Nanometre-scale probing of spin waves using single-electron spins

Quantum Sensing of Spin Dynamics Using Boron-Vacancy Centers in Hexagonal Boron Nitride

Spin defects embedded in solid-state systems are appealing for quantum sensing of materials and for quantum science and engineering. The spin-sensitive photoluminescence of optically active spin defects in Van der Waals based materials, such as the boron-vacancy (V_{B}^{-}) center in hexagonal boron nitride, enables its application as a quantum sensor to detect weak, spatially localized magnetic static and dynamic fields. However, the utility of V_{B}^{-} centers to probe spin dynamics in magnetic systems has yet to be demonstrated; this is essential to establish the V_{B}^{-} as a modular sensing platform that can be seamlessly integrated with emergent quantum materials to probe a wide range of static and dynamic phenomena. Here, we use V_{B}^{-} centers to experimentally probe uniform mode magnon dynamics and optically perform ferromagnetic resonance spectroscopy on a thin magnetic film.

Room Temperature Relaxometry of Single Nitrogen Vacancy Centers in Proximity to α-RuCl3 Nanoflakes

Nitrogen vacancy (NV) center-based magnetometry has been proven to be a versatile sensor for various classes of magnetic materials in broad temperature and frequency ranges. Here, we use the longitudinal relaxation time T1 of single NV centers to investigate the spin dynamics of nanometer-thin flakes of α-RuCl3 at room temperature. We observe a significant reduction in the T1 in the presence of α-RuCl3 in the proximity of NVs, which we attribute to paramagnetic spin noise confined in the 2D hexagonal planes. Furthermore, the T1 time exhibits a monotonic increase with an applied magnetic field. We associate this trend with the alteration of the spin and charge noise in α-RuCl3 under an external magnetic field. These findings suggest that the influence of the spin dynamics of α-RuCl3 on the T1 of the NV center can be used to gain information about the material itself and the technique to be used on other 2D materials.

Parametric magnon transduction to spin qubits

The integration of heterogeneous modular units for building large-scale quantum networks requires engineering mechanisms that allow suitable transduction of quantum information. Magnon-based transducers are especially attractive due to their wide range of interactions and rich nonlinear dynamics, but most of the work to date has focused on linear magnon transduction in the traditional system composed of yttrium iron garnet and diamond, two materials with difficult integrability into wafer-scale quantum circuits. In this work, we present a different approach by using wafer-compatible materials to engineer a hybrid transducer that exploits magnon nonlinearities in a magnetic microdisc to address quantum spin defects in silicon carbide. The resulting interaction scheme points to the unique transduction behavior that can be obtained when complementing quantum systems with nonlinear magnonics.

Magnon-mediated qubit coupling determined via dissipation measurements

Controlled interaction between localized and delocalized solid-state spin systems offers a compelling platform for on-chip quantum information processing with quantum spintronics. Hybrid quantum systems (HQSs) of localized nitrogen-vacancy (NV) centers in diamond and delocalized magnon modes in ferrimagnets-systems with naturally commensurate energies-have recently attracted significant attention, especially for interconnecting isolated spin qubits at length-scales far beyond those set by the dipolar coupling. However, despite extensive theoretical efforts, there is a lack of experimental characterization of the magnon-mediated interaction between NV centers, which is necessary to develop such hybrid quantum architectures. Here, we experimentally determine the magnon-mediated NV-NV coupling from the magnon-induced self-energy of NV centers. Our results are quantitatively consistent with a model in which the NV center is coupled to magnons by dipolar interactions. This work provides a versatile tool to characterize HQSs in the absence of strong coupling, informing future efforts to engineer entangled solid-state systems.

Resolving Nonclassical Magnon Composition of a Magnetic Ground State via a Qubit

Recently gained insights into equilibrium squeezing and entanglement harbored by magnets point toward exciting opportunities for quantum science and technology, while concrete protocols for exploiting these are needed. Here, we theoretically demonstrate that a direct dispersive coupling between a qubit and a noneigenmode magnon enables detecting the magnonic number states' quantum superposition that forms the ground state of the actual eigenmode-squeezed magnon-via qubit excitation spectroscopy. Furthermore, this unique coupling is found to enable control over the equilibrium magnon squeezing and a deterministic generation of squeezed even Fock states via the qubit state and its excitation. Our work demonstrates direct dispersive coupling to noneigenmodes, realizable in spin systems, as a general pathway to exploiting the equilibrium squeezing and related quantum properties thereby motivating a search for similar realizations in other platforms.

Layer-Dependent Magnetism and Spin Fluctuations in Atomically Thin van der Waals Magnet CrPS4

van der Waals (vdW) magnets, an emerging family of two-dimensional (2D) materials, have received tremendous attention due to their rich fundamental physics and significant potential for cutting-edge technological applications. In contrast to the conventional bulk counterparts, vdW magnets exhibit significant tunability of local material properties, such as stacking engineered interlayer coupling and layer-number dependent magnetic and electronic interactions, which promise to deliver previously unavailable merits to develop multifunctional microelectronic devices. As a further ingredient of this emerging topic, here we report nanoscale quantum sensing and imaging of the atomically thin vdW magnet chromium thiophosphate CrPS4, revealing its characteristic layer-dependent 2D static magnetism and dynamic spin fluctuations. We also show a large tunneling magnetoresistance in CrPS4-based spin filter vdW heterostructures. The excellent material stability and robust strategy against environmental degradation in combination with tailored magnetic properties highlight the potential of CrPS4 in developing state-of-the-art 2D spintronic devices for next-generation information technologies.

