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Magnons, the quanta of spin waves, are magnetic excitations of matter spanning through the entire crystal's Brillouin zone and covering a wide range of frequencies ranging from sub-gigahertz to hundreds of terahertz. Magnons play a crucial role in many condensed matter phenomena, such as the reduction of saturation magnetization with increasing temperature or Bose-Einstein condensation. However, current experimental techniques cannot resolve magnons with wavevectors between 30 and 300$\,$rad$\,\mu$m$^{-1}$. In this letter, we address this gap by tailoring the light in Brillouin light scattering process with dielectric periodic nanoresonators and thus gaining access to the previously unmeasurable spin waves with full wavevector resolution using table-top optical setup. Filling this gap can stimulate further experimental investigations of the fundamental phenomena associated with magnons but also stimulate the application of magnonics in computational and microwave devices. In addition, the same methodology can be applied to other excitations of matter, such as phonons, opening up new possibilities in e.g. mechanobiological studies.

Modern quantum technologies and hybrid quantum systems offer the opportunity to utilize magnons on the level of single excitations. Long lifetimes, low decoherence rates, and a strong coupling rate to other subsystems propose the ferrimagnet yttrium iron garnet (YIG), grown on a gadolinium gallium garnet (GGG) substrate, as a suitable platform to host magnonic quantum states. However, the magnetic damping at cryogenic temperatures significantly increases due to the paramagnetic character and the highly inhomogeneous stray field of GGG, as recent experiments and simulations pointed out. Here, we report on temperature dependent ferromagnetic resonance (FMR) spectroscopy studies in YIG-GGG thin-films with different sample geometries. We experimentally demonstrate how to eliminate the asymmetric stray field-induced linewidth broadening via microstructuring of the YIG film. Additionally, our experiments reveal evidence of a non-Gilbert like behavior of the linewidth at cryogenic temperatures, independent of the inhomogeneous GGG stray field., Comment: 8 pages, 3 figures

We demonstrate a magnonic diode based on a bilayer structure of Yttrium Iron Garnet (YIG) and Cobalt Iron Boron (CoFeB). The bilayer exhibits pronounced non-reciprocal spin-wave propagation, enabled by dipolar coupling and the magnetic properties of the two layers. The YIG layer provides low damping and efficient spin-wave propagation, while the CoFeB layer introduces strong magnetic anisotropy, critical for achieving diode functionality. Experimental results, supported by numerical simulations, show unidirectional propagation of Magnetostatic Surface Spin Waves (MSSW), significantly suppressing backscattered waves. This behavior was confirmed through wavevector-resolved and micro-focused Brillouin Light Scattering measurements and is supported by numerical simulations. The proposed YIG/SiO$_2$/CoFeB bilayer magnonic diode demonstrates the feasibility of leveraging non-reciprocal spin-wave dynamics for functional magnonic devices, paving the way for energy-efficient, wave-based signal processing technologies.

Quantum magnonics aims to exploit the quantum mechanical properties of magnons for nanoscale quantum information technologies. Ferrimagnetic yttrium iron garnet (YIG), which offers the longest magnon lifetimes, is a key material typically grown on gadolinium gallium garnet (GGG) substrates for structural compatibility. However, the increased magnetic damping in YIG/GGG systems below 50$\,$K poses a challenge for quantum applications. Here, we study the damping in a 97$\,$nm-thick YIG film on a 500$\,\mu$m-thick GGG substrate at temperatures down to 30$\,$mK using ferromagnetic resonance (FMR) spectroscopy. We show that the dominant physical mechanism for the observed tenfold increase in FMR linewidth at millikelvin temperatures is the non-uniform bias magnetic field generated by the partially magnetized paramagnetic GGG substrate. Numerical simulations and analytical theory show that the GGG-driven linewidth enhancement can reach up to 6.7 times. In addition, at low temperatures and frequencies above 18$\,$GHz, the FMR linewidth deviates from the viscous Gilbert-damping model. These results allow the partial elimination of the damping mechanisms attributed to GGG, which is necessary for the advancement of solid-state quantum technologies.

Although micro-focused Brillouin light scattering (BLS) has been used for more than twenty years, it lacks a complete theoretical description. This complicates the analysis of experimental data and significantly limits the information that can be obtained. To fill this knowledge gap, we have developed a semi-analytical model based on the mesoscopic continuous medium approach. The model consists of the following steps: calculation of the incident electric field and the dynamic susceptibility, calculation of the induced polarisation, and calculation of the emitted electric field and its propagation towards the detector. We demonstrate the model on the examples of the measurements of thermal and coherently excited spin waves. However, the used approach is general and can describe any micro-focused Brillouin light scattering experiment. The model can also bring new analytical approaches to mechanobiology experiments or to characterization of acoustic wave based devices.

