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State tomography allows to characterize quantum states, and was recently applied to reveal the dynamic magnetization state of a parametrically driven magnet. The identification of non-classical states, such as squeezed states, relies on a careful analysis of their emission and their distinction from thermal and vacuum fluctuations. A technique allowing to detect equilibrium magnetization fluctuations is a crucial first step in this regard. In this Letter, we show that inductive magnon noise spectroscopy (iMNS) allows to characterize the thermal magnetization fluctuations of a ferromagnetic thin film in a broadband coplanar waveguide-based scheme. Relative to a cold microwave background, the microwaves emitted by the equilibrium magnetization fluctuations can be detected via spectrum analysis. We provide a comprehensive picture of our microwave system by quantitatively modeling its response, including the thermalizing influence of the cables. The model allows for direct comparison to low-power broadband ferromagnetic resonance measurements with excellent agreement, corroborating the equilibrium character of the iMNS measurement by probing the linear response of the equilibrium state. Our work thus demonstrates broadband access to the equilibrium properties of magnetization fluctuations using a purely inductive approach., Comment: 6 pages and 4 figures; including Supplemental Material with 4 pages, 2 figures and 1 table

We present a cavity-electromechanical system comprising a superconducting quantum interference device which is embedded in a microwave resonator and coupled via a pick-up loop to a 6 $\mu$g magnetically-levitated superconducting sphere. The motion of the sphere in the magnetic trap induces a frequency shift in the SQUID-cavity system. We use microwave spectroscopy to characterize the system, and we demonstrate that the electromechanical interaction is tunable. The measured displacement sensitivity of $10^{-7} \, \mathrm{m} / \sqrt{\mathrm{Hz}}$, defines a path towards ground-state cooling of levitated particles with Planck-scale masses at millikelvin environment temperatures.

Tailored magnon-phonon hybrid systems, where high overtone bulk acoustic resonators couple resonantly to the magnonic mode of a ferromagnetic thin film, are considered optimal for the creation of acoustic phonons with a defined circular polarization. This class of devices is therefore ideal for the investigation of phonon propagation properties and assessing their capacity to transport angular momentum in the classical and potentially even in the quantum regime. Here, we study the coupling between the magnons in a ferromagnetic \ch{Co25Fe75} thin film and the transverse acoustic phonons in a bulk acoustic wave resonators formed by the sapphire substrate onto which the film is deposited. Using broadband ferromagnetic resonance experiments as a function of temperature, we investigate the strength of the coherent magnon-phonon interaction and the individual damping rates of the magnons and phonons participating in the process. This demonstrates that this coupled magnon-phonon system can reach a cooperativity $C\approx 1$ at cryogenic temperatures. Our experiments also showcase the potential of strongly coupled magnon-phonon systems for strain sensing applications., Comment: 12 pages, 8 figures

Converting angular momentum between different degrees of freedom within a magnetic material results from a dynamic interplay between electrons, magnons and phonons. This interplay is pivotal to implementing spintronic device concepts that rely on spin angular momentum transport. We establish a new concept for long-range angular momentum transport that further allows to address and isolate the magnonic contribution to angular momentum transport in a nanostructured metallic ferromagnet. To this end, we electrically excite and detect spin transport between two parallel and electrically insulated ferromagnetic metal strips on top of a diamagnetic substrate. Charge-to-spin current conversion within the ferromagnetic strip generates electronic spin angular momentum that is transferred to magnons via electron-magnon coupling. We observe a finite angular momentum flow to the second ferromagnetic strip across a diamagnetic substrate over micron distances, which is electrically detected in the second strip by the inverse charge-to-spin current conversion process. We discuss phononic and dipolar interactions as the likely cause to transfer angular momentum between the two strips. Moreover, our work provides the experimental basis to separate the electronic and magnonic spin transport and thereby paves the way towards magnonic device concepts that do not rely on magnetic insulators., Comment: 6 pages, 4 figures, see ancillary filles for supplemental material

A magnonic spin current crossing a ferromagnet-metal interface is accompanied by spin current shot noise arising from the discrete quanta of spin carried by magnons. In thin films, e.g., the spin of so-called squeezed magnons have been shown to deviate from the common value $\hbar$, with corresponding changes in the spin noise. In experiments, spin currents are typically converted to charge currents via the inverse spin Hall effect. We here analyze the magnitude of the spin current shot noise in the charge channel for a typical electrically detected spin pumping experiment, and find that the voltage noise originating from the spin current shot noise is much smaller than the inevitable Johnson-Nyquist noise. Furthermore, we find that due to the local nature of the spin-charge conversion, the ratio of spin current shot noise and Johnson-Nyquist noise cannot be systematically enhanced by tuning the sample geometry, in contrast to the linear increase in dc spin pumping voltage with sample length. Instead, the ratio depends sensitively on material-specific transport properties. Our analysis thus provides guidance for the experimental detection of squeezed magnons through spin pumping shot noise., Comment: Revised manuscript title, added paragraph of interpretation of the shot noise enhancement with temperature, added brief discussion of the low temperature limit, references added

