Terahertz magnetic field enhancement in an asymmetric spiral metamaterial

We use finite element simulations in both the frequency and the time-domain to study the terahertz resonance characteristics of a metamaterial (MM) comprising a spiral connected to a straight arm. The MM acts as a RLC circuit whose resonance frequency can be precisely tuned by varying the characteristic geometrical parameters of the spiral: inner and outer radius, width and number of turns. We provide a simple analytical model that uses these geometrical parameters as input to give accurate estimates of the resonance frequency. Finite element simulations show that linearly polarized terahertz radiation efficiently couples to the MM thanks to the straight arm, inducing a current in the spiral, which in turn induces a resonant magnetic field enhancement at the center of the spiral. We observe a large (approximately 40 times) and uniform (over an area of ∼10 μm2) enhancement of the magnetic field for narrowband terahertz radiation with frequency matching the resonance frequency of the MM. When a broadband, single-cycle terahertz pulse propagates towards the MM, the peak magnetic field of the resulting band-passed waveform still maintains a six-fold enhancement compared to the peak impinging field. Using existing laser-based terahertz sources, our MM design allows to generate magnetic fields of the order of 2 T over a time scale of several picoseconds, enabling the investigation of nonlinear ultrafast spin dynamics in table-top experiments. Furthermore, our MM can be implemented to generate intense near-field narrowband, multi-cycle electromagnetic fields to study generic ultrafast resonant terahertz dynamics in condensed matter

Evidence of extreme domain wall speeds under ultrafast optical excitation

Time-resolved ultrafast EUV magnetic scattering was used to test a recent prediction of >10 km/s domain wall speeds by optically exciting a magnetic sample with a nanoscale labyrinthine domain pattern. Ultrafast distortion of the diffraction pattern was observed at markedly different timescales compared to the magnetization quenching. The diffraction pattern distortion shows a threshold-dependence with laser fluence, not seen for magnetization quenching, consistent with a picture of domain wall motion with pinning sites. Supported by simulations, we show that a speed of $\approx$ 66 km/s for highly curved domain walls can explain the experimental data. While our data agree with the prediction of extreme, non-equilibrium wall speeds locally, it differs from the details of the theory, suggesting that additional mechanisms are required to fully understand these effects.Comment: 5 pages, 4 figures; Supplemental Material: 8 pages, 9 figure

Inertial spin dynamics in ferromagnets

The understanding of how spins move and can be manipulated at pico- and femtosecond timescales has implications for ultrafast and energy-efficient data-processing and storage applications. However, the possibility of realizing commercial technologies based on ultrafast spin dynamics has been hampered by our limited knowledge of the physics behind processes on this timescale. Recently, it has been suggested that inertial effects should be considered in the full description of the spin dynamics at these ultrafast timescales, but a clear observation of such effects in ferromagnets is still lacking. Here, we report direct experimental evidence of intrinsic inertial spin dynamics in ferromagnetic thin films in the form of a nutation of the magnetization at a frequency of ~0.5 THz. This allows us to reveal that the angular momentum relaxation time in ferromagnets is on the order of 10 ps

Symmetry-dependent ultrafast manipulation of nanoscale magnetic domains

Femtosecond optical pumping of magnetic materials has been used to achieve ultrafast switching and recently to nucleate symmetry-broken magnetic states. However, when the magnetic order parameter already presents a broken-symmetry state, such as a domain pattern, the dynamics are poorly understood and consensus remains elusive. Here, we resolve the controversies in the literature by studying the ultrafast response of magnetic domain patterns with varying degrees of translation symmetry with ultrafast x-ray resonant scattering. A data analysis technique is introduced to disentangle the isotropic and anisotropic components of the x-ray scattering. We find that the scattered intensity exhibits a radial shift restricted to the isotropic component, indicating that the far-from-equilibrium magnetization dynamics are intrinsically related to the spatial features of the domain pattern. Our results suggest alternative pathways for the spatiotemporal manipulation of magnetism via far-from-equilibrium dynamics and by carefully tuning the ground-state magnetic textures

