Strong Coupling between Magnons and Microwave Photons in On-Chip Ferromagnet-Superconductor Thin-Film Devices

Strong Photon-Magnon Coupling Using a Lithographically Defined Organic Ferrimagnet

A cavity-magnonic system composed of a superconducting microwave resonator coupled to a magnon mode hosted by the organic-based ferrimagnet vanadium tetracyanoethylene (V[TCNE]x) is demonstrated. This work is motivated by the challenge of scalably integrating a low-damping magnetic system with planar superconducting circuits. V[TCNE]x has ultra-low intrinsic damping, can be grown at low processing temperatures on arbitrary substrates, and can be patterned via electron beam lithography. The devices operate in the strong coupling regime, with a cooperativity exceeding 1000 for coupling between the Kittel mode and the resonator mode at T≈0.4 K, suitable for scalable quantum circuit integration. Higher-order magnon modes are also observed with much narrower linewidths than the Kittel mode. This work paves the way for high-cooperativity hybrid quantum devices in which magnonic circuits can be designed and fabricated as easily as electrical wires.

Scanning Spin Probe Based on Magnonic Vortex Quantum Cavities

Performing nanoscale scanning electron paramagnetic resonance (EPR) requires three essential ingredients: First, a static magnetic field together with field gradients to Zeeman split the electronic energy levels with spatial resolution; second, a radio frequency (rf) magnetic field capable of inducing spin transitions; finally, a sensitive detection method to quantify the energy absorbed by spins. This is usually achieved by combining externally applied magnetic fields with inductive coils or cavities, fluorescent defects, or scanning probes. Here, we theoretically propose the realization of an EPR scanning sensor merging all three characteristics into a single device: the vortex core stabilized in ferromagnetic thin-film discs. On one hand, the vortex ground state generates a significant static magnetic field and field gradients. On the other hand, the precessional motion of the vortex core around its equilibrium position produces a circularly polarized oscillating magnetic field, which is enough to produce spin transitions. Finally, the spin-magnon coupling broadens the vortex gyrotropic frequency, suggesting a direct measure of the presence of unpaired electrons. Moreover, the vortex core can be displaced by simply using external magnetic fields of a few mT, enabling EPR scanning microscopy with large spatial resolution. Our numerical simulations show that, by using low damping magnets, it is theoretically possible to detect single spins located on the disc's surface. Vortex nanocavities could also attain strong coupling to individual spin molecular qubits with potential applications to mediate qubit-qubit interactions or to implement qubit readout protocols.

Study of Elastic and Structural Properties of BaFe2As2 Ultrathin Film Using Picosecond Ultrasonics

We obtain the through-thickness elastic stiffness coefficient (C33) in nominal 9 nm and 60 nm BaFe2As2 (Ba-122) thin films by using picosecond ultrasonics. Particularly, we reveal the increase in elastic stiffness as film thickness decreases from bulk value down to 9 nm, which we attribute to the increase in intrinsic strain near the film-substrate interface. Our density functional theory (DFT) calculations reproduce the observed acoustic oscillation frequencies well. In addition, temperature dependence of longitudinal acoustic (LA) phonon mode frequency for 9 nm Ba-122 thin film is reported. The frequency change is attributed to the change in Ba-122 orthorhombicity (a-b)/(a+b). This conclusion can be corroborated by our previous ultrafast ellipticity measurements in 9 nm Ba-122 thin film, which exhibit strong temperature dependence and indicate the structural phase transition temperature Ts.

Strong on-Chip Microwave Photon-Magnon Coupling Using Ultralow-Damping Epitaxial Y3Fe5O12 Films at 2 K

Y₃Fe₅O₁₂ is arguably the best magnetic material for magnonic quantum information science (QIS) because of its extremely low damping. We report ultralow damping at 2 K in epitaxial Y₃Fe₅O₁₂ thin films grown on a diamagnetic Y₃Sc₂Ga₃O₁₂ substrate that contains no rare-earth elements. Using these ultralow damping YIG films, we demonstrate for the first time strong coupling between magnons in patterned YIG thin films and microwave photons in a superconducting Nb resonator. This result paves the road toward scalable hybrid quantum systems that integrate superconducting microwave resonators, YIG film magnon conduits, and superconducting qubits into on-chip QIS devices.