Revealing intrinsic domains and fluctuations of moiré magnetism by a wide-field quantum microscope

Moiré magnetism featured by stacking engineered atomic registry and lattice interactions has recently emerged as an appealing quantum state of matter at the forefront of condensed matter physics research. Nanoscale imaging of moiré magnets is highly desirable and serves as a prerequisite to investigate a broad range of intriguing physics underlying the interplay between topology, electronic correlations, and unconventional nanomagnetism. Here we report spin defect-based wide-field imaging of magnetic domains and spin fluctuations in twisted double trilayer (tDT) chromium triiodide CrI3. We explicitly show that intrinsic moiré domains of opposite magnetizations appear over arrays of moiré supercells in low-twist-angle tDT CrI3. In contrast, spin fluctuations measured in tDT CrI3 manifest little spatial variations on the same mesoscopic length scale due to the dominant driving force of intralayer exchange interaction. Our results enrich the current understanding of exotic magnetic phases sustained by moiré magnetism and highlight the opportunities provided by quantum spin sensors in probing microscopic spin related phenomena on two-dimensional flatland.

Breaking Down the Magnonic Wiedemann-Franz Law in the Hydrodynamic Regime

Recent experiments have shown an indication of a hydrodynamic magnon behavior in ultrapure ferromagnetic insulators; however, its direct observation is still lacking. Here, we derive a set of coupled hydrodynamic equations and study the thermal and spin conductivities for such a magnon fluid. We reveal the drastic breakdown of the magnonic Wiedemann-Franz law as a hallmark of the hydrodynamics regime, which will become key evidence for the experimental realization of an emergent hydrodynamic magnon behavior. Therefore, our results pave the way toward the direct observation of magnon fluids.

Relaxometry with Nitrogen Vacancy (NV) Centers in Diamond

Relaxometry is a technique which makes use of a specific crystal lattice defect in diamond, the so-called NV center. This defect consists of a nitrogen atom, which replaces a carbon atom in the diamond lattice, and an adjacent vacancy. NV centers allow converting magnetic noise into optical signals, which dramatically increases the sensitivity of the readout, allowing for nanoscale resolution. Analogously to T1 measurements in conventional magnetic resonance imaging (MRI), relaxometry allows the detection of different concentrations of paramagnetic species. However, since relaxometry allows very local measurements, the detected signals are from nanoscale voxels around the NV centers. As a result, it is possible to achieve subcellular resolutions and organelle specific measurements.A relaxometry experiment starts with polarizing the spins of NV centers in the diamond lattice, using a strong laser pulse. Afterward the laser is switched off and the NV centers are allowed to stochastically decay into the equilibrium mix of different magnetic states. The polarized configuration exhibits stronger fluorescence than the equilibrium state, allowing one to optically monitor this transition and determine its rate. This process happens faster at higher levels of magnetic noise. Alternatively, it is possible to conduct T1 relaxation measurements from the dark to the bright equilibrium by applying a microwave pulse which brings NV centers into the -1 state instead of the 0 state. One can record a spectrum of T1 at varying strengths of the applied magnetic field. This technique is called cross-relaxometry. Apart from detecting magnetic signals, responsive coatings can be applied which render T1 sensitive to other parameters as pH, temperature, or electric field. Depending on the application there are three different ways to conduct relaxometry experiments: relaxometry in moving or stationary nanodiamonds, scanning magnetometry, and relaxometry in a stationary bulk diamond with a stationary sample on top.In this Account, we present examples for various relaxometry modes as well as their advantages and limitations. Due to the simplicity and low cost of the approach, relaxometry has been implemented in many different instruments and for a wide range of applications. Herein we review the progress that has been achieved in physics, chemistry, and biology. Many articles in this field have a proof-of-principle character, and the full potential of the technology still waits to be unfolded. With this Account, we would like to stimulate discourse on the future of relaxometry.

Wide field imaging of van der Waals ferromagnet Fe3GeTe2 by spin defects in hexagonal boron nitride

Emergent color centers with accessible spins hosted by van der Waals materials have attracted substantial interest in recent years due to their significant potential for implementing transformative quantum sensing technologies. Hexagonal boron nitride (hBN) is naturally relevant in this context due to its remarkable ease of integration into devices consisting of low-dimensional materials. Taking advantage of boron vacancy spin defects in hBN, we report nanoscale quantum imaging of low-dimensional ferromagnetism sustained in Fe₃GeTe₂/hBN van der Waals heterostructures. Exploiting spin relaxometry methods, we have further observed spatially varying magnetic fluctuations in the exfoliated Fe₃GeTe₂ flake, whose magnitude reaches a peak value around the Curie temperature. Our results demonstrate the capability of spin defects in hBN of investigating local magnetic properties of layered materials in an accessible and precise way, which can be extended readily to a broad range of miniaturized van der Waals heterostructure systems.

Hexagonal boron nitride (h-BN) has been used extensively to encapsulate other van der Waals materials, protecting them from environmental degradation, and allowing integration into more complex heterostructures. Here, the authors make use of boron vacancy spin defects in h-BN using them to image the magnetic properties of a Fe₃GeTe₂ flake.

