulses allow coherent steering of spins over a potential barrier, and we report the corresponding temporal and spectral fingerprints. This goal is achieved by coupling spins in antiferromagnetic TmFeO3 (thulium orthoferrite) with the locally enhanced terahertz electric field of custom-tailored antennas. Within their duration of one picosecond, the intense terahertz pulses abruptly change the magnetic anisotropy and trigger a large-amplitude ballistic spin motion. A characteristic phase flip, an asymmetric splitting of the collective spin resonance and a long-lived offset of the Faraday signal are hallmarks of coherent spin switching into adjacent potential minima, in agreement with numerical simulations. The switchable states can be selected by an external magnetic bias. The low dissipation and the antenna’s subwavelength spatial definition could facilitate scalable spin devices operating at terahertz rates.

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Fig. 1: Antenna-enhanced THz spin dynamics.
Fig. 2: THz-induced nonlinear spin dynamics.
Fig. 3: Microscopic picture of ballistic spin motion.
Fig. 4: Ballistic steering of spins.

Data availability

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

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Acknowledgements

The authors thank A. M. Balbashov for bulk crystals of orthoferrites of an exceptionally high quality, I. Gronwald for assistance with electron-beam lithography, J. Fabian and M. S. Sherwin for fruitful discussions and T. Rasing for continuous support. The work in Regensburg was supported by the DFG through grant number HU 1598/2 and SFB 1277 (Project A05) as well as by the European Research Council through grant no. 305003 (QUANTUMsubCYCLE). The work in Nijmegen was supported by the European Research Council ERC Grant Agreement number 339813 (Exchange) and NWO (The Netherlands Organization for Scientific Research). The work in Moscow was supported by RSF grant number 17-12-01333. D.C.V. acknowledges the support of NSF DMR 1710639.

Reviewer information

Nature thanks Uwe Bovensiepen, Jakob Walowski and Guo Ping Zhang for their contribution to the peer review of this work.

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Affiliations

Authors

Contributions

S.S., C.L., S.B. and R.H. designed and implemented the antenna structures. R.V.M. and A.V.K. identified the bulk material for the project. S.S., C.L., S.B., T.E., C.P.S. and D.C.V. carried out the experiment with support from R.V.M. The theoretical modelling was carried out by C.L., S.S., S.B., A.K.Z. and R.V.M. A.V.K. and R.H. supervised the study. All authors analysed the data, discussed the results and contributed to the writing of the manuscript.

Corresponding authors

Correspondence to C. Lange or R. V. Mikhaylovskiy.

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Extended data figures and tables

Extended Data Fig. 1 Experimental set-up.

a, Microscope image of the gold bowtie antenna with a resonance frequency of 0.65 THz and a feed gap of 3.5 µm, structured onto the TmFeO3 sample. b, Diagram of the experiment. The Ti:sapphire amplifier generates 33-fs light pulses centred at a wavelength of 807 nm, with a  pulse energy (Epulse) of 5.5 mJ, and a repetition rate (νrep) of 3 kHz. The near-infrared beam (red solid line) is dispersed by the grating (G, top right) as visualized by the red, green and blue lines, imprinting a pulse front tilt. Two cylindrical lenses image and focus the laser light into a cryogenically cooled lithium niobate crystal (LiNbO3). WG, pair of wire grid polarizers controlling the intensity and the polarization state of the generated THz pulses. ITO, indium tin oxide coated fused silica window. The THz-induced polarization changes are decoded with the help of a half-wave plate (λ/2), a Wollaston polarizer (WP) and a pair of photodiodes, and subsequently detected with a lock-in amplifier. DL, mechanical delay line. ENIR, polarization of the near-infrared probe pulse (red dashed line). ETHz, polarization of the THz beam (bright red-shaded area). The inset indicates the orientation of the static magnetic field, Bext, as a function of the angle α relative to the orientation Bext,0 used for the measurements in the first part of the manuscript. c, Electro-optically detected THz field, ETHz, generated by tilted-pulse front optical rectification. d, Corresponding spectral amplitude of the THz transient shown in c. The blue arrows indicate the frequencies of the Tm3+ ground-state transitions relevant for our experiment.

Extended Data Fig. 2 Scaling of the residual offset for large delay times.

Polarization rotation signal at a delay time of t = 950 ps as a function of the THz electric peak field, ETHz. The data are extracted from time-resolved measurements in the feed gap of an antenna structurally similar to the one discussed in the main text with a feed gap of 3.5 µm and a broad resonance around 0.65 THz, optimized to the Tm3+ ground-state transitions. Lattice temperature T = 81 K. In the spin switching regime (grey-shaded area), ETHz > 0.65 MV cm−1, the slope of the polarization rotation signal is substantially increased. Error bars, standard deviation of θ. Dashed lines, guides to the eye.