Generation of robust optical entanglement in cavity optomagnonics

We propose a scheme to realize robust optical entanglement in cavity optomagnonics, where two optical whispering gallery modes (WGMs) couple to a magnon mode in a yttrium iron garnet (YIG) sphere. The beam-splitter-like and two-mode squeezing magnon-photon interactions can be realized simultaneously when the two optical WGMs are driven by external fields. Entanglement between the two optical modes is then generated via their coupling with magnons. By exploiting the destructive quantum interference between the bright modes of the interface, the effects of initial thermal occupations of magnons can be eliminated. Moreover, the excitation of the Bogoliubov dark mode is capable of protecting the optical entanglement from thermal heating effects. Therefore, the generated optical entanglement is robust against thermal noise and the requirement of cooling the magnon mode is relaxed. Our scheme may find applications in the study of magnon-based quantum information processing.

Enhanced Tripartite Interactions in Spin-Magnon-Mechanical Hybrid Systems

Coherent tripartite interactions among degrees of freedom of completely different nature are instrumental for quantum information and simulation technologies, but they are generally difficult to realize and remain largely unexplored. Here, we predict a tripartite coupling mechanism in a hybrid setup comprising a single nitrogen-vacancy (NV) center and a micromagnet. We propose to realize direct and strong tripartite interactions among single NV spins, magnons, and phonons via modulating the relative motion between the NV center and the micromagnet. Specifically, by introducing a parametric drive (two-phonon drive) to modulate the mechanical motion (such as the center-of-mass motion of a NV spin in diamond trapped in an electrical trap or a levitated micromagnet in a magnetic trap), we can obtain a tunable and strong spin-magnon-phonon coupling at the single quantum level, with up to 2 orders of magnitude enhancement for the tripartite coupling strength. This enables, for example, tripartite entanglement among solid-state spins, magnons, and mechanical motions in quantum spin-magnonics-mechanics with realistic experimental parameters. This protocol can be readily implemented with the well-developed techniques in ion traps or magnetic traps and could pave the way for general applications in quantum simulations and information processing based on directly and strongly coupled tripartite systems.

Coherent Coupling of Two Remote Magnonic Resonators Mediated by Superconducting Circuits

We demonstrate microwave-mediated distant magnon-magnon coupling on a superconducting circuit platform, incorporating chip-mounted single-crystal Y_{3}Fe_{5}O_{12} (YIG) spheres. Coherent level repulsion and dissipative level attraction between the magnon modes of the two YIG spheres are demonstrated. The former is mediated by cavity photons of a superconducting resonator, and the latter is mediated by propagating photons of a coplanar waveguide. Our results open new avenues toward exploring integrated hybrid magnonic networks for coherent information processing on a quantum-compatible superconducting platform.

Observation of magnon-magnon coupling with high cooperativity in Ni80Fe20cross-shaped nanoring array

We report here an experimental observation of dynamic dipolar coupling induced magnon-magnon coupling and spin wave (SW) mode splitting in Ni₈₀Fe₂₀cross-shaped nanoring array. Remarkably, we observe an anticrossing feature with minimum frequency gap of 0.96 GHz and the corresponding high cooperativity value of 2.25. Interestingly, splitting of the highest frequency SW mode occurs due to the anisotropic dipolar interactions between the cross nanorings. Furthermore, using micromagnetic simulations we demonstrate that the coupled SW modes propagate longer as opposed to other modes present in this system. Our work paves the way towards integrated hybrid systems-based quantum magnonics and on-chip coherent information transfer.

Ultrastrong photon-to-magnon coupling in multilayered heterostructures involving superconducting coherence via ferromagnetic layers

The critical step for future quantum industry demands realization of efficient information exchange between different-platform hybrid systems that can harvest advantages of distinct platforms. The major restraining factor for the progress in certain hybrids is weak coupling strength between the elemental particles. In particular, this restriction impedes a promising field of hybrid magnonics. In this work, we propose an approach for realization of on-chip hybrid magnonic systems with unprecedentedly strong coupling parameters. The approach is based on multilayered microstructures containing superconducting, insulating, and ferromagnetic layers with modified photon phase velocities and magnon eigenfrequencies. The enhanced coupling strength is provided by the radically reduced photon mode volume. Study of the microscopic mechanism of the photon-to-magnon coupling evidences formation of the long-range superconducting coherence via thick strong ferromagnetic layers in superconductor/ferromagnet/superconductor trilayer in the presence of magnetization precession. This discovery offers new opportunities in microwave superconducting spintronics for quantum technologies.