Quantum Imaging of Magnetic Phase Transitions and Spin Fluctuations in Intrinsic Magnetic Topological Nanoflakes

Topological materials featuring exotic band structures, unconventional current flow patterns, and emergent organizing principles offer attractive platforms for the development of next-generation transformative quantum electronic technologies. The family of MnBi₂Te₄ (Bi₂Te₃)_n materials is naturally relevant in this context due to their nontrivial band topology, tunable magnetism, and recently discovered extraordinary quantum transport behaviors. Despite numerous pioneering studies to date, the local magnetic properties of MnBi₂Te₄ (Bi₂Te₃)_n remain an open question, hindering a comprehensive understanding of their fundamental material properties. Exploiting nitrogen-vacancy (NV) centers in diamond, we report nanoscale quantum imaging of the magnetic phase transitions and spin fluctuations in exfoliated MnBi₄Te₇ flakes, revealing the underlying spin transport physics and magnetic domains at the nanoscale. Our results highlight the unique advantage of NV centers in exploring the magnetic properties of emergent quantum materials, opening new opportunities for investigating the interplay between topology and magnetism.

Frequency multiplication by collective nanoscale spin-wave dynamics

Frequency multiplication is a process in modern electronics in which harmonics of the input frequency are generated in nonlinear electronic circuits. Devices based on the propagation and interaction of spin waves are a promising alternative to conventional electronics. The characteristic frequency of these excitations is in the gigahertz (GHz) range and devices are not readily interfaced with conventional electronics. Here, we locally probe the magnetic excitations in a soft magnetic material by optical methods and show that megahertz-range excitation frequencies cause switching effects on the micrometer scale, leading to phase-locked spin-wave emission in the GHz range. Indeed, the frequency multiplication process inside the magnetic medium covers six octaves and opens exciting perspectives for spintronic applications, such as all-magnetic mixers or on-chip GHz sources.

Noninvasive measurements of spin transport properties of an antiferromagnetic insulator

Antiferromagnetic insulators (AFIs) are of substantial interest because of their potential in the development of next-generation spintronic devices. One major effort in this emerging field is to harness AFIs for long-range spin information communication and storage. Here, we report a noninvasive method to optically access the intrinsic spin transport properties of an archetypical AFI α-Fe₂O₃ via nitrogen-vacancy (NV) quantum spin sensors. By NV relaxometry measurements, we successfully detect the frequency-dependent dynamic fluctuations of the spin density of α-Fe₂O₃ along the Néel order parameter, from which an intrinsic spin diffusion constant of α-Fe₂O₃ is experimentally measured in the absence of external spin biases. Our results highlight the significant opportunity offered by NV centers in diagnosing the underlying spin transport properties in a broad range of high-frequency magnetic materials such as two-dimensional magnets, spin liquids, and magnetic Weyl semimetals, which are challenging to access by the conventional measurement techniques.

Applications of nanomagnets as dynamical systems: II

In Part I of this topical review, we discussed dynamical phenomena in nanomagnets, focusing primarily on magnetization reversal with an eye to digital applications. In this part, we address mostly wave-like phenomena in nanomagnets, with emphasis on spin waves in myriad nanomagnetic systems and methods of controlling magnetization dynamics in nanomagnet arrays which may have analog applications. We conclude with a discussion of some interesting spintronic phenomena that undergird the rich physics exhibited by nanomagnet assemblies.

Directional Excitation of a High-Density Magnon Gas Using Coherently Driven Spin Waves

Controlling magnon densities in magnetic materials enables driving spin transport in magnonic devices. We demonstrate the creation of large, out-of-equilibrium magnon densities in a thin-film magnetic insulator via microwave excitation of coherent spin waves and subsequent multimagnon scattering. We image both the coherent spin waves and the resulting incoherent magnon gas using scanning-probe magnetometry based on electron spins in diamond. We find that the gas extends unidirectionally over hundreds of micrometers from the excitation stripline. Surprisingly, the gas density far exceeds that expected for a boson system following a Bose-Einstein distribution with a maximum value of the chemical potential. We characterize the momentum distribution of the gas by measuring the nanoscale spatial decay of the magnetic stray fields. Our results show that driving coherent spin waves leads to a strong out-of-equilibrium occupation of the spin-wave band, opening new possibilities for controlling spin transport and magnetic dynamics in target directions.

Strong Correlation Between Superconductivity and Ferromagnetism in an Fe-Chalcogenide Superconductor

The interplay among topology, superconductivity, and magnetism promises to bring a plethora of exotic and unintuitive behaviors in emergent quantum materials. The family of Fe-chalcogenide superconductors FeTe_xSe_1-x are directly relevant in this context due to their intrinsic topological band structure, high-temperature superconductivity, and unconventional pairing symmetry. Despite enormous promise and expectation, the local magnetic properties of FeTe_xSe_1-x remain largely unexplored, which prevents a comprehensive understanding of their underlying material properties. Exploiting nitrogen vacancy (NV) centers in diamond, here we report nanoscale quantum sensing and imaging of magnetic flux generated by exfoliated FeTe_xSe_1-x flakes, demonstrating strong correlation between superconductivity and ferromagnetism in FeTe_xSe_1-x. The coexistence of superconductivity and ferromagnetism in an established topological superconductor opens up new opportunities for exploring exotic spin and charge transport phenomena in quantum materials. The demonstrated coupling between NV centers and FeTe_xSe_1-x may also find applications in developing hybrid architectures for next-generation, solid-state-based quantum information technologies.

Precision Magnetometers for Aerospace Applications: A Review

Aerospace technologies are crucial for modern civilization; space-based infrastructure underpins weather forecasting, communications, terrestrial navigation and logistics, planetary observations, solar monitoring, and other indispensable capabilities. Extraplanetary exploration—including orbital surveys and (more recently) roving, flying, or submersible unmanned vehicles—is also a key scientific and technological frontier, believed by many to be paramount to the long-term survival and prosperity of humanity. All of these aerospace applications require reliable control of the craft and the ability to record high-precision measurements of physical quantities. Magnetometers deliver on both of these aspects and have been vital to the success of numerous missions. In this review paper, we provide an introduction to the relevant instruments and their applications. We consider past and present magnetometers, their proven aerospace applications, and emerging uses. We then look to the future, reviewing recent progress in magnetometer technology. We particularly focus on magnetometers that use optical readout, including atomic magnetometers, magnetometers based on quantum defects in diamond, and optomechanical magnetometers. These optical magnetometers offer a combination of field sensitivity, size, weight, and power consumption that allows them to reach performance regimes that are inaccessible with existing techniques. This promises to enable new applications in areas ranging from unmanned vehicles to navigation and exploration.

