Time-resolved Scanning Transmission X-ray Microscopy Research Articles

Coherent Magnons with Giant Nonreciprocity at Nanoscale Wavelengths.

Nonreciprocal wave propagation arises in systems with broken time-reversal symmetry and is key to the functionality of devices, such as isolators or circulators, in microwave, photonic, and acoustic applications. In magnetic systems, collective wave excitations known as magnon quasiparticles have so far yielded moderate nonreciprocities, mainly observed by means of incoherent thermal magnon spectra, while their occurrence as coherent spin waves (magnon ensembles with identical phase) is yet to be demonstrated. Here, we report the direct observation of strongly nonreciprocal propagating coherent spin waves in a patterned element of a ferromagnetic bilayer stack with antiparallel magnetic orientations. We use time-resolved scanning transmission X-ray microscopy (TR-STXM) to directly image the layer-collective dynamics of spin waves with wavelengths ranging from 5 μm down to 100 nm emergent at frequencies between 500 MHz and 5 GHz. The experimentally observed nonreciprocity factor of these counter-propagating waves is greater than 10 with respect to both group velocities and specific wavelengths. Our experimental findings are supported by the results from an analytic theory, and their peculiarities are further discussed in terms of caustic spin-wave focusing.

Imaging of short-wavelength spin waves in a nanometer-thick YIG/Co bilayer

We report the imaging of short-wavelength spin waves in a continuous nanometer-thick YIG film with a Co stripe patterned on top. Dynamic dipolar coupling between the YIG film and the Co stripe lowers the spin-wave wavelength when spin waves enter the YIG/Co bilayer region from the bare YIG film, causing partial reflection at the YIG/Co edge. We use time-resolved scanning transmission x-ray microscopy to image the mode conversion process down to a wavelength of 280 nm and extract the spin-wave dispersion, decay length, and magnetic damping in the YIG/Co bilayer. We also analyze spin-wave reflection from the YIG/Co edge and its dependence on the wavelength of incoming and transmitted spin waves.

Evaluation protocol for revealing magnonic contrast in TR-STXM measurements

We present a statistically motivated method to extract magnonic contrast from time-resolved scanning transmission x-ray microscopy (TR-STXM) measurements. TR-STXM is an element-specific method for resolving spin-dynamics in space and time. It offers nanometer spatial resolution and picosecond temporal resolution. The presented method makes it possible to obtain phase and amplitude profiles of spin-waves from STXM measurements. Furthermore, it allows for a rigorous transformation to reciprocal magnon k⃗-space, revealing k⃗-dependent magnon properties such as the magnon dispersion in three dimensions and for all directions of the magnetic anisotropy. We demonstrate our method using X-band ferromagnetic resonance on a micrometer-sized permalloy assembly.

Spatially-resolved dynamic sampling of different phasic magnetic resonances of nanoparticle ensembles in a magnetotactic bacterium Magnetospirillum magnetotacticum

Nanoscaled magnetic particle ensembles are promising building blocks for realizing magnon based binary logic. Element-specific real-space monitoring of magnetic resonance modes with sampling rates in the GHz regime is imperative for the experimental verification of future complex magnonic devices. Here we present the observation of different phasic magnetic resonance modes using the element-specific technique of time-resolved scanning transmission x-ray microscopy within a chain of dipolarly coupled Fe3O4 nanoparticles (40–50 nm particle size) inside a single cell of a magnetotactic bacterium Magnetospirillum magnetotacticum. The particles are probed with 25 nm resolution at the Fe L3 x-ray absorption edge in response to a microwave excitation of 4.07 GHz. A plethora of resonance modes is observed within multiple particle segments oscillating in- and out-of-phase, well resembled by micromagnetic simulations.

Realization of a magnonic analog adder with frequency-division multiplexing

Being able to accurately control the interaction of spin waves is a crucial challenge for magnonics in order to offer an alternative wave-based computing scheme for certain technological applications. Especially in neural networks and neuromorphic computing, wave-based approaches can offer significant advantages over traditional CMOS-based binary computing schemes with regard to performance and power consumption. In this work, we demonstrate precise modulation of phase- and amplitude-sensitive interference of coherent spin waves in a yttrium–iron–garnet based magnonic analog adder device, while also showing the feasibility of frequency-division multiplexing. Using time-resolved scanning transmission x-ray microscopy, the interference was directly observed, giving an important proof of concept for this kind of analog computing device and its underlying working principle. This constitutes a step toward wave-based analog computing using magnons as an information carrier.