Quantum Interfaces to the Nanoscale

Scalable quantum information systems would store, manipulate, and transmit quantum information locally and across a quantum network, but no single qubit technology is currently robust enough to perform all necessary tasks. Defect centers in solid-state materials have emerged as potential intermediaries between other physical manifestations of qubits, such as superconducting qubits and photonic qubits, to leverage their complementary advantages. It remains an open question, however, how to design and to control quantum interfaces to defect centers. Such interfaces would enable quantum information to be moved seamlessly between different physical systems. Understanding and constructing the required interfaces would, therefore, unlock the next big steps in quantum computing, sensing, and communications. In this Perspective, we highlight promising coupling mechanisms, including dipole-, phonon-, and magnon-mediated interactions, and discuss how contributions from nanotechnologists will be paramount in realizing quantum information processors in the near-term.

Coherent Gate Operations in Hybrid Magnonics

Electromagnonics-the hybridization of spin excitations and electromagnetic waves-has been recognized as a promising candidate for coherent information processing in recent years. Among its various implementations, the lack of available approaches for real-time manipulation on the system dynamics has become a common and urgent limitation. In this work, by introducing a fast and uniform modulation technique, we successfully demonstrate a series of benchmark coherent gate operations in hybrid magnonics, including semiclassical analogies of Landau-Zener transitions, Rabi oscillations, Ramsey interference, and controlled mode swap operations. Our approach lays the groundwork for dynamical manipulation of coherent signals in hybrid magnonics and can be generalized to a broad range of applications.

Roadmap of spin-orbit torques

Spin-orbit torque (SOT) is an emerging technology that enables the efficient manipulation of spintronic devices. The initial processes of interest in SOTs involved electric fields, spin-orbit coupling, conduction electron spins and magnetization. More recently interest has grown to include a variety of other processes that include phonons, magnons, or heat. Over the past decade, many materials have been explored to achieve a larger SOT efficiency. Recently, holistic design to maximize the performance of SOT devices has extended material research from a nonmagnetic layer to a magnetic layer. The rapid development of SOT has spurred a variety of SOT-based applications. In this Roadmap paper, we first review the theories of SOTs by introducing the various mechanisms thought to generate or control SOTs, such as the spin Hall effect, the Rashba-Edelstein effect, the orbital Hall effect, thermal gradients, magnons, and strain effects. Then, we discuss the materials that enable these effects, including metals, metallic alloys, topological insulators, two-dimensional materials, and complex oxides. We also discuss the important roles in SOT devices of different types of magnetic layers, such as magnetic insulators, antiferromagnets, and ferrimagnets. Afterward, we discuss device applications utilizing SOTs. We discuss and compare three-terminal and two-terminal SOT-magnetoresistive random-access memories (MRAMs); we mention various schemes to eliminate the need for an external field. We provide technological application considerations for SOT-MRAM and give perspectives on SOT-based neuromorphic devices and circuits. In addition to SOT-MRAM, we present SOT-based spintronic terahertz generators, nano-oscillators, and domain wall and skyrmion racetrack memories. This paper aims to achieve a comprehensive review of SOT theory, materials, and applications, guiding future SOT development in both the academic and industrial sectors.

Phase-resolved electrical detection of hybrid magnonic devices

We demonstrate the electrical detection of magnon-magnon hybrid dynamics in yttrium iron garnet/permalloy (YIG/Py) thin film bilayer devices. Direct microwave current injection through the conductive Py layer excites the hybrid dynamics consisting of the uniform mode of Py and the first standing spin wave (n = 1) mode of YIG, which are coupled via interfacial exchange. Both the two hybrid modes, with Py or YIG dominated excitations, can be detected via the spin rectification signals from the conductive Py layer, providing phase resolution of the coupled dynamics. The phase characterization is also applied to a nonlocally excited Py device, revealing the additional phase shift due to the perpendicular Oersted field. Our results provide a device platform for exploring hybrid magnonic dynamics and probing their phases, which are crucial for implementing coherent information processing with magnon excitations.