Nanoscale Vector AC Magnetometry with a Single Nitrogen-Vacancy Center in Diamond

Detection of AC magnetic fields at the nanoscale is critical in applications ranging from fundamental physics to materials science. Isolated quantum spin defects, such as the nitrogen-vacancy center in diamond, can achieve the desired spatial resolution with high sensitivity. Still, vector AC magnetometry currently relies on using different orientations of an ensemble of sensors, with degraded spatial resolution, and a protocol based on a single NV is lacking. Here we propose and experimentally demonstrate a protocol that exploits a single NV to reconstruct the vectorial components of an AC magnetic field by tuning a continuous driving to distinct resonance conditions. We map the spatial distribution of an AC field generated by a copper wire on the surface of the diamond. The proposed protocol combines high sensitivity, broad dynamic range, and sensitivity to both coherent and stochastic signals, with broad applications in condensed matter physics, such as probing spin fluctuations.

A Molecular Approach to Quantum Sensing

The second quantum revolution hinges on the creation of materials that unite atomic structural precision with electronic and structural tunability. A molecular approach to quantum information science (QIS) promises to enable the bottom-up creation of quantum systems. Within the broad reach of QIS, which spans fields ranging from quantum computation to quantum communication, we will focus on quantum sensing. Quantum sensing harnesses quantum control to interrogate the world around us. A broadly applicable class of quantum sensors would feature adaptable environmental compatibility, control over distance from the target analyte, and a tunable energy range of interaction. Molecules enable customizable "designer" quantum sensors with tunable functionality and compatibility across a range of environments. These capabilities offer the potential to bring unmatched sensitivity and spatial resolution to address a wide range of sensing tasks from the characterization of dynamic biological processes to the detection of emergent phenomena in condensed matter. In this Outlook, we outline the concepts and design criteria central to quantum sensors and look toward the next generation of designer quantum sensors based on new classes of molecular sensors.

Magnetic domains and domain wall pinning in atomically thin CrBr3 revealed by nanoscale imaging

The emergence of atomically thin van der Waals magnets provides a new platform for the studies of two-dimensional magnetism and its applications. However, the widely used measurement methods in recent studies cannot provide quantitative information of the magnetization nor achieve nanoscale spatial resolution. These capabilities are essential to explore the rich properties of magnetic domains and spin textures. Here, we employ cryogenic scanning magnetometry using a single-electron spin of a nitrogen-vacancy center in a diamond probe to unambiguously prove the existence of magnetic domains and study their dynamics in atomically thin CrBr₃. By controlling the magnetic domain evolution as a function of magnetic field, we find that the pinning effect is a dominant coercivity mechanism and determine the magnetization of a CrBr₃ bilayer to be about 26 Bohr magnetons per square nanometer. The high spatial resolution of this technique enables imaging of magnetic domains and allows to locate the sites of defects that pin the domain walls and nucleate the reverse domains. Our work highlights scanning nitrogen-vacancy center magnetometry as a quantitative probe to explore nanoscale features in two-dimensional magnets.

Van der Waals (vdW) magnets have allowed researchers to explore the two dimensional limit of magnetisation; however experimental challenges have hindered analysis of magnetic domains. Here, using an NV centre based probe, the authors analyse the nature of magnetic domains in the vdW magnet, CrBr₃.

Imaging non-collinear antiferromagnetic textures via single spin relaxometry

Antiferromagnetic materials are promising platforms for next-generation spintronics owing to their fast dynamics and high robustness against parasitic magnetic fields. However, nanoscale imaging of the magnetic order in such materials with zero net magnetization remains a major experimental challenge. Here we show that non-collinear antiferromagnetic spin textures can be imaged by probing the magnetic noise they locally produce via thermal populations of magnons. To this end, we perform nanoscale, all-optical relaxometry with a scanning quantum sensor based on a single nitrogen-vacancy (NV) defect in diamond. Magnetic noise is detected through an increase of the spin relaxation rate of the NV defect, which results in an overall reduction of its photoluminescence signal under continuous laser illumination. As a proof-of-concept, the efficiency of the method is demonstrated by imaging various spin textures in synthetic antiferromagnets, including domain walls, spin spirals and antiferromagnetic skyrmions. This imaging procedure could be extended to a large class of intrinsic antiferromagnets and opens up new opportunities for studying the physics of localized spin wave modes for magnonics.

Sequential Bayesian experiment design for adaptive Ramsey sequence measurements

The Ramsey sequence is a canonical example of a quantum phase measurement for a spin qubit. In Ramsey measurements, the measurement efficiency can be optimized through careful selection of settings for the phase accumulation time setting, τ. This paper implements a sequential Bayesian experiment design protocol in low-fidelity Ramsey measurements, and its performance is compared to a previously reported adaptive heuristic protocol, a quantum phase estimation algorithm, and random setting choices. A workflow allowing measurements and design calculations to run concurrently largely eliminates computation time from measurement overhead. When precession frequency is the lone parameter to estimate, the Bayesian design is faster by factors of roughly 2 and 4 and 5 relative to the adaptive heuristic, random τ choices and the quantum phase estimation algorithm respectively. When four parameters are to be determined, Bayesian experiment design and random τ choices can converge to roughy equivalent sensitivity, but the Bayesian method converges 4 times faster.