Periodogram-Based Detection of Unknown Frequencies in Time-Resolved Scanning Transmission X-ray Microscopy.

Pump-probe time-resolved imaging is a powerful technique that enables the investigation of dynamical processes. Signal-to-noise and sampling rate restrictions normally require that cycles of an excitation are repeated many times with the final signal reconstructed using a reference. However, this approach imposes restrictions on the types of dynamical processes that can be measured, namely, that they are phase locked to a known external signal (e.g., a driven oscillation or impulse). This rules out many interesting processes such as auto-oscillations and spontaneously forming populations, e.g., condensates. In this work we present a method for time-resolved imaging, based on the Schuster periodogram, that allows for the reconstruction of dynamical processes where the intrinsic frequency is not known. In our case we use time of arrival detection of X-ray photons to reconstruct magnetic dynamics without using a priori information on the dynamical frequency. This proof-of-principle demonstration will allow for the extension of pump-probe time-resolved imaging to the important class of processes where the dynamics are not locked to a known external signal and in its presented formulation can be readily adopted for X-ray imaging and also adapted for wider use.

Nonstationary spin waves in a single rectangular permalloy microstrip under uniform magnetic excitation

Ferromagnetic resonance modes in a single rectangular ${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}$ microstrip were directly imaged using time-resolved scanning transmission x-ray microscopy combined with a phase-locked ferromagnetic resonance excitation scheme, and the findings were corroborated by micromagnetic simulations. Although under uniform excitation in a single confined microstructure typically standing spin waves are expected, all imaged spin waves showed a nonstationary character both at and off resonance, the latter being additionally detected with microantenna-based ferromagnetic resonance. The effect of the edge quality on the spin waves was observed in micromagnetic simulations.

Symmetry and curvature effects on spin waves in vortex-state hexagonal nanotubes

Analytic and numerical studies on curved magnetic nano-objects predict numerous exciting effects that can be referred to as magneto-chiral effects, which do not originate from intrinsic Dzyaloshinskii-Moriya interaction or interface-induced anisotropies. In constrast, these chiral effects stem from isotropic exchange or dipole-dipole interaction, present in all magnetic materials, which acquire asymmetric contributions in case of curved geometry of the specimen. As a result, for example, the spin-wave dispersion in round magnetic nanotubes becomes asymmetric, namely spin waves of the same frequency propagating in opposite directions along the nanotube exhibit different wavelenghts. Here, using time-resolved scanning transmission X-ray microscopy experiments, standard micromagntic simulations and a dynamic-matrix approach, we show that the spin-wave spectrum undergoes additional drastic changes when transitioning from a continuous to a discrete rotational symmetry, i.e. from round to hexagonal nanotubes, which are much easier to fabricate. The polygonal shape introduces localization of the modes both to the sharp, highly curved corners and flat edges. Moreover, due to the discrete rotational symmetry, the degenerate nature of the modes with azimuthal wave vectors known from round tubes is partly lifted, resulting in singlet and duplet modes. For comparison with our experiments, we calculate the microwave absorption from the numerically obtained mode profiles which shows that a dedicated antenna design is paramount for magnonic applications in 3D nano-structures. To our knowledge these are the first experiments directly showing real space spin-wave propagation in 3D nano objects.

Phase resolved observation of spin wave modes in antidot lattices

Antidot lattices have proven to be a powerful tool for spin wave band structure manipulation. Utilizing time-resolved scanning transmission x-ray microscopy, we are able to experimentally image edge-localized spin wave modes in an antidot lattice with a lateral confinement down to <80 nm×130 nm. At higher frequencies, spin wave dragonfly patterns formed by the demagnetizing structures of the antidot lattice are excited. Evaluating their relative phase with respect to the propagating mode within the antidot channel reveals that the dragonfly modes are not directly excited by the antenna but need the propagating mode as an energy mediator. Furthermore, micromagnetic simulations reveal that additional dispersion branches exist for a tilted external field geometry. These branches correspond to asymmetric spin wave modes that cannot be excited in a non-tilted field geometry due to the symmetry restriction. In addition to the band having a negative slope, these asymmetric modes also cause an unexpected transformation of the band structure, slightly reaching into the otherwise empty bandgap between the low frequency edge modes and the fundamental mode. The presented phase resolved investigation of spin waves is a crucial step for spin wave manipulation in magnonic crystals.