Nanomagnonic Cavities for Strong Spin-Magnon Coupling and Magnon-Mediated Spin-Spin Interactions

We present a theoretical approach to use ferromagnetic or ferrimagnetic nanoparticles as microwave nanomagnonic cavities to concentrate microwave magnetic fields into deeply subwavelength volumes ∼10^{-13}  mm^{3}. We show that the field in such nanocavities can efficiently couple to isolated spin emitters (spin qubits) positioned close to the nanoparticle surface reaching the single magnon-spin strong-coupling regime and mediate efficient long-range quantum state transfers between isolated spin emitters. Nanomagnonic cavities thus pave the way toward magnon-based quantum networks and magnon-mediated quantum gates.

Floquet Cavity Electromagnonics

Hybrid magnonics has recently attracted intensive attention as a promising platform for coherent information processing. In spite of its rapid development, on-demand control over the interaction of magnons with other information carriers, in particular, microwave photons in electromagnonic systems, has been long missing, significantly limiting the potential broad applications of hybrid magnonics. Here, we show that, by introducing Floquet engineering into cavity electromagnonics, coherent control on the magnon-microwave photon coupling can be realized. Leveraging the periodic temporal modulation from a Floquet drive, our first-of-its-kind Floquet cavity electromagnonic system enables the manipulation of the interaction between hybridized cavity electromagnonic modes. Moreover, we have achieved a new coupling regime in such systems: the Floquet ultrastrong coupling, where the Floquet splitting is comparable with or even larger than the level spacing of the two interacting modes, beyond the conventional rotating-wave picture. Our findings open up new directions for magnon-based coherent signal processing.

Experimental parameters, combined dynamics, and nonlinearity of a magnonic-opto-electronic oscillator (MOEO)

We report the construction and characterization of a comprehensive magnonic-opto-electronic oscillator (MOEO) system based on 1550-nm photonics and yttrium iron garnet (YIG) magnonics. The system exhibits a rich and synergistic parameter space because of the ability to control individual photonic, electronic, and magnonic components. Taking advantage of the spin wave dispersion of YIG, the frequency self-generation as well as the related nonlinear processes becomes sensitive to the external magnetic field. Besides being known as a band-pass filter and a delay element, the YIG delay line possesses spin wave modes that can be controlled to mix with the optoelectronic modes to generate higher-order harmonic beating modes. With the high sensitivity and external tunability, the MOEO system may find usefulness in sensing applications in magnetism and spintronics beyond optoelectronics and photonics.

Magnonic Quadrupole Topological Insulator in Antiskyrmion Crystals

We uncover that antiskyrmion crystals provide an experimentally accessible platform to realize a magnonic quadrupole topological insulator, whose hallmark signatures are robust magnonic corner states. Furthermore, we show that tuning an applied magnetic field can trigger the self-assembly of antiskyrmions carrying a fractional topological charge along the sample edges. Crucially, these fractional antiskyrmions restore the symmetries needed to enforce the emergence of the magnonic corner states. Using the machinery of nested Wilson loops, adapted to magnonic systems supported by noncollinear magnetic textures, we demonstrate the quantization of the bulk quadrupole moment, edge dipole moments, and corner charges.

Magnon laser based on Brillouin light scattering

An analogous laser action of magnons has become a subject of interest, and it is crucial for the study of nonlinear magnons spintronics. In this Letter, we demonstrate the magnon laser behavior based on Brillouin light scattering in a ferrimagnetic insulator sphere, which supports optical whispering gallery modes and magnon resonances. We show that the excited magnon plays what has traditionally been the role of the Stokes wave and is coherently amplified during the Brillouin scattering process, making the magnon laser possible. Furthermore, the stimulating excited magnon number increasing exponentially with the input light power can be manipulated by adjusting the external magnetic field. In addition to providing insight into magneto-optical interaction, the study of the magnon laser action will help to develop novel, to the best of our knowledge, technologies for handling spin-wave excitations, and it could affect scientific fields beyond magnonics. Potential applications range from preparing coherent magnon sources to operating on-chip functional magnetic devices.

Resonant thermal energy transfer to magnons in a ferromagnetic nanolayer

Energy harvesting is a concept which makes dissipated heat useful by transferring thermal energy to other excitations. Most of the existing principles are realized in systems which are heated continuously. We present the concept of high-frequency energy harvesting where the dissipated heat in a sample excites resonant magnons in a thin ferromagnetic metal layer. The sample is excited by femtosecond laser pulses with a repetition rate of 10 GHz, which results in temperature modulation at the same frequency with amplitude ~0.1 K. The alternating temperature excites magnons in the ferromagnetic nanolayer which are detected by measuring the net magnetization precession. When the magnon frequency is brought onto resonance with the optical excitation, a 12-fold increase of the amplitude of precession indicates efficient resonant heat transfer from the lattice to coherent magnons. The demonstrated principle may be used for energy harvesting in various nanodevices operating at GHz and sub-THz frequency ranges.