In easy-plane antiferromagnets, the nature of the elementary excitations of the spin system is captured by the precession of the magnon pseudospin around its equilibrium pseudofield, manifesting itself in the magnon Hanle effect. Here, we investigate the impact of growth-induced changes in the magnetic anisotropy on this effect in the antiferromagnetic insulator $\alpha$-Fe$_2$O$_3$ (hematite). To this end, we compare the structural, magnetic, and magnon-based spin transport properties of $\alpha$-Fe$_2$O$_3$ films with different thicknesses grown by pulsed laser deposition in molecular and atomic oxygen atmospheres. While in films grown with molecular oxygen a spin-reorientation transition (Morin transition) is absent down to $10\,$K, we observe a Morin transition for those grown by atomic-oxygen-assisted deposition, indicating a change in magnetic anisotropy. Interestingly, even for a $19\,$nm thin $\alpha$-Fe$_2$O$_3$ film grown with atomic oxygen we still detect a Morin transition at $125\,$K. We characterize the magnon Hanle effect in these $\alpha$-Fe$_2$O$_3$ films via all-electrical magnon transport measurements. The films grown with atomic oxygen show a markedly different magnon spin signal from those grown in molecular oxygen atmospheres. Most importantly, the maximum magnon Hanle signal is significantly enhanced and the Hanle peak is shifted to lower magnetic field values for films grown with atomic oxygen. These observations suggest a change of magnetic anisotropy for $\alpha$-Fe$_2$O$_3$ films fabricated by atomic-oxygen-assisted deposition resulting in an increased oxygen content in these films. Our findings provide new insights into the possibility to fine-tune the magnetic anisotropy in $\alpha$-Fe$_2$O$_3$ and thereby to engineer the magnon Hanle effect.

Magnomechanical devices, in which magnetic excitations couple to mechanical vibrations, have been discussed as efficient and broadband microwave signal transducers in the classical and quantum limit. We experimentally investigate the magnetoelastic coupling between the ferromagnetic resonance (FMR) modes in a metallic Co$_{25}$Fe$_{75}$ thin film, featuring ultra-low magnetic damping as well as sizable magnetostriction, and standing transverse elastic phonon modes in sapphire, silicon and gadolinium gallium garnet by performing broadband FMR spectroscopy at cryogenic temperatures. For all these substrate materials, we observe an interaction between the resonant acoustic and magnetic modes, which can be tailored by the propagation direction of the acoustic mode with respect to the crystallographic axes. We identify these phonon modes as transverse shear waves propagating with slightly different velocities with relative magnitudes of $\Delta v/v\simeq10^{-5}$, i.e., all substrates show phononic birefringence. Upon appropriately choosing the phononic mode, the hybrid magnomechanical system enters the Purcell enhanced coupling regime., Comment: 7 oages, 4 figures

Lithium niobate (LNO) is a well established material for surface acoustic wave (SAW) devices including resonators, delay lines and filters. Recently, multi-layer substrates based on LNO thin films have become commercially available. Here, we present a systematic low-temperature study of the performance of SAW devices fabricated on LNO-on-insulator and LNO-on-Silicon substrates and compare them to bulk LNO devices. Our study aims at assessing the performance of these substrates for quantum acoustics, i.e. the integration with superconducting circuits operating in the quantum regime. To this end, we design SAW resonators with a target frequency of 5 GHz and perform experiments at millikelvin temperatures and microwave power levels corresponding to single photons or phonons. The devices are investigated regarding their internal quality factors as a function of the excitation power and temperature, which allows us to characterize and quantify losses and identify the dominating loss mechanism. For the measured devices, fitting the experimental data shows that the quality factors are limited by the coupling of the resonator to a bath of two-level-systems. Our results suggest that SAW devices on thin film LNO on silicon have comparable performance to devices on bulk LNO and are viable for use in SAW-based quantum acoustic devices., Comment: 13 pages, 4 figures

We report the levitation of a superconducting lead-tin sphere with 100 micrometer diameter (corresponding to a mass of 5.6 micrograms) in a static magnetic trap formed by two coils in an anti-Helmholtz configuration, with adjustable resonance frequencies up to 240 hertz. The center-of-mass motion of the sphere is monitored magnetically using a dc superconducting quantum interference device as well as optically and exhibits quality factors of up to 2.6e7. We also demonstrate 3D magnetic feedback control of the sphere's motion. The setup is housed in a dilution refrigerator operating at 15 millikelvin. By implementing a cryogenic vibration isolation system we can attenuate environmental vibrations at 200 hertz by approximately seven orders of magnitude. The combination of low temperature, large mass and high quality factor as well as adjustable resonance frequencies provides a promising platform for testing quantum physics in previously unexplored regimes with high mass and long coherence times., Comment: Updated to published version

The precession of magnon pseudospin about the equilibrium pseudofield, the latter capturing the nature of magnonic eigen-excitations in an antiferromagnet, gives rise to the magnon Hanle effect. Its realization via electrically injected and detected spin transport in an antiferromagnetic insulator demonstrates its high potential for devices and as a convenient probe for magnon eigenmodes and the underlying spin interactions in the antiferromagnet. Here, we observe a nonreciprocity in the Hanle signal measured in hematite using two spatially separated platinum electrodes as spin injector/detector. Interchanging their roles was found to alter the detected magnon spin signal. The recorded difference depends on the applied magnetic field and reverses sign when the signal passes its nominal maximum at the so-called compensation field. We explain these observations in terms of a spin transport direction-dependent pseudofield. The latter leads to a nonreciprocity, which is found to be controllable via the applied magnetic field. The observed nonreciprocal response in the readily available hematite films opens interesting opportunities for realizing exotic physics predicted so far only for antiferromagnets with special crystal structures.

