Magnetic anisotropy and GGG substrate stray field in YIG films down to millikelvin temperatures.

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 µm-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 crystallographic 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 ultralow millikelvin temperatures, crucial for developing quantum magnonic devices.

Three-dimensional magnetic nanotextures with high-order vorticity in soft magnetic wireframes.

Additive nanotechnology enable curvilinear and three-dimensional (3D) magnetic architectures with tunable topology and functionalities surpassing their planar counterparts. Here, we experimentally reveal that 3D soft magnetic wireframe structures resemble compact manifolds and accommodate magnetic textures of high order vorticity determined by the Euler characteristic, χ. We demonstrate that self-standing magnetic tetrapods (homeomorphic to a sphere; χ = + 2) support six surface topological solitons, namely four vortices and two antivortices, with a total vorticity of + 2 equal to its Euler characteristic. Alternatively, wireframe structures with one loop (homeomorphic to a torus; χ = 0) possess equal number of vortices and antivortices, which is relevant for spin-wave splitters and 3D magnonics. Subsequent introduction of n holes into the wireframe geometry (homeomorphic to an n-torus; χ < 0) enables the accommodation of a virtually unlimited number of antivortices, which suggests their usefulness for non-conventional (e.g., reservoir) computation. Furthermore, complex stray-field topologies around these objects are of interest for superconducting electronics, particle trapping and biomedical applications.

Steering of Vortices by Magnetic Field Tilting in Open Superconductor Nanotubes.

In planar superconductor thin films, the places of nucleation and arrangements of moving vortices are determined by structural defects. However, various applications of superconductors require reconfigurable steering of fluxons, which is hard to realize with geometrically predefined vortex pinning landscapes. Here, on the basis of the time-dependent Ginzburg-Landau equation, we present an approach for the steering of vortex chains and vortex jets in superconductor nanotubes containing a slit. The idea is based on the tilting of the magnetic field B at an angle α in the plane perpendicular to the axis of a nanotube carrying an azimuthal transport current. Namely, while at α=0∘, vortices move paraxially in opposite directions within each half-tube; an increase in α displaces the areas with the close-to-maximum normal component |Bn| to the close(opposite)-to-slit regions, giving rise to descending (ascending) branches in the induced-voltage frequency spectrum fU(α). At lower B values, upon reaching the critical angle αc, the close-to-slit vortex chains disappear, yielding fU of the nf1 type (n≥1: an integer; f1: the vortex nucleation frequency). At higher B values, fU is largely blurry because of multifurcations of vortex trajectories, leading to the coexistence of a vortex jet with two vortex chains at α=90∘. In addition to prospects for the tuning of GHz-frequency spectra and the steering of vortices as information bits, our findings lay the foundation for on-demand tuning of vortex arrangements in 3D superconductor membranes in tilted magnetic fields.

Highly sensitive single-molecule detection of macromolecule ion beams.

The analysis of proteins in the gas phase benefits from detectors that exhibit high efficiency and precise spatial resolution. Although modern secondary electron multipliers already address numerous analytical requirements, additional methods are desired for macromolecules at energies lower than currently used in post-acceleration detection. Previous studies have proven the sensitivity of superconducting detectors to high-energy particles in time-of-flight mass spectrometry. Here, we demonstrate that superconducting nanowire detectors are exceptionally well suited for quadrupole mass spectrometry and exhibit an outstanding quantum yield at low-impact energies. At energies as low as 100 eV, the sensitivity of these detectors surpasses conventional ion detectors by three orders of magnitude, and they offer the possibility to discriminate molecules by their impact energy and charge. We demonstrate three developments with these compact and sensitive devices, the recording of 2D ion beam profiles, photochemistry experiments in the gas phase, and advanced cryogenic electronics to pave the way toward highly integrated detectors.

3D Magnonic Conduits by Direct Write Nanofabrication.