Nonequilibrium sub–10 nm spin-wave soliton formation in FePt nanoparticles

Magnetic nanoparticles such as FePt in the L1 0 phase are the bedrock of our current data storage technology. As the grains become smaller to keep up with technological demands, the superparamagnetic limit calls for materials with higher magnetocrystalline anisotropy. This, in turn, reduces the magnetic exchange length to just a few nanometers, enabling magnetic structures to be induced within the nanoparticles. Here, we describe the existence of spin-wave solitons, dynamic localized bound states of spin-wave excitations, in FePt nanoparticles. We show with time-resolved x-ray diffraction and micromagnetic modeling that spin-wave solitons of sub–10 nm sizes form out of the demagnetized state following femtosecond laser excitation. The measured soliton spin precession frequency of 0.1 THz positions this system as a platform to develop novel miniature devices

Ultrafast spin dynamics at the nanoscale : using coherent X-ray and terahertz radiation

The field of ultrafast magnetism is driven by the growing need for faster and more efficient magnetic data storage, which comprises the vast majority of the digital information worldwide. However, after more than two decades of intense research, the understanding of the fundamental physical processes governing the transfer of angular momentum necessary for magnetic switching, is still lacking, partially hampered by the appropriate experimental tools. This situation is rapidly changing with the advent of X-ray free electron lasers (XFEL), which combine high temporal and spatial resolutions, necessary for a complete view of the physics at play.  In the first work presented in this thesis, we demonstrate the capabilities of the recently built Spectroscopy and Coherent Scattering (SCS) instrument at the European XFEL. We perform ultrafast time-resolved small angle X-ray scattering (SAXS) on nanometre magnetic domains, combining ultrafast temporal resolution with high spatial resolution. We also demonstrate X-ray holographic reconstruction of similar magnetic domains. Our results show that the efficient data acquisition for holographic imaging is possible thanks to the MHz-operation of the European XFEL, paving the way for new studies and ultimately to create femtosecond movies of magnetism at the nanoscale.  In the second work of this thesis, we describe a subsequent experiment at the SCS instrument, where we focus on the impact of symmetry breaking on the ultrafast dynamics of magnetic domains by looking at the diffracted SAXS data. Surprisingly, we observe a different ultrafast response depending on the anisotropy of the domains. We observe a clear contraction of the isotropic scattering ring in the reciprocal wavevector space (characteristic of randomly oriented domains), while no such contraction is observed in the anisotropic scattering pattern (distinctive of stripe-ordered domains). While the fundamental physical reason for the occurrence of the shift in wavevector space remains unexplained, we find that they correlate well with the domain symmetry. Our observation underlines the importance of symmetry as a critical variable for far-from-equilibrium dynamics.  Finally, in the last work of the thesis, we look at the possibility of triggering ultrafast spin dynamics using intense THz magnetic field pulses. Typically, ultrafast spin dynamics is triggered using femtosecond lasers in the visible range. While readily available, these pulses cause highly non-equilibrium processes to take place because of the excitation energies in the eV range, comparable to the width of a typical electronic band. The potential excitation of all possible states within a band makes it difficult to disentangle which are the fundamental physical processes responsible for ultrafast demagnetization. On the other hand, radiation in the THz frequency range (meV energy range) directly couples to the magnetization without the risk of masking key processes. However, intense THz radiation is not easily generated because the relatively long wavelengths hamper the focusing capabilities due to the diffraction limit. To address this issue, we propose a metamaterial structure that enhances the THz magnetic field component of a free-space coupled THz field by more than one order of magnitude and exceeding the 1 T value. A table-top ultrafast time-resolved Faraday microscope setup with sub-micrometer resolution was built in order to investigate this experimentally

Ultrafast spin dynamics at the nanoscale : using coherent X-ray and terahertz radiation