Recent Advances in Single Crystal Diamond Device Fabrication for Photonics, Sensing and Nanomechanics

In the last two decades, the use of diamond as a material for applications in nanophotonics, optomechanics, quantum information, and sensors tremendously increased due to its outstanding mechanical properties, wide optical transparency, and biocompatibility. This has been possible owing to advances in methods for growth of high-quality single crystal diamond (SCD), nanofabrication methods and controlled incorporation of optically active point defects (e.g., nitrogen vacancy centers) in SCD. This paper reviews the recent advances in SCD nano-structuring methods for realization of micro- and nano-structures. Novel fabrication methods are discussed and the different nano-structures realized for a wide range of applications are summarized. Moreover, the methods for color center incorporation in SCD and surface treatment methods to enhance their properties are described. Challenges in the upscaling of SCD nano-structure fabrication, their commercial applications and future prospects are discussed.

Universal Prethermal Dynamics in Heisenberg Ferromagnets

We study the far from equilibrium prethermal dynamics of magnons in Heisenberg ferromagnets. We show that such systems exhibit universal self-similar scaling in momentum and time of the quasiparticle distribution function, with the scaling exponents independent of microscopic details or initial conditions. We argue that the SU(2) symmetry of the Hamiltonian, which leads to a strong momentum-dependent magnon-magnon scattering amplitude, gives rise to qualitatively distinct prethermal dynamics from that recently observed in Bose gases. We compute the scaling exponents using the Boltzmann kinetic equation and incoherent initial conditions that can be realized with microwave pumping of magnons. We also compare our numerical results with analytic estimates of the scaling exponents and demonstrate the robustness of the scaling to variations in the initial conditions. Our predictions can be tested in quench experiments of spin systems in optical lattices and pump-probe experiments in ferromagnetic insulators such as yttrium iron garnet.

Magnetic resonance imaging of spin-wave transport and interference in a magnetic insulator

Spin waves-the elementary excitations of magnetic materials-are prime candidate signal carriers for low-dissipation information processing. Being able to image coherent spin-wave transport is crucial for developing interference-based spin-wave devices. We introduce magnetic resonance imaging of the microwave magnetic stray fields that are generated by spin waves as a new approach for imaging coherent spin-wave transport. We realize this approach using a dense layer of electronic sensor spins in a diamond chip, which combines the ability to detect small magnetic fields with a sensitivity to their polarization. Focusing on a thin-film magnetic insulator, we quantify spin-wave amplitudes, visualize spin-wave dispersion and interference, and demonstrate time-domain measurements of spin-wave packets. We theoretically explain the observed anisotropic spin-wave patterns in terms of chiral spin-wave excitation and stray-field coupling to the sensor spins. Our results pave the way for probing spin waves in atomically thin magnets, even when embedded between opaque materials.

Broadband multi-magnon relaxometry using a quantum spin sensor for high frequency ferromagnetic dynamics sensing

Development of sensitive local probes of magnon dynamics is essential to further understand the physical processes that govern magnon generation, propagation, scattering, and relaxation. Quantum spin sensors like the NV center in diamond have long spin lifetimes and their relaxation can be used to sense magnetic field noise at gigahertz frequencies. Thus far, NV sensing of ferromagnetic dynamics has been constrained to the case where the NV spin is resonant with a magnon mode in the sample meaning that the NV frequency provides an upper bound to detection. In this work we demonstrate ensemble NV detection of spinwaves generated via a nonlinear instability process where spinwaves of nonzero wavevector are parametrically driven by a high amplitude microwave field. NV relaxation caused by these driven spinwaves can be divided into two regimes; one- and multi-magnon NV relaxometry. In the one-magnon NV relaxometry regime the driven spinwave frequency is below the NV frequencies. The driven spinwave undergoes four-magnon scattering resulting in an increase in the population of magnons which are frequency matched to the NVs. The dipole magnetic fields of the NV-resonant magnons couple to and relax nearby NV spins. The amplitude of the NV relaxation increases with the wavevector of the driven spinwave mode which we are able to vary up to 3 × 10⁶ m^-1, well into the part of the spinwave spectrum dominated by the exchange interaction. Increasing the strength of the applied magnetic field brings all spinwave modes to higher frequencies than the NV frequencies. We find that the NVs are relaxed by the driven spinwave instability despite the absence of any individual NV-resonant magnons, suggesting that multiple magnons participate in creating magnetic field noise below the ferromagnetic gap frequency which causes NV spin relaxation.

Nanoscale Detection of Magnon Excitations with Variable Wavevectors Through a Quantum Spin Sensor

We report the optical detection of magnons with a broad range of wavevectors in magnetic insulator Y₃Fe₅O₁₂ thin films by proximate nitrogen-vacancy (NV) single-spin sensors. Through multimagnon scattering processes, the excited magnons generate fluctuating magnetic fields at the NV electron spin resonance frequencies, which accelerate the relaxation of NV spins. By measuring the variation of the emitted spin-dependent photoluminescence of the NV centers, magnons with variable wavevectors up to ∼5 × 10⁷ m^-1 can be optically accessed, providing an alternative perspective to reveal the underlying spin behaviors in magnetic systems. Our results highlight the significant opportunities offered by NV single-spin quantum sensors in exploring nanoscale spin dynamics of emergent spintronic materials.