Quantum magnonics investigates the quantum-mechanical properties of magnons such as quantum coherence or entanglement for solid-state quantum information technologies at the nanoscale. The most promising material for quantum magnonics is the ferrimagnetic yttrium iron garnet (YIG), which hosts magnons with the longest lifetimes. YIG films of the highest quality are grown on a paramagnetic gadolinium gallium garnet (GGG) substrate. The literature has reported that ferromagnetic resonance (FMR) frequencies of YIG/GGG decrease at temperatures below 50 K despite the increase in YIG magnetization. We investigated a 97 nm-thick YIG film grown on 500 $\mathrm{\mu}$m-thick GGG substrate through a series of experiments conducted at temperatures as low as 30 mK, and using both analytical and numerical methods. Our findings suggest that the primary factor contributing to the FMR frequency shift is the stray magnetic field created by the partially magnetized GGG substrate. This stray field is antiparallel to the applied external field and is highly inhomogeneous, reaching up to 40 mT in the center of the sample. At temperatures below 500 mK, the GGG field exhibits a saturation that cannot be described by the standard Brillouin function for a paramagnet. Including the calculated GGG field in the analysis of the FMR frequency versus temperature dependence allowed the determination of the cubic and uniaxial anisotropies. We find that the total anisotropy increases more than three times with the decrease in temperature down to 2 K. Our findings enable accurate predictions of the YIG/GGG magnetic systems behavior at low and ultra-low millikelvin temperatures, crucial for developing quantum magnonic devices.

We report on experimental observation of unidirectional propagation of zero-momentum magnons in synthetic antiferromagnet consisting of strained CoFeB/Ru/CoFeB trilayer. Inherent non-reciprocity of spin waves in synthetic antiferromagnets with uniaxial anisotropy results in smooth and monotonous dispersion relation around Gamma point, where the direction of the phase velocity is reversed, while the group velocity direction is conserved. The experimental observation of this phenomenon by intensity-, phase-, and time-resolved Brillouin light scattering microscopy is corroborated by analytical models and micromagnetic simulations.

We study theoretically and experimentally the process of Brillouin light scattering on an array of silicon disks on a thin Permalloy layer. We show that phase-resolved Brillouin light scattering microscopy performed on an array of weakly interacting dielectric nanoresonators can detect nanoscale waves and measure their dispersion. In our experiment, we were able to map the evolution of the phase of the spin wave with a wavelength of 209 nm with a precision of 6 nm. These results demonstrate the feasibility of all-optical phase-resolved characterization of nanoscale spin waves.

Performing propagating spin-wave spectroscopy of thin films at millikelvin temperatures is the next step towards the realisation of large-scale integrated magnonic circuits for quantum applications. Here we demonstrate spin-wave propagation in a $100\,\mathrm{nm}$-thick yttrium-iron-garnet film at the temperatures down to $45 \,\mathrm{mK}$, using stripline nanoantennas deposited on YIG surface for the electrical excitation and detection. The clear transmission characteristics over the distance of $10\,\mu \mathrm{m}$ are measured and the subtracted spin-wave group velocity and the YIG saturation magnetisation agree well with the theoretical values. We show that the gadolinium-gallium-garnet substrate influences the spin-wave propagation characteristics only for the applied magnetic fields beyond $75\,\mathrm{mT}$, originating from a GGG magnetisation up to $47 \,\mathrm{kA/m}$ at $45 \,\mathrm{mK}$. Our results show that the developed fabrication and measurement methodologies enable the realisation of integrated magnonic quantum nanotechnologies at millikelvin temperatures., Comment: 6 pages, 5 figures

Spin waves are studied intensively for their intriguing properties and potential use in future technology platforms for the transfer and processing of information and microwave signals. The development of devices and materials for spin-wave systems requires a lot of measurement time and effort, and thus increasing the measurement throughput by extending the instrumentation capabilities is of the essence. In this letter, we report on a new and straightforward approach to increase the measurement throughput by fully exploiting the wideband detection nature of the Brillouin light scattering technique in single-shot experiments using a white-noise RF generator., Comment: 5 pages + 3 supplementary pages, 4 figures, 3 supplementary figures

Spin waves are ideal candidates for wave-based computing, but the construction of magnetic circuits is blocked by a lack of an efficient mechanism to excite long-running exchange spin waves with normalised amplitudes. Here, we solve the challenge by exploiting the deeply nonlinear phenomena of forward-volume spin waves in 200 nm wide nanoscale waveguides and validate our concept with microfocused Brillouin light scattering spectroscopy. An unprecedented nonlinear frequency shift of >2 GHz is achieved, corresponding to a magnetisation precession angle of 55{\deg} and enabling the excitation of exchange spin waves with a wavelength of down to ten nanometres with an efficiency of >80%. The amplitude of the excited spin waves is constant and independent of the input microwave power due to the self-locking nonlinear shift, enabling robust adjustment of the spin wave amplitudes in future on-chip magnonic integrated circuits., Comment: 21 pages, 5 figures