We study the static and dynamic magnetic properties of epitaxially strained $\gamma$-$\mathrm{Fe_2O_3}$ (maghemite) thin films grown via pulsed-laser deposition on MgO substrates by SQUID magnetometry and cryogenic broadband ferromagnetic resonance experiments. SQUID magnetometry measurements reveal hysteretic magnetization curves for magnetic fields applied both in- and out of the sample plane. From the magnetization dynamics of our thin films, we find a small negative effective magnetization in agreement with a strain induced perpendicular magnetic anisotropy. Moreover, we observe a non-linear evolution of the ferromagnetic resonance-linewidth as function of the microwave frequency and explain this finding with a model based on slowly relaxing impurities, the so-called slow relaxor model. By investigating the magnetization dynamics in our maghemite thin films as a function of frequency and temperature, we can isolate the temperature dependent contribution of the slowly relaxing impurities to the resonance linewidth and, in particular, observe a sign change in the effective magnetization. This finding provides evidence for a transition of the magnetic anisotropy from a perpendicular easy axis to an easy in-plane anisotropy for reduced temperatures., Comment: 10 pages, 8 figures

"Pumping" of phonons by a dynamic magnetization promises to extend the range and functionality of magnonic devices. We explore the impact of phonon pumping on room-temperature ferromagnetic resonance (FMR) spectra of bilayers of thin yttrium iron garnet (YIG) films on thick gadolinium gallium garnet substrates over a wide frequency range. At low frequencies the Kittel mode hybridizes coherently with standing ultrasound waves of a bulk acoustic resonator to form magnon polarons that induce rapid oscillations of the magnetic susceptibility, as reported before. At higher frequencies, the phonon resonances overlap, merging into a conventional FMR line, but with an increased line width. The frequency dependence of the increased line broadening follows the predictions from phonon pumping theory in the thick substrate limit. In addition, we find substantial magnon-phonon coupling of a perpendicular standing spin wave (PSSW) mode. This evidences the importance of the mode overlap between the acoustic and magnetic modes, and provides a route towards engineering the magnetoelastic mode coupling., Comment: 6 pages, 3 figures

We systematically study the performance of compact lumped element planar microwave $\mathrm{Nb_{70}Ti_{30}N}$ (NbTiN) resonators operating at 5 GHz in external in-plane magnetic fields up to 440 mT, a broad temperature regime from 2.2 K up to 13 K, as well as mK temperatures. For comparison, the resonators have been fabricated on thermally oxidized and pristine, (001) oriented silicon substrates. When operating the resonators in the multi-photon regime at $T=2.2$ K, we find internal quality factors $Q_{\mathrm{int}}\simeq$ $2\cdot10^5$ for NbTiN resonators grown on pristine Si substrates, while resonators grown on thermally oxidized substrates show a reduced value of $Q_{\mathrm{int}}\simeq$ $1\cdot10^4$, providing evidence for additional loss channels for the latter substrate. In addition, we investigate the $Q$-factors of the resonators on pristine Si substrates at millikelvin temperatures to asses their applicability for quantum applications. We find $Q_{\mathrm{int}}\simeq$ $2\cdot10^5$ in the single photon regime and $Q_{\mathrm{int}}\simeq$ $5\cdot10^5$ in the high power regime at $T=7$ mK., Comment: 14 pages, 4 figures

Antiferromagnetic materials host pairs of spin-up and spin-down magnons which can be described in terms of a magnonic pseudospin. The close analogy between this magnonic pseudospin systems and that of electronic charge carriers led to the prediction of fascinating phenomena in antiferromagnets. Recently, the associated dynamics of antiferromagnetic pseudospin has been experimentally demonstrated and, in particular, the first observation of the magnon Hanle effect has been reported. We here expand the magnonic spin transport description by explicitly taking into account contributions of finite-spin low-energy magnons. In our experiments we realize the spin injection and detection process by two Platinum strips and investigate the influence of the Pt-strips on the generation and diffusive transport of magnons in films of the antiferromagnetic insulator hematite. For both a 15 nm and a 100 nm thick film, we find a distinct signal caused by the magnon Hanle effect. However, the magnonic spin signal exhibits clear differences in both films. In contrast to the thin film, for the thicker one, we observe an oscillating behavior in the high magnetic field range as well as an additional offset signal in the low magnetic field regime. We attribute this offset signal to the presence of finite-spin low-energy magnons.

For applications making use of magnonic spin currents damping effects, which decrease the spin conductivity, have to be minimized. We here investigate the magnon transport in an yttrium iron garnet thin film with strongly reduced effective magnetization. We show that in a three-terminal device the effective magnon conductivity can be increased by a factor of up to six by a current applied to a modulator electrode, which generates damping compensation above a threshold current. Moreover, we find a linear dependence of this threshold current on the applied magnetic field. We can explain this behavior by the reduced effective magnetization and the associated nearly circular magnetization precession.

Nano-electromechanical systems implement the opto-mechanical interaction combining electromagnetic circuits and mechanical elements. We investigate an inductively coupled nano-electromechanical system, where a superconducting quantum interference device (SQUID) realizes the coupling. We show that the resonance frequency of the mechanically compliant string embedded into the SQUID loop can be controlled in two different ways: (i) the bias magnetic flux applied perpendicular to the SQUID loop, (ii) the magnitude of the in-plane bias magnetic field contributing to the nano-electromechanical coupling. These findings are quantitatively explained by the inductive interaction contributing to the effective spring constant of the mechanical resonator. In addition, we observe a residual field dependent shift of the mechanical resonance frequency, which we attribute to the finite flux pinning of vortices trapped in the magnetic field biased nanostring., Comment: 5 pages, 3 figures