Utilising NV based quantum sensing for velocimetry at the nanoscale

Nitrogen-Vacancy (NV) centers in diamonds have been shown in recent years to be excellent magnetometers on the nanoscale. One of the recent applications of the quantum sensor is retrieving the Nuclear Magnetic Resonance (NMR) spectrum of a minute sample, whose net polarization is well below the Signal-to-Noise Ratio (SNR) of classic devices. The information in the magnetic noise of diffusing particles has also been shown in decoherence spectroscopy approaches to provide a method for measuring different physical parameters. Similar noise is induced on the NV center by a flowing liquid. However, when the noise created by diffusion effects is more dominant than the noise of the drift, it is unclear whether the velocity can be efficiently estimated. Here we propose a non-intrusive setup for measuring the drift velocity near the surface of a flow channel based on magnetic field quantum sensing using NV centers. We provide a detailed analysis of the sensitivity for different measurement protocols, and we show that our nanoscale velocimetry scheme outperforms current fluorescence based approaches even when diffusion noise is dominant. Our scheme can be applied for the investigation of microfluidic channels, where the drift velocity is usually low and the flow properties are currently unclear. A better understanding of these properties is essential for the future development of microfluidic and nanofluidic infrastructures.

Chiral Pumping of Spin Waves

We report a theory for the coherent and incoherent chiral pumping of spin waves into thin magnetic films through the dipolar coupling with a local magnetic transducer, such as a nanowire. The ferromagnetic resonance of the nanowire is broadened by the injection of unidirectional spin waves that generates a nonequilibrium magnetization in only half of the film. A temperature gradient between the local magnet and film leads to a unidirectional flow of incoherent magnons, i.e., a chiral spin Seebeck effect.

Nonlocal Spin Transport as a Probe of Viscous Magnon Fluids

Magnons in ferromagnets behave as a viscous fluid over a length scale, the momentum-relaxation length, below which momentum-conserving scattering processes dominate. We show theoretically that in this hydrodynamic regime viscous effects lead to a sign change in the magnon chemical potential, which can be detected as a sign change in the nonlocal resistance measured in spin transport experiments. This sign change is observable when the injector-detector distance becomes comparable to the momentum-relaxation length. Taking into account momentum- and spin-relaxation processes, we consider the quasiconservation laws for momentum and spin in a magnon fluid. The resulting equations are solved for nonlocal spin transport devices in which spin is injected and detected via metallic leads. Because of the finite viscosity we also find a backflow of magnons close to the injector lead. Our work shows that nonlocal magnon spin transport devices are an attractive platform to develop and study magnon-fluid dynamics.

Quantum-Impurity Relaxometry of Magnetization Dynamics

Prototypes of quantum impurities, such as NV and SiV color centers in diamond, have garnered much attention due to their minimally invasive and high-resolution magnetic field and thermal sensing. Here, we investigate quantum-impurity relaxometry as a method for probing collective excitations in magnetic insulators. We develop a general framework to relate the measurable quantum-impurity relaxation rates to the intrinsic dynamic properties of a magnetic system via the noise emitted by the latter. We suggest, in particular, that the quantum-impurity relaxometry is sensitive to dynamic phase transitions, such as magnon condensation, and can be deployed to detect signatures of the associated coherent spin dynamics, both in ferromagnetic and antiferromagnetic systems. Finally, we discuss prospects to nonintrusively probe spin-transport regimes and measure the associated transport coefficients in magnetic insulators.

Probing a Spin Transfer Controlled Magnetic Nanowire with a Single Nitrogen-Vacancy Spin in Bulk Diamond

The point-like nature and exquisite magnetic field sensitivity of the nitrogen vacancy (NV) center in diamond can provide information about the inner workings of magnetic nanocircuits in complement with traditional transport techniques. Here, we use a single NV in bulk diamond to probe the stray field of a ferromagnetic nanowire controlled by spin transfer (ST) torques. We first report an unambiguous measurement of ST tuned, parametrically driven, large-amplitude magnetic oscillations. At the same time, we demonstrate that such magnetic oscillations alone can directly drive NV spin transitions, providing a potential new means of control. Finally, we use the NV as a local noise thermometer, observing strong ST damping of the stray field noise, consistent with magnetic cooling from room temperature to ∼150 K.

Nanoscale Spin Manipulation with Pulsed Magnetic Gradient Fields from a Hard Disc Drive Writer

The individual and coherent control of solid-state based electron spins is important covering fields from quantum information processing and quantum metrology to material research and medical imaging. Especially for the control of individual spins in nanoscale networks, the generation of strong, fast, and localized magnetic fields is crucial. Highly engineered devices that demonstrate most of the desired features are found in nanometer size magnetic writers of hard disk drives (HDD). Currently, however, their nanoscale operation in particular comes at the cost of excessive magnetic noise. Here, we present HDD writers as a tool for the efficient manipulation of single as well as multiple spins. We show that their tunable gradients of up to 100 μT/nm can be used to spectrally address individual spins on the nanoscale. Their gigahertz bandwidth allows one to switch control fields within nanoseconds, faster than characteristic time scales such as Rabi and Larmor periods, spin-spin couplings, or optical transitions, thus extending the set of feasible spin manipulations. We used the fields to drive spin transitions through nonadiabatic fast passages or to enable the optical readout of spin states in strong misaligned fields. Building on these techniques, we further apply the large magnetic field gradients for microwave selective addressing of single spins and show its use for the nanoscale optical colocalization of two emitters.