Magnonics is a prospective beyond CMOS technology which uses magnons, the quanta of spin waves, for low-power information processing. Many magnonic concepts and devices were recently demonstrated at macro- and microscale, and now these concepts need to be realized at nanoscale. Brillouin light scattering spectroscopy and microscopy (BLS) has become a standard technique for spin wave visualization and characterization, and enabled many pioneering magnonic experiments. However, due to its fundamental limit in maximum detectable magnon momentum, the conventional BLS cannot be used to detect nanoscale spin waves. Here we show that optically induced Mie resonances in dielectric nanoparticles can be used to extend the range of accessible spin wave wavevectors beyond the BLS fundamental limit. The method is universal and can be used in many magnonic experiments dealing with thermally excited as well as coherently excited high-momentum, short-wavelength spin waves. This discovery significantly extends the usability and relevance of the BLS technique for nanoscale magnonic research.

Magnonics is seen nowadays as a candidate technology for energy-efficient data processing in classical and quantum systems. Pronounced nonlinearity, anisotropy of dispersion relations and phase degree of freedom of spin waves require advanced methodology for probing spin waves at room as well as at mK temperatures. Yet, the use of the established optical techniques like Brillouin light scattering (BLS) or magneto optical Kerr effect (MOKE) at ultra-low temperatures is forbiddingly complicated. By contrast, microwave spectroscopy can be used at all temperatures but is usually lacking spatial and wavenumber resolution. Here, we develop a variable-gap propagating spin-wave spectroscopy (VG-PSWS) method for the deduction of the dispersion relation of spin waves in wide frequency and wavenumber range. The method is based on the phase-resolved analysis of the spin-wave transmission between two antennas with variable spacing, in conjunction with theoretical data treatment. We validate the method for the in-plane magnetized CoFeB and YIG thin films in $k\perp B$ and $k\parallel B$ geometries by deducing the full set of material and spin-wave parameters, including spin-wave dispersion, hybridization of the fundamental mode with the higher-order perpendicular standing spin-wave modes and surface spin pinning. The compatibility of microwaves with low temperatures makes this approach attractive for cryogenic magnonics at the nanoscale., Comment: 9 pages, 5 figures

Curvature-induced effects allow us to tailor the static and dynamic response of a magnetic system with a high degree of freedom. We study corrugated magnonic waveguides deposited on a sinusoidally modulated substrate prepared by focused electron beam deposition. The surface curvature in films with thicknesses comparable to the amplitude of modulation locally modifies the contributions of dipolar and exchange energies and results in an effective anisotropy term which can be tuned on-demand based on the exact geometry. We show, by Brillouin light scattering microscopy, that without the presence of an external magnetic field, spin waves propagate over a distance 10$\times$larger in the corrugated waveguide than in the planar waveguide. Further, we analyze the influence of the modulation amplitude on spin-wave propagation and conclude that for moderate modulation amplitudes, the spin-wave decay length is not affected. For larger amplitudes, the decay length decreases linearly with increasing modulation., Comment: 5 pages, 4 figures

Skyrmions and antiskyrmions are topologically protected spin structures with opposite topological charge. Particularly in coexisting phases, these two types of magnetic quasi-particles may show fascinating physics and potential for spintronic devices. While skyrmions are observed in a wide range of materials, until now antiskyrmions were exclusive to materials with D2d symmetry. In this work, we show first and second-order antiskyrmions stabilized by magnetic dipole-dipole interaction in Fe/Gd-based multilayers. We modify the magnetic properties of the multilayers by Ir insertion layers. Using Lorentz transmission electron microscopy imaging, we observe coexisting antiskyrmions, Bloch skyrmions, and type-2 bubbles and determine the range of material properties and magnetic fields where the different spin objects form and dissipate. We perform micromagnetic simulations to obtain more insight into the studied system and conclude that the reduction of saturation magnetization and uniaxial anisotropy leads to the existence of this zoo of different spin objects and that they are primarily stabilized by dipolar interaction.

