Extreme Domain Wall Speeds Observed in Ferromagnets

The manipulation of magnetic domains is of paramount interest because of its potential applications in spintronics and next generation technologies for mass storage. In current storage devices, such as hard disk drives, information is processed using either magnetic fields or spin currents. However, existing technologies are limited in speed, not only due to engineering factors but also because of fundamental limits in driving domain walls at high speed. The motion of domains driven using conventional magnetic field and spin currents is limited to a speed of about 0.5 km/s, due to the phenomenon named Walker breakdown. Above this threshold speed, domains become unstable and develop different spin dynamics. Interestingly, recent theoretical investigations have predicted that speeds exceeding 10 km/s are achievable in ferromagnetic materials when driven by an optical laser pulse.

In this work, we optically excited a CoFe/Ni multilayer sample and measured the ultrafast response of magnetic domains using small angle X-ray scattering at Diffraction and Projection Imaging (DiProI) beamline of the FERMI free electron laser. Figure 1a shows the experimental setup, a magnetic force microscopy (MFM) image, a representative scattering image on the detector and the results from the novel 2D fitting routine used to extract the main signal contributes. The MFM image reveals coexisting labyrinthine (highly curved) and stripe (linear) magnetic domains. The arrow on MFM image indicates the direction of linear texture. The experimental and fitted scattering images (see Figure 1b) consist of two primary components, one is an isotropic ring that originates from the labyrinthine domains and two anisotropic lobes that originate from stripe-like structures in the magnetic pattern. Using a novel 2D fitting routine, we were able to isolate the different time dependence of the magnetic response from the labyrinthine and stripe domains.

Figure 1: Experimental schematic and evolution of labyrinthine domain pattern as a function of delay time. (a) Optical pump - EUV magnetic scattering probe experimental setup with highlighted an MFM image of the domain sample pattern. The white arrow indicates the preferential direction of the linear texture of the domain pattern. Magnetic diffraction scattering on the CCD is fitted with a 2D phenomenological model, from which we separate the ring and lobe components. (b) Isolated isotropic (ring) and anisotropic (lobes) fit components with arrows indicating the radius (q_R, q_L) and full-width half maximum (Γ_R, ΓL) of scattering. Time-resolved (a) amplitude (A_R), (b) ring radius (q_R), and (c) width (Γ_R) obtained from the fit of the isotropic scattering (ring). Delay curves are plotted for a range of measured fluence values from 0.8 to 13.4 mJ/cm². The scattering amplitude, which is proportional to magnetization, decays immediately following laser excitation indicating demagnetization which recovers on picosecond timescales. The ring radius (q_R) and width (Γ_R) of the isotropic scattering approximate the average real-space domain size and correlation length of the labyrinthine domains, respectively.

Figures 1 c-d show the amplitude, scattered radius, and full-width at half-maximum of scattering from labyrinthine domains as a function of laser pulse fluence respectively. In the early stages, the optical excitation causes the well-known ultrafast demagnetization effect, as seen by the change in the scattering strength in figure 1c. Simultaneously, a shift in the scattered peak position and width is also observed, indicating a non-trivial change in domain periodicity. While a similar quench in magnetization was observed for stripe domains, the peak position and width did not change do the same degree. This suggests that the curvature of domain walls plays a crucial role in optically driven domain walls.

Figure 2: Simulated modification of domain pattern and calculated domain wall velocity. (a) Simulated modified domain pattern (black and white domains) and initial state (colored outline). The colour of the outline denotes the initial wall curvature. The comparison clearly shows that regions with high curvature (dark red and blue) undergo noticeable domain wall motion. (b) Fluence dependence of calculated domain wall velocity for labyrinthine domains estimated using experimental results and micromagnetic simulations.

Combining our experimental results with micromagnetic simulations, we estimate that the observed modification of curved domains can be explained by the motion of domain walls at highly curved regions (see Figure 2a) with speeds of up to 66 km/s (see Figure 2b). This speed is ten times higher than the speed of sound in the material and one hundred times higher than previously reported domain wall speeds in ferromagnets.

Our findings open a new avenue for modifying magnetic textures at ever increasing speed via optical manipulation of spin order and demonstrates that far from equilibrium excitations can give rise to phenomenon which are inaccessible to conventional methods.

This research was conducted by the following research team:

Rahul Jangid^1,2, Nanna Zhou Hagström^1,3, Meera Madhavi¹, Kyle Rockwell⁴, Justin M. Sha5⁴, Jeffrey A. Brock⁶, Matteo Pancaldi⁷, Dario De Angelis⁷, Flavio Capotondi⁷, Emanuele Pedersoli⁷, Hans T. Nembach^8,9, Mark W. Keller⁵, Stefano Bonetti^3,10, Eric E. Fullerton⁶, Ezio Iacocca⁴, Roopali Kukreja¹ and Thomas J. Silva^5
1 Department of Materials Science and Engineering, University of California Davis, Davis, California, USA
² National Synchrotron Light Source II, Brookhaven National Laboratory, Upton, New York, USA
³ Department of Physics, Stockholm University, Stockholm, Sweden
⁴ Center for Magnetism and Magnetic Nanostructures, University of Colorado Colorado Springs, Colorado Springs, Colorado, USA
⁵ Quantum Electromagnetics Division, National Institute of Standards and Technology, Boulder, Colorado, USA
⁶ Center for Memory and Recording Research, University of California San Diego, La Jolla, California, USA
⁷ Elettra-Sincrotrone Trieste S.C.p.A., Trieste, Italy
⁸ Department of Physics, University of Colorado, Boulder, Colorado, USA
⁹ Physical Measurement Laboratory, National Institute of Standards and Technology, Boulder, Colorado, USA
¹⁰ Department of Molecular Sciences and Nanosystems, Ca’ Foscari University of Venice, Venezia, Italy

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