Voltage-driven, local, and efficient excitation of nitrogen-vacancy centers in diamond

Magnetic sensing technology has found widespread application in a diverse set of industries including transportation, medicine, and resource exploration. These uses often require highly sensitive instruments to measure the extremely small magnetic fields involved, relying on difficult-to-integrate superconducting quantum interference devices and spin-exchange relaxation-free magnetometers. A potential alternative, nitrogen-vacancy (NV) centers in diamond, has shown great potential as a high-sensitivity and high-resolution magnetic sensor capable of operating in an unshielded, room-temperature environment. Transitioning NV center-based sensors into practical devices, however, is impeded by the need for high-power radio frequency (RF) excitation to manipulate them. We report an advance that combines two different physical phenomena to enable a highly efficient excitation of the NV centers: magnetoelastic drive of ferromagnetic resonance and NV-magnon coupling. Our work demonstrates a new pathway that combine acoustics and magnonics that enables highly energy-efficient and local excitation of NV centers without the need for any external RF excitation and, thus, could lead to completely integrated, on-chip, atomic sensors.

Magnetostatic twists in room-temperature skyrmions explored by nitrogen-vacancy center spin texture reconstruction

Magnetic skyrmions are two-dimensional non-collinear spin textures characterized by an integer topological number. Room-temperature skyrmions were recently found in magnetic multilayer stacks, where their stability was largely attributed to the interfacial Dzyaloshinskii-Moriya interaction. The strength of this interaction and its role in stabilizing the skyrmions is not yet well understood, and imaging of the full spin structure is needed to address this question. Here, we use a nitrogen-vacancy centre in diamond to measure a map of magnetic fields produced by a skyrmion in a magnetic multilayer under ambient conditions. We compute the manifold of candidate spin structures and select the physically meaningful solution. We find a Néel-type skyrmion whose chirality is not left-handed, contrary to preceding reports. We propose skyrmion tube-like structures whose chirality rotates through the film thickness. We show that NV magnetometry, combined with our analysis method, provides a unique tool to investigate this previously inaccessible phenomenon.

Control and local measurement of the spin chemical potential in a magnetic insulator

The spin chemical potential characterizes the tendency of spins to diffuse. Probing this quantity could provide insight into materials such as magnetic insulators and spin liquids and aid optimization of spintronic devices. Here we introduce single-spin magnetometry as a generic platform for nonperturbative, nanoscale characterization of spin chemical potentials. We experimentally realize this platform using diamond nitrogen-vacancy centers and use it to investigate magnons in a magnetic insulator, finding that the magnon chemical potential can be controlled by driving the system's ferromagnetic resonance. We introduce a symmetry-based two-fluid theory describing the underlying magnon processes, measure the local thermomagnonic torque, and illustrate the detection sensitivity using electrically controlled spin injection. Our results pave the way for nanoscale control and imaging of spin transport in mesoscopic systems.

Environmental noise spectroscopy with qubits subjected to dynamical decoupling

A qubit subjected to pure dephasing due to classical Gaussian noise can be turned into a spectrometer of this noise by utilizing its readout under properly chosen dynamical decoupling (DD) sequences to reconstruct the power spectral density of the noise. We review the theory behind this DD-based noise spectroscopy technique, paying special attention to issues that arise when the environmental noise is non-Gaussian and/or it has truly quantum properties. While we focus on the theoretical basis of the method, we connect the discussed concepts with specific experiments, and provide an overview of environmental noise models relevant for solid-state based qubits, including quantum-dot based spin qubits, superconducting qubits, and NV centers in diamond.

Superresolution optical magnetic imaging and spectroscopy using individual electronic spins in diamond

Nitrogen vacancy (NV) color centers in diamond are a leading modality for both superresolution optical imaging and nanoscale magnetic field sensing. In this work, we address the key challenge of performing optical magnetic imaging and spectroscopy selectively on multiple NV centers that are located within a diffraction-limited field-of-view. We use spin-RESOLFT microscopy to enable precision nanoscale mapping of magnetic field patterns with resolution down to ~20 nm, while employing a low power optical depletion beam. Moreover, we use a shallow NV to demonstrate the detection of proton nuclear magnetic resonance (NMR) signals exterior to the diamond, with 50 nm lateral imaging resolution and without degrading the proton NMR linewidth.

Double-Quantum Spin-Relaxation Limits to Coherence of Near-Surface Nitrogen-Vacancy Centers

We probe the relaxation dynamics of the full three-level spin system of near-surface nitrogen-vacancy (NV) centers in diamond to define a T_{1} relaxation time that sets the T_{2}≤2T_{1} coherence limit of the NV's subset qubit superpositions. We find that double-quantum spin relaxation via electric field noise dominates T_{1} of near-surface NVs at low applied magnetic fields. Furthermore, we differentiate 1/f^{α} spectra of electric and magnetic field noise using a novel noise-spectroscopy technique, with broad applications in probing surface-induced decoherence at material interfaces.

Quantum interpolation for high-resolution sensing

Recent advances in engineering and control of nanoscale quantum sensors have opened new paradigms in precision metrology. Unfortunately, hardware restrictions often limit the sensor performance. In nanoscale magnetic resonance probes, for instance, finite sampling times greatly limit the achievable sensitivity and spectral resolution. Here we introduce a technique for coherent quantum interpolation that can overcome these problems. Using a quantum sensor associated with the nitrogen vacancy center in diamond, we experimentally demonstrate that quantum interpolation can achieve spectroscopy of classical magnetic fields and individual quantum spins with orders of magnitude finer frequency resolution than conventionally possible. Not only is quantum interpolation an enabling technique to extract structural and chemical information from single biomolecules, but it can be directly applied to other quantum systems for superresolution quantum spectroscopy.