Spin waves have the potential to be used as a new platform for data transfer and processing as they can reach wavelengths in the nanometer range and frequencies in the terahertz range. To realize a spin-wave device, it is essential to be able to manipulate the amplitude as well as the phase of spin waves. Several theoretical and recently also experimental works have shown that the spin-wave phase can be manipulated by the transmission through a domain wall (DW). Here, we study propagation of spin waves through a DW by means of micro-focused Brillouin light scattering microscopy ($\mu$BLS). The acquired 2D spin-wave intensity maps reveal that spin-wave transmission through a N\'eel DW is influenced by a topologically enforced circular Bloch line in the DW center and that the propagation regime depends on the spin-wave frequency. In the first regime, two spin-wave beams propagating around the circular Bloch line are formed, whereas in the second regime, spin waves propagate in a single central beam through the circular Bloch line. Phase-resolved $\mu$BLS measurements reveal a phase shift upon transmission through the domain wall for both regimes. Micromagnetic modelling of the transmitted spin waves unveils a distortion of their phase fronts which needs to be taken into account when interpreting the measurements and designing potential devices. Moreover, we show, by means of micromagnetic simulations, that an external magnetic field can be used to move the circular Bloch line within the DW and to manipulate spin-wave propagation., Comment: 5 pages, 4 figures

Metastable face-centered-cubic Fe78Ni22 thin films grown on Cu(001) substrates are excellent candidates for focused ion beam direct writing of magnonic structures due to their favorable magnetic properties after ion-beam-induced transformation. The focused ion beam transforms the originally nonmagnetic fcc phase into the ferromagnetic bcc phase with additional control over the direction of uniaxial magnetic in-plane anisotropy. The magnetocrystalline anisotropy in transformed areas is strong enough to stabilize the magnetization in transverse direction to the long axis of narrow waveguides. Therefore, it is possible to propagate spin waves in these waveguides without the presence of an external magnetic field in the favorable Demon-Eshbach geometry. Phase-resolved micro-focused Brillouin light scattering yields the dispersion relation of these waveguides in zero as well as in nonzero external magnetic fields.

We have studied the growth of metastable face-centered-cubic, non-magnetic Fe78Ni22 thin films on silicon substrates. These films undergo a magnetic (paramagnetic to ferromagnetic) and structural (fcc to bcc) phase transformation upon ion beam irradiation and thus can serve as a template for direct writing of magnetic nanostructures by the focused ion beam. So far, these films were prepared only on single crystal Cu(100) substrates. We show that transformable Fe78Ni22 thin films can also be prepared on a hydrogen-terminated Si(100) with a 130-nm-thick Cu(100) buffer layer. The H-Si(100) substrates can be prepared by hydrofluoric acid etching or by annealing at 1200{\deg}C followed by adsorption of atomic hydrogen. The Cu(100) buffer layer and Fe78Ni22 fcc metastable thin film were deposited by thermal evaporation in an ultra-high vacuum. The films were consequently transformed in-situ by 4keV Ar+ ion irradiation and ex-situ by a 30 keV Ga+ focused ion beam, and their magnetic properties were studied by magneto-optical Kerr effect magnetometry. The substitution of expensive copper single crystal substrate by standard silicon wafers dramatically expands application possibilities of metastable paramagnetic thin films for focused ion beam direct magnetic patterning.

Focused ion beam irradiation of metastable Fe$_{78}$Ni$_{22}$ thin films grown on Cu(100) substrates is used to create ferromagnetic, body-centered-cubic patterns embedded into paramagnetic, face-centered-cubic surrounding. The structural and magnetic phase transformation can be controlled by varying parameters of the transforming gallium ion beam. The focused ion beam parameters as ion dose, number of scans, and scanning direction can be used not only to control a degree of transformation, but also to change the otherwise four-fold in-plane magnetic anisotropy into the uniaxial anisotropy along specific crystallographic direction. This change is associated with a preferred growth of specific crystallographic domains. The possibility to create magnetic patterns with continuous magnetization transitions and at the same time to create patterns with periodical changes in magnetic anisotropy makes this system an ideal candidate for rapid prototyping of a large variety of nanostructured samples. Namely spin-wave waveguides and magnonic crystals can be easily combined into complex devices in a single fabrication step., Comment: 11 pages, 4 figures

We have used time-resolved x-ray photoemission electron microscopy to investigate the magnetization dynamics induced by nanosecond current pulses in NiFe/Cu/Co nanostripes. A large tilt of the NiFe magnetization in the direction transverse to the stripe is observed during the pulses. We show that this effect cannot be quantitatively understood from the amplitude of the Oersted field and the shape anisotropy. High frequency oscillations observed at the onset of the pulses are attributed to precessional motion of the NiFe magnetization about the effective field. We discuss the possible origins of the large magnetization tilt and the potential implications of the static and dynamic effects of the Oersted field on current-induced domain wall motion in such stripes., Comment: Published in Phys. Rev. B 83, 020406 (2011) (Rapid Communications)