Magnonics is a rapidly developing domain of nanomagnetism, with application potential in information processing systems. Realisation of this potential and miniaturisation of magnonic circuits requires their extension into the third dimension. However, so far, magnonic conduits are largely limited to thin films and 2D structures. Here, we introduce 3D magnonic nanoconduits fabricated by the direct write technique of focused-electron-beam induced deposition (FEBID). We use Brillouin light scattering (BLS) spectroscopy to demonstrate significant qualitative differences in spatially resolved spin-wave resonances of 2D and 3D nanostructures, which originates from the geometrically induced non-uniformity of the internal magnetic field. This work demonstrates the capability of FEBID as an additive manufacturing technique to produce magnetic 3D nanoarchitectures and presents the first report of BLS spectroscopy characterisation of FEBID conduits.

Topological transitions in ac/dc-driven superconductor nanotubes.

Extending of nanostructures into the third dimension has become a major research avenue in condensed-matter physics, because of geometry- and topology-induced phenomena. In this regard, superconductor 3D nanoarchitectures feature magnetic field inhomogeneity, non-trivial topology of Meissner currents and complex dynamics of topological defects. Here, we investigate theoretically topological transitions in the dynamics of vortices and slips of the phase of the order parameter in open superconductor nanotubes under a modulated transport current. Relying upon the time-dependent Ginzburg-Landau equation, we reveal two distinct voltage regimes when (i) a dominant part of the tube is in either the normal or superconducting state and (ii) a complex interplay between vortices, phase-slip regions and screening currents determines a rich FFT voltage spectrum. Our findings unveil novel dynamical states in superconductor open nanotubes, such as paraxial and azimuthal phase-slip regions, their branching and coexistence with vortices, and allow for control of these states by superimposed dc and ac current stimuli.

New Dimension in Magnetism and Superconductivity: 3D and Curvilinear Nanoarchitectures.

Traditionally, the primary field, where curvature has been at the heart of research, is the theory of general relativity. In recent studies, however, the impact of curvilinear geometry enters various disciplines, ranging from solid-state physics over soft-matter physics, chemistry, and biology to mathematics, giving rise to a plethora of emerging domains such as curvilinear nematics, curvilinear studies of cell biology, curvilinear semiconductors, superfluidity, optics, 2D van der Waals materials, plasmonics, magnetism, and superconductivity. Here, the state of the art is summarized and prospects for future research in curvilinear solid-state systems exhibiting such fundamental cooperative phenomena as ferromagnetism, antiferromagnetism, and superconductivity are outlined. Highlighting the recent developments and current challenges in theory, fabrication, and characterization of curvilinear micro- and nanostructures, special attention is paid to perspective research directions entailing new physics and to their strong application potential. Overall, the perspective is aimed at crossing the boundaries between the magnetism and superconductivity communities and drawing attention to the conceptual aspects of how extension of structures into the third dimension and curvilinear geometry can modify existing and aid launching novel functionalities. In addition, the perspective should stimulate the development and dissemination of research and development oriented techniques to facilitate rapid transitions from laboratory demonstrations to industry-ready prototypes and eventual products.

Control of the Bose-Einstein Condensation of Magnons by the Spin Hall Effect.

Previously, it has been shown that rapid cooling of yttrium-iron-garnet-platinum nanostructures, preheated by an electric current sent through the Pt layer, leads to overpopulation of a magnon gas and to subsequent formation of a Bose-Einstein condensate (BEC) of magnons. The spin Hall effect (SHE), which creates a spin-polarized current in the Pt layer, can inject or annihilate magnons depending on the electric current and applied field orientations. Here we demonstrate that the injection or annihilation of magnons via the SHE can prevent or promote the formation of a rapid cooling-induced magnon BEC. Depending on the current polarity, a change in the BEC threshold of -8% and +6% was detected. These findings demonstrate a new method to control macroscopic quantum states, paving the way for their application in spintronic devices.

Spin-wave spectroscopy of individual ferromagnetic nanodisks.

The increasing demand for nanoscale magnetic devices requires development of 3D magnetic nanostructures. In this regard, focused electron beam induced deposition (FEBID) is a technique of choice for direct-writing of complex nano-architectures with applications in nanomagnetism, magnon spintronics, and superconducting electronics. However, intrinsic properties of nanomagnets are often poorly known and can hardly be assessed by local optical probe techniques. Here, an original spatially resolved approach is demonstrated for spin-wave spectroscopy of individual circular magnetic elements with sample volumes down to about 10-3 µm3. The key component of the setup is a coplanar waveguide whose microsized central part is placed over a movable substrate with well-separated CoFe-FEBID nanodisks which exhibit standing spin-wave resonances. The circular symmetry of the disks allows for the deduction of the saturation magnetization and the exchange stiffness of the material using an analytical theory. A good correspondence between the results of analytical calculations and micromagnetic simulations is revealed, indicating a validity of the used analytical model going beyond the initial thin-disk approximation used in the theoretical derivation. The presented approach is especially valuable for the characterization of direct-write magnetic elements opening new horizons for 3D nanomagnetism and magnonics.