Extended Data Fig. 3 Qualitative simulation of the beating signature.

a, Polarization rotation calculated by superimposing the responses shown in Fig. 3b—that is, spins oscillating in the equilibrium potential minimum at ϕ0 (relative weight, 0.8) and spins driven into the neighbouring local minimum at ϕ1 (relative weight, 0.2). b, Amplitude spectra of the time-domain data shown in a.

Extended Data Fig. 4 Temperature dependence of spin dynamics.

a, Transient polarization rotation probed in the centre of the feed gap of the antenna discussed in Fig. 4, for a THz far-field amplitude ETHz = 1.0 MV cm−1 and different lattice temperatures, T, between 82.0 K and 84.0 K (shown at right). Dashed lines, baselines. b, Corresponding amplitude spectra of the data shown in a.

Extended Data Fig. 5 Faraday signal for spin dynamics in different magnetic potentials.

a, Magnetic potential (red curve) for a lattice temperature of T = 82.5 K and an angle of Bext, α = 60°, as shown in Fig. 4c. Violet (grey) sphere, initial (switched) spin state. Insets, projection (grey dotted horizontal lines) of the magnetization F(ϕ) (arrows) onto the near-infrared wave vector, kNIR,z (light blue arrow), for different angles ϕ. For ϕ < ϕ0, the projection drops below its initial value and becomes negative for ϕ < −90°, causing a negative transient Faraday signal (Fig. 4e). For ϕ0 < ϕ < ϕ1, kNIR·F(ϕ) > kNIR·F(ϕ0), resulting in the positive initial half-cycle of the Faraday rotation signal (Fig. 4e). b, Magnetic potential for α = 95° (dark red curve) as shown in Fig. 4d. For ϕ < ϕ0, the initial spin deflection leads to kNIR·F(ϕ) < kNIR·F(ϕ0), causing a negative onset of the first oscillation period (Fig. 4e, bottom curve).

Extended Data Fig. 6 Field dependence of spin dynamics for α = 60°.

a, Polarization rotation signal as a function of the delay time, t, for different THz fields, ETHz, between 0.42 MV cm−1 and 1.0 MV cm−1, probed in the centre of the feed gap of the antenna discussed in Fig. 4. The transient negative Faraday signal (dashed-dotted curves) builds up for ETHz ≥ 0.87 MV cm−1. Dashed lines, baselines. b, Corresponding amplitude spectra of the data shown in a.

Extended Data Fig. 7 Electric field enhancement in the near field of a THz nanoantenna.

Enhancement factor ENF/ETHz (colour scale at right) of the near-field peak amplitude ENF compared to the THz electric far-field ETHz calculated by finite-difference simulations for a real THz waveform in the near field of an antenna structure with a feed gap of 10 nm. Assuming a switching threshold of approximately 10 MV cm−1, a far-field amplitude of only 1 kV cm−1 is sufficient to drive coherent spin switching by 90° in the centre of the antenna structure.

Extended Data Fig. 8 Calculated electric near-field characteristics of antenna.

Near-field amplitude ENF as a function of depth z in the centre of the antenna feed gap, for a THz far-field amplitude of ETHz = 0.4 MV cm−1 (‘antenna’, red curve). The electric field distribution expected in the unstructured substrate for ETHz = 1.0 MV cm−1 is shown for comparison (‘bulk’, black line). Red-shaded area, near-field region of the antenna, where the electric field exceeds the value in the bulk structure. Blue-shaded area, bulk part, where the electric field is comparable to the value in the unstructured substrate.

Extended Data Fig. 9 Simulated magneto-optical response for different driving forces.

Calculated polarization rotation signals expected from the antenna structures for a THz far-field amplitude of 0.4 MV cm−1 (blue curves) and 1.0 MV cm−1 (red curves). Calculations including only the displacive (dashed lines) or impulsive (dashed-dotted lines) anisotropy torque do not fit the experimental data. For the switch-off analysis, the parameters Γ for the displacive and κ for the impulsive torque of the full calculation (solid lines) are used. The curves are offset and normalized to the experimental peak value.

Supplementary information

Video1

Visualisation of calculated local spin dynamics in the antenna near-field. Top panel, measured (grey circles) and calculated (red curve) polarisation rotation signal for ETHz = 1.0 MV cm-1 (Fig. 3c, red curve). Lower set of panels, x-y-, x-z- and y-z-projections of the calculated spin dynamics in the antenna near-field as a function of the delay time, t.

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Schlauderer, S., Lange, C., Baierl, S. et al. Temporal and spectral fingerprints of ultrafast all-coherent spin switching. Nature 569, 383–387 (2019). https://doi.org/10.1038/s41586-019-1174-7

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