We demonstrate the low temperature suppression of the platinum (Pt) spin Nernst angle in bilayers consisting of the antiferromagnetic insulator hematite ($\alpha$-Fe$_2$O$_3$) and Pt upon measuring the transverse spin Nernst magnetothermopower (TSNM). We show that the observed signal stems from the interplay between the interfacial spin accumulation in Pt originating from the spin Nernst effect and the orientation of the N\'eel vector of $\alpha$-Fe$_2$O$_3$, rather than its net magnetization. Since the latter is negligible in an antiferromagnet, our device is superior to ferromagnetic structures, allowing to unambiguously distinguish the TSNM from thermally excited magnon transport (TMT), which usually dominates in ferri/ferromagnets due to their non-zero magnetization. Evaluating the temperature dependence of the effect, we observe a vanishing TSNM below ~100 K. We compare these results with theoretical calculations of the temperature dependent spin Nernst conductivity and find excellent agreement. This provides evidence for a vanishing spin Nernst angle of Pt at low temperatures and the dominance of extrinsic contributions to the spin Nernst effect., Comment: 4 pages, 4 figures

The spin Hall magnetoresistance (SMR) allows to investigate the magnetic textures of magnetically ordered insulators in heterostructures with normal metals by magnetotransport experiments. We here report the observation of the SMR in in-situ prepared ferromagnetic EuO/W thin film bilayers with magnetically and chemically well-defined interfaces. We characterize the magnetoresistance effects utilizing angle-dependent and field-dependent magnetotransport measurements as a function of temperature. Applying the established SMR model, we derive and quantify the real and imaginary parts of the complex spin mixing interface conductance. We find that the imaginary part is by one order of magnitude larger than the real part. Both decrease with increasing temperature. This reduction is in agreement with thermal fluctuations in the ferromagnet., Comment: 5 pages, 4 figures

We experimentally study the tunability of the cooperativity in coupled spin--cavity systems by changing the magnetic state of the spin system via an external control parameter. As model system, we use the skyrmion host material Cu$_2$OSeO$_3$ coupled to a microwave cavity resonator. In the different magnetic phases we measure a dispersive coupling between the resonator and the magnon modes and model our results by using the input--output formalism. Our results show a strong tunability of the normalized coupling rate by magnetic field, allowing us to change the magnon--photon cooperativity from 1 to 60 at the phase boundaries of the skyrmion lattice state.

We experimentally demonstrate the formation of room-temperature skyrmions with radii of about 25\,nm in easy-plane anisotropy multilayers with interfacial Dzyaloshinskii-Moriya interaction (DMI). We detect the formation of individual magnetic skyrmions by magnetic force microscopy and find that the skyrmions are stable in out-of-plane fields up to about 200 mT. We determine the interlayer exchange coupling as well as the strength of the interfacial DMI. Additionally, we investigate the dynamic microwave spin excitations by broadband magnetic resonance spectroscopy. From the uniform Kittel mode we determine the magnetic anisotropy and low damping $\alpha_{\mathrm{G}} < 0.04$. We also find clear magnetic resonance signatures in the non-uniform (skyrmion) state. Our findings demonstrate that skyrmions in easy-plane multilayers are promising for spin-dynamical applications.

We have optimized the growth of superconducting TaN thin films on \ch{SiO2} substrates via dc magnetron sputtering and extract a maximum superconducting transition temperature of $T_{\mathrm{c}}=5$ K as well as a maximum critical field $\mu_0H_{\mathrm{c2}}=(13.8\pm0.1)$ T. To investigate the impact of spin-orbit interaction in superconductor/ferromagnet heterostructures, we then analyze the magnetization dynamics of both normal state and superconducting TaN/\ch{Ni80Fe20}(Permalloy, Py)-bilayers as a function of temperature using broadband ferromagnetic resonance (bbFMR) spectroscopy. The phase sensitive detection of the microwave transmission signal is used to quantitatively extract the inverse current-induced torques of the bilayers. The results are compared to our previous study on NbN/Py-bilayers. In the normal state of TaN, we detect a positive damping-like current-induced torque $\sigma_{\mathrm{d}}$ from the inverse spin Hall effect (iSHE) and a small field-like torque $\sigma_{\mathrm{f}}$ attributed to the inverse Rashba-Edelstein effect (iREE) at the TaN/Py-interface. In the superconducting state of TaN, we detect a negative $\sigma_{\mathrm{d}}$ attributed to the quasiparticle mediated inverse spin Hall effect (QMiSHE) and the unexpected manifestation of a large positive field-like $\sigma_{\mathrm{f}}$ of unknown origin matching our previous results for NbN/Py-bilayers., Comment: 6 pages 4 figures

We put forward the concept of an optomagnonic crystal: a periodically patterned structure at the microscale based on a magnetic dielectric, which can co-localize magnon and photon modes. The co-localization in small volumes can result in large values of the photon-magnon coupling at the single quanta level, which opens perspectives for quantum information processing and quantum conversion schemes with these systems. We study theoretically a simple geometry consisting of a one-dimensional array of holes with an abrupt defect, considering the ferrimagnet Yttrium Iron Garnet (YIG) as the basis material. We show that both magnon and photon modes can be localized at the defect, and use symmetry arguments to select an optimal pair of modes in order to maximize the coupling. We show that an optomagnonic coupling in the kHz range is achievable in this geometry, and discuss possible optimization routes in order to improve both coupling strengths and optical losses., Comment: 18 pages, 11 figures

We formulate a theoretical description of antiferromagnetic magnons and their transport in terms of an associated pseudospin. The need and strength of this formulation emerges from the antiferromagnetic eigenmodes being formed from superpositions of spin-up and -down magnons, depending on the material anisotropies. Consequently, a description analogous to that of spin-1/2 electrons is demonstrated while accounting for the bosonic nature of the antiferromagnetic eigenmodes. Introducing the concepts of a pseudospin chemical potential together with a pseudofield and relating magnon spin to pseudospin allows a consistent description of diffusive spin transport in antiferromagnetic insulators with any given anisotropies and interactions. Employing the formalism developed, we elucidate the general features of recent non-local spin transport experiments in antiferromagnetic insulators hosting magnons with different polarisations. The pseudospin formalism developed herein is valid for any pair of coupled bosons and is likely to be useful in other systems comprising interacting bosonic modes., Comment: to appear in Physical Review B