Writing 3D Nanomagnets Using Focused Electron Beams.

Focused electron beam induced deposition (FEBID) is a direct-write nanofabrication technique able to pattern three-dimensional magnetic nanostructures at resolutions comparable to the characteristic magnetic length scales. FEBID is thus a powerful tool for 3D nanomagnetism which enables unique fundamental studies involving complex 3D geometries, as well as nano-prototyping and specialized applications compatible with low throughputs. In this focused review, we discuss recent developments of this technique for applications in 3D nanomagnetism, namely the substantial progress on FEBID computational methods, and new routes followed to tune the magnetic properties of ferromagnetic FEBID materials. We also review a selection of recent works involving FEBID 3D nanostructures in areas such as scanning probe microscopy sensing, magnetic frustration phenomena, curvilinear magnetism, magnonics and fluxonics, offering a wide perspective of the important role FEBID is likely to have in the coming years in the study of new phenomena involving 3D magnetic nanostructures.

Crystalline Niobium Carbide Superconducting Nanowires Prepared by Focused Ion Beam Direct Writing.

Superconducting planar nanostructures are widely used in applications, e.g., for highly sensitive magnetometers and in basic research, e.g., to study finite size effects or vortex dynamics. In contrast, 3D superconducting nanostructures, despite their potential in quantum information processing and nanoelectronics, have been addressed only in a few pioneering experiments. This is due to the complexity of fabricating 3D nanostructures by conventional techniques such as electron-beam lithography and to the scarce number of superconducting materials available for direct-writing techniques, which enable the growth of 3D free-standing nanostructures. Here, we present a comparative study of planar nanowires and free-standing 3D nanowires fabricated by focused electron- and ion (Ga+)-beam induced deposition (FEBID and FIBID) using the precursor Nb(NMe2)3(N- t-Bu). FEBID nanowires contain about 67 atomic percent C, 22 atomic percent N, and 11 atomic percent Nb, while FIBID samples are composed of 43 atomic percent C, 13 atomic percent N, 15.5 atomic percent Ga, and 28.5 atomic percent Nb. Transmission electron microscopy shows that FEBID samples are amorphous, while FIBID samples exhibit a fcc NbC polycrystalline structure, with grains about 15-20 nm in diameter. Electrical transport measurements show that FEBID nanowires are highly resistive following a variable-range-hopping behavior. In contradistinction, FIBID planar nanowires become superconducting at Tc ≈ 5 K. In addition, the critical temperature of free-standing 3D nanowires is as high as Tc ≈ 11 K, which is close to the value of bulk NbC. In conclusion, FIBID-NbC is a promising material for the fabrication of superconducting nanowire single-photon detectors (SNSPD) and for the development of 3D superconductivity with applications in quantum information processing and nanoelectronics.

Spin-Wave Phase Inverter upon a Single Nanodefect.

Local modification of magnetic properties of nanoelements is a key to design future-generation magnonic devices in which information is carried and processed via spin waves. One of the biggest challenges here is to fabricate simple and miniature phase-controlling elements with broad tunability. Here, we successfully realize such spin-wave phase shifters upon a single nanogroove milled by a focused ion beam in a Co-Fe microsized magnonic waveguide. By varying the groove depth and the in-plane bias magnetic field, we continuously tune the spin-wave phase and experimentally evidence a complete phase inversion. The microscopic mechanism of the phase shift is based on the combined action of the nanogroove as a geometrical defect and the lower spin-wave group velocity in the waveguide under the groove where the magnetization is reduced due to the incorporation of Ga ions during the ion-beam milling. The proposed phase shifter can easily be on-chip integrated with spin-wave logic gates and other magnonic devices. Our findings are crucial for designing nanomagnonic circuits and for the development of spin-wave nano-optics.

