Nonlinear Magnetization Dynamics Driven by Strong Terahertz Fields

Matthias Hudl, Massimiliano d’Aquino, Matteo Pancaldi, See-Hun Yang, Mahesh G. Samant, Stuart S. P. Parkin, Hermann A. Dürr, Claudio Serpico, Matthias C. Hoffmann, and Stefano Bonetti

Phys. Rev. Lett. 123, 197204 – Published 8 November 2019

Abstract

We present a comprehensive experimental and numerical study of magnetization dynamics in a thin metallic film triggered by single-cycle terahertz pulses of $\sim 20 MV / m$ electric field amplitude and $\sim 1 ps$ duration. The experimental dynamics is probed using the femtosecond magneto-optical Kerr effect, and it is reproduced numerically using macrospin simulations. The magnetization dynamics can be decomposed in three distinct processes: a coherent precession of the magnetization around the terahertz magnetic field, an ultrafast demagnetization that suddenly changes the anisotropy of the film, and a uniform precession around the equilibrium effective field that is relaxed on the nanosecond time scale, consistent with a Gilbert damping process. Macrospin simulations quantitatively reproduce the observed dynamics, and allow us to predict that novel nonlinear magnetization dynamics regimes can be attained with existing tabletop terahertz sources.

Received 21 March 2019

DOI:https://doi.org/10.1103/PhysRevLett.123.197204

Physics Subject Headings (PhySH)

Demagnetization Ferromagnetism Magnetism Magneto-optical effect Spin dynamics Ultrafast magnetic effects

Ferromagnets Magnetic multilayers Thin films

Femtosecond laser irradiation Femtosecond laser spectroscopy Landau-Lifschitz-Gilbert equation Magneto-optical Kerr effect Methods in magnetism Optical pumping Terahertz techniques Ultrafast pump-probe spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Matthias Hudl¹, Massimiliano d’Aquino², Matteo Pancaldi ¹, See-Hun Yang³, Mahesh G. Samant³, Stuart S. P. Parkin^3,4, Hermann A. Dürr⁵, Claudio Serpico⁶, Matthias C. Hoffmann⁷, and Stefano Bonetti ^1,8,*

¹Department of Physics, Stockholm University, 106 91 Stockholm, Sweden
²Department of Engineering, University of Naples “Parthenope”, 80143 Naples, Italy
³IBM Almaden Research Center, San Jose, California 95120, USA
⁴Max-Planck Institut für Mikrostrukturphysik, 06120 Halle, Germany
⁵Department of Physics and Astronomy, Uppsala University, 751 20 Uppsala, Sweden
⁶DIETI, University of Naples Federico II, 80125 Naples, Italy
⁷SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
⁸Department of Molecular Sciences and Nanosystems, Ca’ Foscari University of Venice, 30172 Venezia Mestre, Italy

^*stefano.bonetti@fysik.su.se

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Issue

Vol. 123, Iss. 19 — 8 November 2019

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Images

Figure 1
(a) Schematic drawing of the experimental setup: BD—Balanced detection using two photodiodes and a lock-in amplifier, WP—Wollaston prism, EM $+$ S—Electromagnet with out-of-plane field and sample, OAPM—Off-axis parabolic mirror, P—Wire grid polarizer, LNO—Lithium niobate, and M—Mirror. (b) Sample geometry: The electric field component of the THz pulse at the sample position is oriented parallel to the $y$ -axis direction, $E_{THz} ∥ y$ , and the magnetic field component parallel to the $x$ -axis direction, $H_{THz} ∥ x$ . A static magnetic field $H_{Ext}$ is applied along the $z$ -axis direction. (c)–(f) Experimental MOKE data showing the influence of reversing the external magnetic field ( $\pm H_{Ext}$ , $H_{THz} = const$ ) on the THz-induced demagnetization (c) and on the FMR oscillations (d). The influence of reversing the THz magnetic field pulse ( $\pm H_{THz}$ , $H_{Ext} = const$ ) on the THz-induced demagnetization and on the FMR oscillations is shown in panels (e) and (f). (The shaded green area is a guide to the eye.)
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Figure 2
Experimental data showing the magnetic field dependence of the FMR. (a) MOKE signal for different out-of-plane fields $μ_{0} H_{Ext}$ —20, 50, 75, 100, 125, 150, 175, and 185 mT in ascending order. The solid line is a damped sine function fitted to the experimental data. Both fit and data curves are displaced on the $y$ axis by a constant offset. (b) Fourier transformation of the data shown in (a) vs FMR amplitude. (c) FMR frequency as a function of the in-plane component of $H_{Ext}$ . The solid line corresponds to the Kittel equation, Eq. (1).
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Figure 3
Comparison of experimental data (open markers) and macrospin simulations (solid lines). (a) THz-induced demagnetization for an external applied field of $μ_{0} H_{Ext} \sim 450 mT$ and a THz pulse of $E_{THz} = 18 MV / m$ ( $μ_{0} H_{THz} \sim 60 mT$ ). The blue markers and lines correspond to $+ H_{THz}$ , and the orange markers and lines to $- H_{THz}$ . (b) Experimental data and macrospin simulations under similar conditions as (a) showing FMR on a longer timescale.
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Figure 4
Comparison of macrospin simulation data for moderate ( $20 MV / m$ ) and high ( $200 MV / m$ ) THz-peak-field stimulus. The external magnetic field is set to $μ_{0} H_{Ext} = 450 mT$ , i.e., replicating the experimental conditions from Fig. 3. Panel (a) shows the relative change of the $M_{y}$ (blue line) and $M_{z}$ (light blue line) magnetization component for a $E_{THz}$ peak field of $20 MV / m$ and (b) shows the corresponding Fourier spectrum. (c) and (d) show the simulation data and corresponding Fourier spectrum for an $E_{THz}$ peak field of $200 MV / m$ , respectively.
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