Mechanical resonator networks are currently discussed in the context of model systems giving insight into problems of condensed matter physics including effects in topological phases. Here, we discuss networks based on three high-quality factor nanomechanical string resonators (nanostrings) made from highly tensile-stressed Si$_{3}$N$_{4}$. The strings are strongly coupled via a shared support and thus can form a fully mechanical, classical multi-level system. Moreover, the individual strings are tunable in frequency, which allows one to explore their coupling behaviour using continuous wave spectroscopy and time domain techniques. In particular, such systems allow for the experimental exploration of quantum phenomena such as Landau-Zener transition dynamics by studying their classical analogues. Here, we extend the previous work performed on two coupled strings to three coupled resonators and discuss the additional features of the inter-string dynamics, such as the classical analog of Landau-Zener transition dynamics in a three-mode system. classical analog of Landau-Zener transition dynamics in a three-mode system., Comment: 6 pages, 4 figures

All-electrical generation and detection of pure spin currents is a promising way towards controlling the diffusive magnon transport in magnetically ordered insulators. We quantitatively compare two measurement schemes, which allow to measure the magnon spin transport in a three-terminal device based on a yttrium iron garnet thin film. We demonstrate that the dc charge current method based on the current reversal technique and the ac charge current method utilizing first and second harmonic lock-in detection can both efficiently distinguish between electrically and thermally injected magnons. In addition, both measurement schemes allow to investigate the modulation of magnon transport induced by an additional dc charge current applied to the center modulator strip. However, while at low modulator charge current both schemes yield identical results, we find clear differences above a certain threshold current. This difference originates from nonlinear effects of the modulator current on the magnon conductance.

We report on experiments demonstrating coherent control of magnon spin transport and pseudospin dynamics in a thin film of the antiferromagnetic insulator hematite utilizing two Pt strips for all-electrical magnon injection and detection. The measured magnon spin signal at the detector reveals an oscillation of its polarity as a function of the externally applied magnetic field. We quantitatively explain our experiments in terms of diffusive magnon transport and a coherent precession of the magnon pseudospin caused by the easy-plane anisotropy and the Dzyaloshinskii-Moriya interaction. This experimental observation can be viewed as the magnonic analogue of the electronic Hanle effect and the Datta-Das transistor, unlocking the high potential of antiferromagnetic magnonics towards the realization of rich electronics-inspired phenomena., Comment: 6 pages, 3 figures

We investigate the injection of quasiparticle spin currents into a superconductor via spin pumping from an adjacent FM layer.$\;$To this end, we use NbN/\ch{Ni80Fe20}(Py)-heterostructures with a Pt spin sink layer and excite ferromagnetic resonance in the Py-layer by placing the samples onto a coplanar waveguide (CPW). A phase sensitive detection of the microwave transmission signal is used to quantitatively extract the inductive coupling strength between sample and CPW, interpreted in terms of inverse current-induced torques, in our heterostructures as a function of temperature. Below the superconducting transition temperature $T_{\mathrm{c}}$, we observe a suppression of the damping-like torque generated in the Pt layer by the inverse spin Hall effect (iSHE), which can be understood by the changes in spin current transport in the superconducting NbN-layer. Moreover, below $T_{\mathrm{c}}$ we find a large field-like current-induced torque., Comment: 4 pages, 4 figures

SrIrO$_3$ with its large spin-orbit coupling and low charge conductivity has emerged as a potential candidate for efficient spin-orbit torque magnetization control in spintronic devices. We here report on the influence of an interfacial oxide layer on spin pumping experiments in Ni$_{80}$Fe$_{20}$ (NiFe)/SrIrO$_3$ bilayer heterostructures. To investigate this scenario we have carried out broadband ferromagnetic resonance (BBFMR) measurements, which indicate the presence of an interfacial antiferromagnetic oxide layer. We performed in-plane BBFMR experiments at cryogenic temperatures, which allowed us to simultaneously study dynamic spin pumping properties (Gilbert damping) and static magnetic properties (such as the effective magnetization and magnetic anisotropy). The results for NiFe/SrIrO$_3$ bilayer thin films were analyzed and compared to those from a NiFe/NbN/SrIrO$_3$ trilayer reference sample, where a spin-transparent, ultra-thin NbN layer was inserted to prevent oxidation of NiFe. At low temperatures, we observe substantial differences in the magnetization dynamics parameters of these samples, which can be explained by an antiferromagnetic interfacial layer in the NiFe/SrIrO$_3$ bilayers., Comment: 5 pages, 4 figures

Antiferromagnetic materials promise improved performance for spintronic applications, as they are robust against external magnetic field perturbations and allow for faster magnetization dynamics compared to ferromagnets. The direct observation of the antiferromagnetic state, however, is challenging due to the absence of a macroscopic magnetization. Here, we show that the spin Hall magnetoresistance (SMR) is a versatile tool to probe the antiferromagnetic spin structure via simple electrical transport experiments by investigating the easy-plane antiferromagnetic insulators $\alpha$-Fe2O3 (hematite) and NiO in bilayer heterostructures with a Pt heavy metal top electrode. While rotating an external magnetic field in three orthogonal planes, we record the longitudinal and the transverse resistivities of Pt and observe characteristic resistivity modulations consistent with the SMR effect. We analyze both their amplitude and phase and compare the data to the results from a prototypical collinear ferrimagnetic Y3Fe5O12/Pt bilayer. The observed magnetic field dependence is explained in a comprehensive model, based on two magnetic sublattices and taking into account magnetic field-induced modifications of the domain structure. Our results show that the SMR allows us to understand the spin configuration and to investigate magnetoelastic effects in antiferromagnetic multi-domain materials. Furthermore, in $\alpha$-Fe2O3/Pt bilayers, we find an unexpectedly large SMR amplitude of $2.5 \times 10^{-3}$, twice as high as for prototype Y3Fe5O12/Pt bilayers, making the system particularly interesting for room-temperature antiferromagnetic spintronic applications.