Microwave Radiation Detection with an Ultrathin Free-Standing Superconducting Niobium Nanohelix.

We present a superconducting bolometer fabricated by a rolled-up technology that allows one to combine the two-dimensionality (2D) of the superconducting layer with a helical spiral curvature. The bolometer is formed as a free-standing Nb nanohelix acting as an ultrathin transition-edge sensor (TES) and having a negligible thermal contact to the substrate. We demonstrate the functionality of the thin-film TES by examining its microwave-detection performance in comparison with a commercial cryogenic bolometer from QMC Instruments. The nanohelix has been revealed to feature a noise equivalent power (NEP) of about 2 × 10-10 W Hz-1/2 at a microwave radiation power of 9 W m-2, which is 4 orders of magnitude smaller than the NEP of the QMC sensor at a similar radiation power. Furthermore, the forecast for the nanohelix is a 1 to 2 orders of magnitude shorter response time as compared to sensors based on commonly used 1 µm thick Si3N4 membranes. The reason is the extremely low heat capacity of the 50 nm thick supporting material and the few contact points between the TES and the substrate. Our findings indicate that microwave radiation detection can be substantially improved by extending 2D superconducting structures into the 3D space.

Mobile fluxons as coherent probes of periodic pinning in superconductors.

The interaction of (quasi)particles with a periodic potential arises in various domains of science and engineering, such as solid-state physics, chemical physics, and communication theory. An attractive test ground to investigate this interaction is represented by superconductors with artificial pinning sites, where magnetic flux quanta (Abrikosov vortices) interact with the pinning potential U(r) = U(r + R) induced by a nanostructure. At a combination of microwave and dc currents, fluxons act as mobile probes of U(r): The ac component shakes the fluxons in the vicinity of their equilibrium points which are unequivocally determined by the local pinning force counterbalanced by the Lorentz force induced by the dc current, linked to the curvature of U(r) which can then be used for a successful fitting of the voltage responses. A good correlation of the deduced dependences U(r) with the cross sections of the nanostructures points to that pinning is primarily caused by vortex length reduction. Our findings pave a new route to a non-destructive evaluation of periodic pinning in superconductor thin films. The approach should also apply to a broad class of systems whose evolution in time can be described by the coherent motion of (quasi)particles in a periodic potential.

Tunable magnetism on the lateral mesoscale by post-processing of Co/Pt heterostructures.

Controlling magnetic properties on the nanometer-scale is essential for basic research in micro-magnetism and spin-dependent transport, as well as for various applications such as magnetic recording, imaging and sensing. This has been accomplished to a very high degree by means of layered heterostructures in the vertical dimension. Here we present a complementary approach that allows for a controlled tuning of the magnetic properties of Co/Pt heterostructures on the lateral mesoscale. By means of in situ post-processing of Pt- and Co-based nano-stripes prepared by focused electron beam induced deposition (FEBID) we are able to locally tune their coercive field and remanent magnetization. Whereas single Co-FEBID nano-stripes show no hysteresis, we find hard-magnetic behavior for post-processed Co/Pt nano-stripes with coercive fields up to 850 Oe. We attribute the observed effects to the locally controlled formation of the CoPt L10 phase, whose presence has been revealed by transmission electron microscopy.

Vortex ratchet reversal in an asymmetric washboard pinning potential subject to combined dc and ac stimuli.

The mixed-state resistive response of a superconductor thin film with an asymmetric washboard pinning potential subject to superimposed dc and ac currents of arbitrary amplitudes and frequency at finite temperature is theoretically investigated. The problem is considered in the single-vortex approximation, relying upon the exact solution of the Langevin equation in terms of a matrix continued fraction. The dc voltage response and the absorbed power in ac response are analyzed as functions of dc bias and ac current amplitude and frequency in a wide range of corresponding dimensionless parameters. Predictions are made of (i) a reversal of the rectified voltage at small dc biases and strong ac drives and (ii) a non-monotonic enhancement of the absorbed power in the nonlinear ac response at far sub-depinning frequencies. It is elucidated how and why both these effects appear due to the competition of the fixed internal and the tunable, dc bias-induced external asymmetry of the potential as the only reason. This is distinct from other scenarios used for explaining the vortex ratchet reversal effect so far.