Local dynamics of topological magnetic defects in the itinerant helimagnet FeGe

Chiral magnetic interactions induce complex spin textures including helical and conical spin spirals, as well as particle-like objects such as magnetic skyrmions and merons. These spin textures are the basis for innovative device paradigms and give rise to exotic topological phenomena, thus being of interest for both applied and fundamental sciences. Present key questions address the dynamics of the spin system and emergent topological defects. Here we analyse the micromagnetic dynamics in the helimagnetic phase of FeGe. By combining magnetic force microscopy, single-spin magnetometry and Landau–Lifschitz–Gilbert simulations we show that the nanoscale dynamics are governed by the depinning and subsequent motion of magnetic edge dislocations. The motion of these topologically stable objects triggers perturbations that can propagate over mesoscopic length scales. The observation of stochastic instabilities in the micromagnetic structure provides insight to the spatio-temporal dynamics of itinerant helimagnets and topological defects, and discloses open challenges regarding their technological usage.

Topological defects may strongly influence the evolution of a materials' micromagnetic structure whilst their manipulation forms the basis for emerging technological concepts. Here, the authors study the depinning and motion of magnetic edge dislocations in the domain structure of helimagnetic FeGe.

Fast nanoscale addressability of nitrogen-vacancy spins via coupling to a dynamic ferromagnetic vortex

The core of a ferromagnetic vortex domain creates a strong, localized magnetic field, which can be manipulated on nanosecond timescales, providing a platform for addressing and controlling individual nitrogen-vacancy centre spins in diamond at room temperature, with nanometre-scale resolution. Here, we show that the ferromagnetic vortex can be driven into proximity with a nitrogen-vacancy defect using small applied magnetic fields, inducing significant nitrogen-vacancy spin splitting. We also find that the magnetic field gradient produced by the vortex is sufficient to address spins separated by nanometre-length scales. By applying a microwave-frequency magnetic field, we drive both the vortex and the nitrogen-vacancy spins, resulting in enhanced coherent rotation of the spin state. Finally, we demonstrate that by driving the vortex on fast timescales, sequential addressing and coherent manipulation of spins is possible on ∼100 ns timescales.

Nitrogen vacancies in diamond present single spin defects which may be used as nanoscale magnetic sensors. Here, Wolf et al. demonstrate how a ferromagnetic vortex in an adjacent micromagnet allows for fast nanoscale addressability of individual defect spins in nanodiamonds.

Magneto-optical imaging of thin magnetic films using spins in diamond

Imaging the fields of magnetic materials provides crucial insight into the physical and chemical processes surrounding magnetism, and has been a key ingredient in the spectacular development of magnetic data storage. Existing approaches using the magneto-optic Kerr effect, x-ray and electron microscopy have limitations that constrain further development, and there is increasing demand for imaging and characterisation of magnetic phenomena in real time with high spatial resolution. Here we show how the magneto-optical response of an array of negatively-charged nitrogen-vacancy spins in diamond can be used to image and map the sub-micron stray magnetic field patterns from thin ferromagnetic films. Using optically detected magnetic resonance, we demonstrate wide-field magnetic imaging over 100 × 100 μm² with sub-micron spatial resolution at video frame rates, under ambient conditions. We demonstrate an all-optical spin relaxation contrast imaging approach which can image magnetic structures in the absence of an applied microwave field. Straightforward extensions promise imaging with sub-μT sensitivity and sub-optical spatial and millisecond temporal resolution. This work establishes practical diamond-based wide-field microscopy for rapid high-sensitivity characterisation and imaging of magnetic samples, with the capability for investigating magnetic phenomena such as domain wall and skyrmion dynamics and the spin Hall effect in metals.

Fourier magnetic imaging with nanoscale resolution and compressed sensing speed-up using electronic spins in diamond

Optically detected magnetic resonance using nitrogen-vacancy (NV) colour centres in diamond is a leading modality for nanoscale magnetic field imaging, as it provides single electron spin sensitivity, three-dimensional resolution better than 1 nm (ref. 5) and applicability to a wide range of physical and biological samples under ambient conditions. To date, however, NV-diamond magnetic imaging has been performed using 'real-space' techniques, which are either limited by optical diffraction to ∼250 nm resolution or require slow, point-by-point scanning for nanoscale resolution, for example, using an atomic force microscope, magnetic tip, or super-resolution optical imaging. Here, we introduce an alternative technique of Fourier magnetic imaging using NV-diamond. In analogy with conventional magnetic resonance imaging (MRI), we employ pulsed magnetic field gradients to phase-encode spatial information on NV electronic spins in wavenumber or 'k-space' followed by a fast Fourier transform to yield real-space images with nanoscale resolution, wide field of view and compressed sensing speed-up.

High-efficiency resonant amplification of weak magnetic fields for single spin magnetometry at room temperature

Magnetic resonance techniques not only provide powerful imaging tools that have revolutionized medicine, but they have a wide spectrum of applications in other fields of science such as biology, chemistry, neuroscience and physics. However, current state-of-the-art magnetometers are unable to detect a single nuclear spin unless the tip-to-sample separation is made sufficiently small. Here, we demonstrate theoretically that by placing a ferromagnetic particle between a nitrogen-vacancy magnetometer and a target spin, the magnetometer sensitivity is improved dramatically. Using materials and techniques that are already experimentally available, our proposed set-up is sensitive enough to detect a single nuclear spin within ten milliseconds of data acquisition at room temperature. The sensitivity is practically unchanged when the ferromagnet surface to the target spin separation is smaller than the ferromagnet lateral dimensions; typically about a tenth of a micrometre. This scheme further benefits when used for nitrogen-vacancy ensemble measurements, enhancing sensitivity by an additional three orders of magnitude.