Light-matter interaction in optomechanical systems is the foundation for ultra-sensitive detection schemes [1,2] as well as the generation of phononic and photonic quantum states [3-10]. Electromechanical systems realize this optomechanical interaction in the microwave regime. In this context, capacitive coupling arrangements demonstrated interaction rates of up to 280 Hz [11]. Complementary, early proposals [12-15] and experiments [16,17] suggest that inductive coupling schemes are tunable and have the potential to reach the vacuum strong-coupling regime. Here, we follow the latter approach by integrating a partly suspended superconducting quantum interference device (SQUID) into a microwave resonator. The mechanical displacement translates into a time varying flux in the SQUID loop, thereby providing an inductive electromechanical coupling. We demonstrate a sideband-resolved electromechanical system with a tunable vacuum coupling rate of up to 1.62 kHz, realizing sub-aN Hz-1/2 force sensitivities. Moreover, we study the frequency splitting of the microwave resonator for large mechanical amplitudes confirming the large coupling. The presented inductive coupling scheme shows the high potential of SQUID-based electromechanics for targeting the full wealth of the intrinsically nonlinear optomechanics Hamiltonian., Comment: 7 pages, 5 figures, supplementary information

We investigate the spin Hall magnetoresistance (SMR) at room temperature in thin film heterostructures of antiferromagnetic, insulating, (0001)-oriented alpha-Fe2O3 (hematite) and Pt. We measure their longitudinal and transverse resistivities while rotating an applied magnetic field of up to 17T in three orthogonal planes. For out-of-plane magnetotransport measurements, we find indications for a multidomain antiferromagnetic configuration whenever the field is aligned along the film normal. For in-plane field rotations, we clearly observe a sinusoidal resistivity oscillation characteristic for the SMR due to a coherent rotation of the Neel vector. The maximum SMR amplitude of 0.25% is, surprisingly, twice as high as for prototypical ferrimagnetic Y3Fe5O12/Pt heterostructures. The SMR effect saturates at much smaller magnetic fields than in comparable antiferromagnets, making the alpha-Fe2O3/Pt system particularly interesting for room-temperature antiferromagnetic spintronic applications., Comment: 10 pages, 9 figures, 61 (updated) references, including supplemental material

We investigate the magnetoelastic properties of $\mathrm{Co_{25}}\mathrm{Fe_{75}}$ and $\mathrm{Co_{10}}\mathrm{Fe_{90}}$ thin films by measuring the mechanical properties of a doubly clamped string resonator covered with multi-layer stacks containing these films. For the magnetostrictive constants we find $\lambda_{\mathrm{Co_{25}}\mathrm{Fe_{75}}}=(-20.68\pm0.25)\times10^{-6}$ and $\lambda_{\mathrm{Co_{10}}\mathrm{Fe_{90}}}=(-9.80\pm0.12)\times10^{-6}$ at room temperature. In stark contrast to the positive magnetostriction previously found in bulk CoFe crystals. $\mathrm{Co_{25}}\mathrm{Fe_{75}}$ thin films unite low damping and sizable magnetostriction and are thus a prime candidate for micromechanical magnonic applications, such as sensors and hybrid phonon-magnon systems., Comment: 4 pages, 4 figures, SI

We report on the determination of the anomalous spin Hall angle in the ferromagnetic metal alloy cobalt-iron (Co$_{25}$Fe$_{75}$, CoFe). This is accomplished by measuring the spin injection/detection efficiency in a multiterminal device with nanowires of platinum (Pt) and CoFe deposited onto the magnetic insulator yttrium iron garnet (Y$_3$Fe$_5$O$_{12}$, YIG). Applying a spin-resistor model to our multiterminal spin transport data, we determine the magnon conductivity in YIG, the spin conductance at the YIG/CoFe interface and finally the anomalous spin Hall angle of CoFe as a function of its spin diffusion length in a single device. Our experiments clearly reveal a negative anomalous spin Hall angle of the ferromagnetic metal CoFe, but a vanishing ordinary spin Hall angle. This is in contrast to the results reported for the ferromagnetic metals Co and permalloy., Comment: 4 pages, 4 figures

We report ultra-low intrinsic magnetic damping in Co$_{\text{25}}$Fe$_{\text{75}}$ heterostructures, reaching the low $10^{-4}$ regime at room temperature. By using a broadband ferromagnetic resonance technique, we extracted the dynamic magnetic properties of several Co$_{\text{25}}$Fe$_{\text{75}}$-based heterostructures with varying ferromagnetic layer thickness. By estimating the eddy current contribution to damping, measuring radiative damping and spin pumping effects, we found the intrinsic damping of a 26\,nm thick sample to be $$\alpha_{\mathrm{0}} \lesssim 3.18\times10^{-4}$. Furthermore, using Brillouin light scattering microscopy we measured spin-wave propagation lengths of up to $(21\pm1)\,\mathrm{\mu m}$ in a 26 nm thick Co$_{\text{25}}$Fe$_{\text{75}}$ heterostructure at room temperature, which is in excellent agreement with the measured damping., Comment: Updated Version