The field of ultrafast magnetism is driven by the growing need for faster and more efficient magnetic data storage, which comprises the vast majority of the digital information worldwide. However, after more than two decades of intense research, the understanding of the fundamental physical processes governing the transfer of angular momentum necessary for magnetic switching, is still lacking, partially hampered by the appropriate experimental tools. This situation is rapidly changing with the advent of X-ray free electron lasers (XFEL), which combine high temporal and spatial resolutions, necessary for a complete view of the physics at play.  In the first work presented in this thesis, we demonstrate the capabilities of the recently built Spectroscopy and Coherent Scattering (SCS) instrument at the European XFEL. We perform ultrafast time-resolved small angle X-ray scattering (SAXS) on nanometre magnetic domains, combining ultrafast temporal resolution with high spatial resolution. We also demonstrate X-ray holographic reconstruction of similar magnetic domains. Our results show that the efficient data acquisition for holographic imaging is possible thanks to the MHz-operation of the European XFEL, paving the way for new studies and ultimately to create femtosecond movies of magnetism at the nanoscale.  In the second work of this thesis, we describe a subsequent experiment at the SCS instrument, where we focus on the impact of symmetry breaking on the ultrafast dynamics of magnetic domains by looking at the diffracted SAXS data. Surprisingly, we observe a different ultrafast response depending on the anisotropy of the domains. We observe a clear contraction of the isotropic scattering ring in the reciprocal wavevector space (characteristic of randomly oriented domains), while no such contraction is observed in the anisotropic scattering pattern (distinctive of stripe-ordered domains). While the fundamental physical reason for the occurrence of the shift in wavevector space remains unexplained, we find that they correlate well with the domain symmetry. Our observation underlines the importance of symmetry as a critical variable for far-from-equilibrium dynamics.  Finally, in the last work of the thesis, we look at the possibility of triggering ultrafast spin dynamics using intense THz magnetic field pulses. Typically, ultrafast spin dynamics is triggered using femtosecond lasers in the visible range. While readily available, these pulses cause highly non-equilibrium processes to take place because of the excitation energies in the eV range, comparable to the width of a typical electronic band. The potential excitation of all possible states within a band makes it difficult to disentangle which are the fundamental physical processes responsible for ultrafast demagnetization. On the other hand, radiation in the THz frequency range (meV energy range) directly couples to the magnetization without the risk of masking key processes. However, intense THz radiation is not easily generated because the relatively long wavelengths hamper the focusing capabilities due to the diffraction limit. To address this issue, we propose a metamaterial structure that enhances the THz magnetic field component of a free-space coupled THz field by more than one order of magnitude and exceeding the 1 T value. A table-top ultrafast time-resolved Faraday microscope setup with sub-micrometer resolution was built in order to investigate this experimentally

Terahertz magnetic field enhancement in an asymmetric spiral metamaterial

We use finite element simulations in both the frequency and the time-domain to study the terahertz resonance characteristics of a metamaterial (MM) comprising a spiral connected to a straight arm. The MM acts as a RLC circuit whose resonance frequency can be precisely tuned by varying the characteristic geometrical parameters of the spiral: inner and outer radius, width and number of turns. We provide a simple analytical model that uses these geometrical parameters as input to give accurate estimates of the resonance frequency. Finite element simulations show that linearly polarized terahertz radiation efficiently couples to the MM thanks to the straight arm, inducing a current in the spiral, which in turn induces a resonant magnetic field enhancement at the center of the spiral. We observe a large (approximately 40 times) and uniform (over an area of ∼10 μm2) enhancement of the magnetic field for narrowband terahertz radiation with frequency matching the resonance frequency of the MM. When a broadband, single-cycle terahertz pulse propagates towards the MM, the peak magnetic field of the resulting band-passed waveform still maintains a six-fold enhancement compared to the peak impinging field. Using existing laser-based terahertz sources, our MM design allows to generate magnetic fields of the order of 2 T over a time scale of several picoseconds, enabling the investigation of nonlinear ultrafast spin dynamics in table-top experiments. Furthermore, our MM can be implemented to generate intense near-field narrowband, multi-cycle electromagnetic fields to study generic ultrafast resonant terahertz dynamics in condensed matter