Why is my image noisy? A look into the terms contributing to a time-resolved X-ray microscopy image.

Through Monte Carlo simulations, we investigate how various experimental parameters can influence the quality of time-resolved scanning transmission X-ray microscopy images. In particular, the effect of the X-ray photon flux, of the thickness of the investigated samples, and of the frequency of the dynamical process under investigation on the resulting time-resolved image are investigated. The ideal sample and imaging conditions that allow for an optimal image quality are then identifed.

Time-resolved imaging of Œrsted field induced magnetization dynamics in cylindrical magnetic nanowires

Recent studies in three-dimensional spintronics propose that the Œrsted field plays a significant role in cylindrical nanowires. However, there is no direct report on its impact on magnetic textures. Here, we use time-resolved scanning transmission x-ray microscopy to image the dynamic response of magnetization in cylindrical Co30Ni70 nanowires subjected to nanosecond Œrsted field pulses. We observe the tilting of longitudinally magnetized domains toward the azimuthal Œrsted field direction and create a robust model to reproduce the differential magnetic contrasts and extract the angle of tilt. Furthermore, we report the compression and expansion, or breathing, of a Bloch-point domain wall that occurs when weak pulses with opposite signs are applied. We expect that this work lays the foundation for and provides an incentive to further studying complex and fascinating magnetization dynamics in nanowires, especially the predicted ultra-fast domain wall motion and associated spin wave emissions.

Spin-Wave Emission from Vortex Cores under Static Magnetic Bias Fields.

We studied the influence of a static in-plane magnetic field on the alternating-field-driven emission of nanoscale spin waves from magnetic vortex cores. Time-resolved scanning transmission X-ray microscopy was used to image spin waves in disk structures of synthetic ferrimagnets and single ferromagnetic layers. For both systems, it was found that an increasing magnetic bias field continuously displaces the wave-emitting vortex core from the center of the disk toward its edge without noticeably altering the spin-wave dispersion relation. In the case of the single-layer disk, an anisotropic lateral expansion of the core occurs at higher magnetic fields, which leads to a directional rather than radial-isotropic emission and propagation of waves. Micromagnetic simulations confirm these findings and further show that focusing effects occur in such systems, depending on the shape of the core and controlled by the static magnetic bias field.

Competing spin wave emission mechanisms revealed by time-resolved x-ray microscopy

Spin wave emission and propagation in magnonic waveguides represent a highly promising alternative for beyond-CMOS computing. It is therefore all the more important to fully understand the underlying physics of the emission process. Here, we use time-resolved scanning transmission x-ray microscopy to directly image the formation process of the globally excited local emission of spin waves in a permalloy waveguide at the nanoscale. Thereby, we observe spin wave emission from the corner of the waveguide as well as from a local oscillation of a domain-wall-like structure within the waveguide. Additionally, an isofrequency contour analysis is used to fully explain the origin of quasicylindrical spin wave excitation from the corner and its concurrent nonreflection and nonrefraction at the domain interface. This study is complemented by micromagnetic simulations which perfectly fit the experimental findings. Thus, we clarify the fundamental question of the emission mechanisms in magnonic waveguides which lay the basis for future magnonic operations.

Time-resolved visualization of the magnetization canting induced by field-like spin–orbit torques

We report on the use of time-resolved scanning transmission x-ray microscopy imaging for the visualization of the dynamical canting of the magnetization induced by field-like spin–orbit torques in a perpendicularly magnetized microwire. In particular, we show how the contributions to the dynamical canting of the magnetization arising from the field-like spin–orbit torque can be separated from the heating-induced effects on the magnetization of the microwire. This method will allow for the imaging of the dynamical effects of spin–orbit torques in device-like structures and buried layers.

Time-of-arrival detection for time-resolved scanning transmission X-ray microscopy imaging.