The ultrastrong coupling of (quasi-)particles has gained considerable attention due to its application potential and richness of the underlying physics. Coupling phenomena arising due to electromagnetic interactions are well explored. In magnetically ordered systems, the quantum-mechanical exchange-interaction should furthermore enable a fundamentally different coupling mechanism. Here, we report the observation of ultrastrong intralayer exchange-enhanced magnon-magnon coupling in a compensated ferrimagnet. We experimentally study the spin dynamics in a gadolinium iron garnet single crystal using broadband ferromagnetic resonance. Close to the ferrimagnetic compensation temperature, we observe ultrastrong coupling of clockwise and anticlockwise magnon modes. The magnon-magnon coupling strength reaches more than 30% of the mode frequency and can be tuned by varying the direction of the external magnetic field. We theoretically explain the observed phenomenon in terms of an exchange-enhanced mode-coupling mediated by a weak cubic anisotropy.

Applications based on spin currents strongly profit from the control and reduction of their effective damping and their transport properties. We here experimentally observe magnon mediated transport of spin (angular) momentum through a 13.4 nm thin yttrium iron garnet film with full control of the magnetic damping via spin-orbit torque. Above a critical spin-orbit torque, the fully compensated damping manifests itself as an increase of magnon conductivity by almost two orders of magnitude. We compare our results to theoretical expectations based on recently predicted current induced magnon condensates and discuss other possible origins of the observed critical behaviour.

We utilize spin Hall magnetoresistance (SMR) measurements to experimentally investigate the pure spin current transport and magnetic properties of nickel ferrite (NiFe2O4,NFO)/normal metal (NM) thin film heterostructures. We use (001)-oriented NFO thin films grown on lattice-matched magnesium gallate substrates by pulsed laser deposition, which significantly improves the magnetic and structural properties of the ferrimagnetic insulator. The NM in our experiments is either Pt or Ta. A comparison of the obtained SMR magnitude for charge currents applied in the [100]- and [110]-direction of NFO yields a change of 50% for Pt at room temperature. We also investigated the temperature dependence of this current direction anisotropy and find that it is qualitatively different for the conductivity and the SMR magnitude. From our results we conclude that the observed current direction anisotropy may originate from an anisotropy of the spin mixing conductance or of the spin Hall effect in these Pt and Ta layers, and/or additional spin-galvanic contributions from the NFO/NM interface.

We present three designs for planar superconducting microwave resonators for electron spin resonance (ESR) experiments. We implement finite element simulations to calculate the resonance frequency and quality factors as well as the three-dimensional microwave magnetic field distribution of the resonators. One particular resonator design offers an increased homogeneity of the microwave magnetic field while the other two show a better confinement of the mode volume. We extend our model simulations to calculate the collective coupling rate between a spin ensemble and a microwave resonator in the presence of an inhomogeneous magnetic resonator field. Continuous-wave ESR experiments of phosphorus donors in $^\mathrm{nat}$Si demonstrate the feasibility of our resonators for magnetic resonance experiments. We extract the collective coupling rate and find a good agreement with our simulation results, corroborating our model approach. Finally, we discuss specific application cases for the different resonator designs.

We report on a novel dynamical phenomenon in electron spin resonance experiments of phosphorus donors. When strongly coupling the paramagnetic ensemble to a superconducting lumped element resonator, the coherent exchange between these two subsystems leads to a train of periodic, self-stimulated echos after a conventional Hahn echo pulse sequence. The presence of these multi-echo signatures is explained using a simple model based on spins rotating on the Bloch sphere, backed up by numerical calculations using the inhomogeneous Tavis-Cummings Hamiltonian.

We present a hybrid system consisting of a superconducting coplanar waveguide resonator coupled to a nanomechanical string and a transmon qubit acting as nonlinear circuit element. We perform spectroscopy for both the transmon qubit and the nanomechanical string. Measuring the ac-Stark shift on the transmon qubit as well as the electromechanically induced absorption on the string allows us to determine the average photon number in the microwave resonator in both the low and high power regimes. In this way, we measure photon numbers that are up to nine orders of magnitude apart. We find a quantitative agreement between the calibration of photon numbers in the microwave resonator using the two methods. Our experiments demonstrate the successful combination of superconducting circuit quantum electrodynamics and nano-electromechanics on a single chip., Comment: 7 pages, 7 figures

We propose and analyze magnetic traps and lattices for electrons in semiconductors. We provide a general theoretical framework and show that thermally stable traps can be generated by magnetically driving the particle's internal spin transition, akin to optical dipole traps for ultra-cold atoms. Next we discuss in detail periodic arrays of magnetic traps, i.e. magnetic lattices, as a platform for quantum simulation of exotic Hubbard models, with lattice parameters that can be tuned in real time. Our scheme can be readily implemented in state-of-the-art experiments, as we particularize for two specific setups, one based on a superconducting circuit and another one based on surface acoustic waves., Comment: 18 pages, 8 figures

We investigate yttrium iron garnet (YIG)/cobalt (Co) heterostructures using broadband ferromagnetic resonance (FMR). We observe an efficient excitation of perpendicular standing spin waves (PSSWs) in the YIG layer when the resonance frequencies of the YIG PSSWs and the Co FMR line coincide. Avoided crossings of YIG PSSWs and the Co FMR line are found and modeled using mutual spin pumping and exchange torques. The excitation of PSSWs is suppressed by a thin aluminum oxide (AlOx) interlayer but persists with a copper (Cu) interlayer, in agreement with the proposed model., Comment: Main text (5 pages, 3 figures), Supplemental Material (12 pages, 6 figures): sample preparation, experimental setup, data processing, determination of the material parameters, linewidth analysis, dynamic spin torque theory, and detailed interfacial spin torque model