Probing magnon-magnon coupling in exchange coupled Y[Formula: see text]Fe[Formula: see text]O[Formula: see text]/Permalloy bilayers with magneto-optical effects

We demonstrate the magnetically-induced transparency (MIT) effect in Y[Formula: see text]Fe[Formula: see text]O[Formula: see text](YIG)/Permalloy (Py) coupled bilayers. The measurement is achieved via a heterodyne detection of the coupled magnetization dynamics using a single wavelength that probes the magneto-optical Kerr and Faraday effects of Py and YIG, respectively. Clear features of the MIT effect are evident from the deeply modulated ferromagnetic resonance of Py due to the perpendicular-standing-spin-wave of YIG. We develop a phenomenological model that nicely reproduces the experimental results including the induced amplitude and phase evolution caused by the magnon-magnon coupling. Our work offers a new route towards studying phase-resolved spin dynamics and hybrid magnonic systems.

Enhanced Magnon-Photon Coupling at the Angular Momentum Compensation Point of Ferrimagnets

We theoretically show that the coupling between magnons in an antiferromagnetically coupled ferrimagnet and microwave photons in a cavity is largely enhanced at the angular momentum compensation point (T_{A}) when T_{A} is distinct from the magnetization compensation point. The origin of the enhanced magnon-photon coupling at T_{A} is identified as the antiferromagnetic spin dynamics combined with a finite magnetization. Moreover, we show that strong magnon-photon coupling can be achieved at high excitation frequency in a ferrimagnet, which is challenging to achieve for a ferromagnet due to low magnon frequency and for an antiferromagnet due to weak magnon-photon coupling. Our results will invigorate research on magnon-photon coupling by proposing ferrimagnets as a versatile platform that offers advantages of both ferromagnets and antiferromagnets.

Conductivitylike Gilbert Damping due to Intraband Scattering in Epitaxial Iron

Confirming the origin of Gilbert damping by experiment has remained a challenge for many decades, even for simple ferromagnetic metals. Here, we experimentally identify Gilbert damping that increases with decreasing electronic scattering in epitaxial thin films of pure Fe. This observation of conductivitylike damping, which cannot be accounted for by classical eddy-current loss, is in excellent quantitative agreement with theoretical predictions of Gilbert damping due to intraband scattering. Our results resolve the long-standing question about a fundamental damping mechanism and offer hints for engineering low-loss magnetic metals for cryogenic spintronics and quantum devices.

Coherent Spin Pumping in a Strongly Coupled Magnon-Magnon Hybrid System

We experimentally identify coherent spin pumping in the magnon-magnon hybrid modes of yttrium iron garnet/permalloy (YIG/Py) bilayers. By reducing the YIG and Py thicknesses, the strong interfacial exchange coupling leads to large avoided crossings between the uniform mode of Py and the spin wave modes of YIG enabling accurate determination of modification of the linewidths due to the dampinglike torque. We identify additional linewidth suppression and enhancement for the in-phase and out-of-phase hybrid modes, respectively, which can be interpreted as concerted dampinglike torque from spin pumping. Furthermore, varying the Py thickness shows that both the fieldlike and dampinglike couplings vary like 1/sqrt[t_{Py}], verifying the prediction by the coupled Landau-Lifshitz equations.

Strong Coupling between Microwave Photons and Nanomagnet Magnons

Coupled microwave photon-magnon hybrid systems offer promising applications by harnessing various magnon physics. At present, in order to realize high coupling strength between the two subsystems, bulky ferromagnets with large spin numbers are utilized, which limits their potential applications for scalable quantum information processing. By enhancing single spin coupling strength using lithographically defined superconducting resonators, we report high cooperativities between a resonator mode and a Kittel mode in nanometer thick Permalloy wires. The on-chip, lithographically scalable, and superconducting quantum circuit compatible design provides a direct route towards realizing hybrid quantum systems with nanomagnets, whose coupling strength can be precisely engineered and dynamic properties can be controlled by various mechanisms derived from spintronic studies.