A setup for time-resolved scanning transmission X-ray microscopy imaging is presented, which allows for an increase in the temporal resolution without the requirement of operating the synchrotron light source with low-α optics through the measurement of the time-of-arrival of the X-ray photons. Measurements of two filling patterns in hybrid mode of the Swiss Light Source are presented as a first proof-of-principle and benchmark for the performances of this new setup. From these measurements, a temporal resolution on the order of 20-30 ps could be determined.

Current-induced dynamical tilting of chiral domain walls in curved microwires

We report on the investigation of current-induced domain wall motion of Néel domain walls in perpendicularly magnetized microwires with curved geometries in the flow regime. The investigation was performed by time-resolved scanning transmission x-ray microscopy. In particular, we studied the dynamical tilting of the Néel domain walls, observing that an asymmetric behavior in the domain wall tilt appears upon an inversion of the polarity of the current pulse driving the motion, an effect not predicted by state-of-the-art theories and micromagnetic modeling.

Direct observation of coherent magnons with suboptical wavelengths in a single-crystalline ferrimagnetic insulator

In the field of magnetism, spin waves are a subject of great interest for fundamental and application-oriented research. Time-resolved scanning transmission x-ray microscopy, a technique that allows for direct spin-wave imaging below the optical resolution limit, is usually limited to thin layers deposited on x-ray transparent membranes. Here, the authors report on a preparation routine that makes single-crystalline materials accessible to this powerful technique. The latter is subsequently implemented on the ferrimagnetic insulator yttrium iron garnet, where spin waves down to 100-nm wavelength are observed.

Nanoscale X-ray imaging of spin dynamics in yttrium iron garnet

Time-resolved scanning transmission x-ray microscopy has been used for the direct imaging of spin-wave dynamics in a thin film yttrium iron garnet (YIG) with sub-200 nm spatial resolution. Application of this x-ray transmission technique to single-crystalline garnet films was achieved by extracting a lamella (13×5×0.185 μm3) of the liquid phase epitaxy grown YIG thin film out of a gadolinium gallium garnet substrate. Spin waves in the sample were measured along the Damon-Eshbach and backward volume directions of propagation at gigahertz frequencies and with wavelengths in a range between 200 nm and 10 μm. The results were compared to theoretical models. Here, the widely used approximate dispersion equation for dipole-exchange spin waves proved to be insufficient for describing the observed Damon-Eshbach type modes. For achieving an accurate description, we made use of the full analytical theory taking mode-hybridization effects into account.

Extracting the Dynamic Magnetic Contrast in Time-Resolved X-ray Transmission Microscopy.

Using a time-resolved detection scheme in scanning transmission X-ray microscopy (STXM), we measured element resolved ferromagnetic resonance (FMR) at microwave frequencies up to 10 GHz and a spatial resolution down to 20 nm at two different synchrotrons. We present different methods to separate the contribution of the background from the dynamic magnetic contrast based on the X-ray magnetic circular dichroism (XMCD) effect. The relative phase between the GHz microwave excitation and the X-ray pulses generated by the synchrotron, as well as the opening angle of the precession at FMR can be quantified. A detailed analysis for homogeneous and inhomogeneous magnetic excitations demonstrates that the dynamic contrast indeed behaves as the usual XMCD effect. The dynamic magnetic contrast in time-resolved STXM has the potential be a powerful tool to study the linear and nonlinear, magnetic excitations in magnetic micro- and nano-structures with unique spatial-temporal resolution in combination with element selectivity.

Nanoscale spin-wave circuits based on engineered reconfigurable spin-textures

Magnonics is gaining momentum as an emerging technology for information processing. The wave character and Joule heating-free propagation of spin-waves hold promises for highly efficient computing platforms, based on integrated magnonic circuits. The realization of such nanoscale circuitry is crucial, although extremely challenging due to the difficulty of tailoring the nanoscopic magnetic properties with conventional approaches. Here we experimentally realize a nanoscale reconfigurable spin-wave circuitry by using patterned spin-textures. By space and time-resolved scanning transmission X-ray microscopy imaging, we directly visualize the channeling and steering of propagating spin-waves in arbitrarily shaped nanomagnonic waveguides, with no need for external magnetic fields or currents. Furthermore, we demonstrate a prototypic circuit based on two converging nanowaveguides, allowing for the tunable spatial superposition and interference of confined spin-waves modes. This work paves the way to the use of engineered spin-textures as building blocks of spin-wave based computing devices.