We investigate the spin Hall magnetoresistance in thin film bilayer heterostructures of the heavy metal Pt and the antiferromagnetic insulator NiO. While rotating an external magnetic field in the easy plane of NiO, we record the longitudinal and the transverse resistivity of the Pt layer and observe an amplitude modulation consistent with the spin Hall magnetoresistance. In comparison to Pt on collinear ferrimagnets, the modulation is phase shifted by 90{\deg} and its amplitude strongly increases with the magnitude of the magnetic field. We explain the observed magnetic field-dependence of the spin Hall magnetoresistance in a comprehensive model taking into account magnetic field induced modifications of the domain structure in antiferromagnets. With this generic model we are further able to estimate the strength of the magnetoelastic coupling in antiferromagnets. Our detailed study shows that the spin Hall magnetoresistance is a versatile tool to investigate the magnetic spin structure as well as magnetoelastic effects, even in antiferromagnetic multidomain materials.

Spin transport in electric conductors is largely determined by two material parameters - spin diffusion length and spin Hall angle. In metals, these are typically determined indirectly by probing magnetoresistance in magnet/metal heterostructures, assuming knowledge of the interfacial properties. We suggest profiling the charge current induced spin Hall spin accumulation in metals, via detection of the magnetic stray field generated by the associated static magnetization, as a direct means of determining spin transport parameters. We evaluate the spatial profile of the stray field as well as the Oersted field generated by the charge current. We thus demonstrate that such a charge current induced spin accumulation is well within the detection limit of contemporary technology. Measuring the stray fields may enable direct access to spin-related properties of metals paving the way for a better and consistent understanding of spin transport therein., Comment: 10 pages, 7 figures

Broadband ferromagnetic resonance (bbFMR) spectroscopy is an established experimental tool to quantify magnetic properties. Due to frequency-dependent transmission of the microwave setup, bbFMR measurements in the frequency domain require a suitable background removal method. Here, we present a measurement and data analysis protocol that allows to perform quantitative frequency-swept bbFMR measurements without the need for a calibration of the microwave setup. The method, its limitations and advantages are described in detail. Finally the method is applied to evaluate FMR spectra of a permalloy thin film. The extracted material parameters are in very good agreement with those obtained using a conventional analysis in field-space.

We study the diffusive transport of magnons through the compensated ferrimagnetic insulator Gd3Fe5O12 (GdIG). The magnons are injected and detected electrically in a non-local measurement configuration via two parallel Pt strips deposited on top of the ferrimagnet. GdIG exhibits a rich magnon spectrum, with several thermally populated magnon bands at room temperature. We observe a strong temperature and field dependence of the non-local voltage in the detector strip. Just below the magnetization compensation temperature we find that the increasing magnetic field causes an unexpected enhancement of the non-local signal. A comparison with GdIG spin wave spectra obtained from atomistic modeling indicates that the thermal magnon population is important for understanding the non-local voltage signal.

We experimentally study magnetic resonances in the helical and conical magnetic phases of the chiral magnetic insulator Cu$_2$OSeO$_3$ at the temperature $T$=5 K. Using a broadband microwave spectroscopy technique based on vector network analysis, we identify three distinct sets of helimagnon resonances in the frequency range 2 GHz $\leq f \leq$ 20 GHz. The extracted resonance frequencies are in accordance with calculations of the helimagnon bandstructure found in an intrinsic chiral magnonic crystal. The periodic modulation of the equilibrium spin direction that leads to the formation of the magnonic crystal is a direct consequence of the chiral magnetic ordering caused by the Dzyaloshinskii-Moriya interaction. The opening of magnon band-gaps allows for excitation of helimagnons with wave vectors that are multiples of the spiral wave vector., Comment: Accepted on November 9th, 2017 for publication at Physical Review Letters (https://journals.aps.org/prl/accepted/5607dY38Rcf14865a08e67543fa3d1c6d0df92c65)

We studied the spin injection in a NiFe(Py)/Si system using broadband ferromagnetic resonance spectroscopy. The Gilbert damping parameter of the Py layer on top of the Si channel was determined as a function of the Si doping concentration and Py layer thickness. For fixed Py thickness we observed an increase of the Gilbert damping parameter with decreasing resistivity of the Si channel. For a fixed Si doping concentration we measured an increasing Gilbert damping parameter for decreasing Py layer thickness. No increase of the Gilbert damping parameter was found Py/Si samples with an insulating interlayer. We attribute our observations to an enhanced spin injection into the low-resistivity Si by spin pumping., Comment: 15 pages, 3 Figures, 2 Tables (to appear Applied Physics Letters)

We investigate the temperature dependent microwave absorption spectrum of an yttrium iron garnet sphere as a function of temperature (5 K to 300 K) and frequency (3 GHz to 43.5 GHz). At temperatures above 100 K, the magnetic resonance linewidth increases linearly with temperature and shows a Gilbert-like linear frequency dependence. At lower temperatures, the temperature dependence of the resonance linewidth at constant external magnetic fields exhibits a characteristic peak which coincides with a non-Gilbert-like frequency dependence. The complete temperature and frequency evolution of the linewidth can be modeled by the phenomenology of slowly relaxing rare-earth impurities and either the Kasuya-LeCraw mechanism or the scattering with optical magnons. Furthermore, we extract the temperature dependence of the saturation magnetization, the magnetic anisotropy and the g-factor.