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The current-induced torque is one of the most important phenomena in spintronics as it provides a way to control magnetic order parameters by electrical means. So far, most studies on the microscopic mechanisms of the current-induced torque have focused on the role of spin current carried by conduction electrons, which exerts spin-transfer torque on the magnetization upon the injection into a ferromagnet. In solids, however, electronic Bloch states originate from the atomic orbitals of the constituent atoms. Thus, while it is natural to expect that such orbital information may be used to control the magnetization because the orbital degree of freedom carries the angular momentum as the spin degree of freedom does, the role of orbitals in the physics of the current-induced torque has been barely investigated. In recent years, we uncovered mechanisms of generating the electronic current carrying finite orbital angular momentum such as the orbital Hall effect (OHE) [1] and proposed to utilize the orbital current for controlling the magnetization [2]. The latter is shortly denoted by “orbital torque” (OT) nowadays.&lt;br/&gt;&lt;br/&gt;In this talk, I review recent theoretical progress in the mechanisms of the OHE and the OT. In the first part, I will explain that the OHE arises in various metals regardless of their strength of the spin-orbit coupling, whose magnitude is typically an order of magnitude larger than that of the spin Hall effect (SHE) in heavy metals [3]. In fact, the SHE is a concomitant effect of the OHE, whose hierarchical relation will be explained. In the second part, I will discuss the mechanisms of the OT. The main problem is that it is hard to distinguish the orbital contribution and the spin contribution to the torque on the magnetization in most torque measurements. This is one of the main difficulties to quantify the OT. Theoretically, we recently developed a general theoretical formalism that tracks the transfer of the angular momentum in solids between the lattice, the local magnetic moment, and the electron’s spin and orbital, and successfully implemented it within the density functional theory framework [4]. This enables us to understand the microscopic nature of the OT and quantify different competing contributions. Finally, I will also discuss unique qualitative features of the OT mechanisms: significant dependence of the interface orbital transparency on the crystallinity and long-range transport and dephasing in a ferromagnet [5].

2022 Joint MMM-INTERMAG

Theory of Orbital Hall Effect and Current-Induced Torques by Orbital Current

The 15th Joint MMM-INTERMAG Conference (2022 Joint) is sponsored jointly by AIP Publishing and the IEEE Magnetics Society. Members of the international scientific and engineering communities interested in recent developments in fundamental and applied magnetism are invited to attend and contribute to the technical sessions. The technical program will include invited and contributed papers in oral and poster sessions, invited symposia, a plenary session, and an evening session, with about 1500 presentations overall. This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

The 2022 Joint Conference will offer both in-person and prerecorded on-demand content.

For tickets to the event, please register at the following link: https://magnetism.org/register

Please register for the Joint MMM-Intermag conference to join the event.

The current-induced torque is one of the most important phenomena in spintronics as it provides a way to control magnetic order parameters by electrical means. So far, most studies on the microscopic mechanisms of the current-induced torque have focused on the role of spin current carried by conduction electrons, which exerts spin-transfer torque on the magnetization upon the injection into a ferromagnet. In solids, however, electronic Bloch states originate from the atomic orbitals of the constituent atoms. Thus, while it is natural to expect that such orbital information may be used to control the magnetization because the orbital degree of freedom carries the angular momentum as the spin degree of freedom does, the role of orbitals in the physics of the current-induced torque has been barely investigated. In recent years, we uncovered mechanisms of generating the electronic current carrying finite orbital angular momentum such as the orbital Hall effect (OHE) [1] and proposed to utilize the orbital current for controlling the magnetization [2]. The latter is shortly denoted by “orbital torque” (OT) nowadays. In this talk, I review recent theoretical progress in the mechanisms of the OHE and the OT. In the first part, I will explain that the OHE arises in various metals regardless of their strength of the spin-orbit coupling, whose magnitude is typically an order of magnitude larger than that of the spin Hall effect (SHE) in heavy metals [3]. In fact, the SHE is a concomitant effect of the OHE, whose hierarchical relation will be explained. In the second part, I will discuss the mechanisms of the OT. The main problem is that it is hard to distinguish the orbital contribution and the spin contribution to the torque on the magnetization in most torque measurements. This is one of the main difficulties to quantify the OT. Theoretically, we recently developed a general theoretical formalism that tracks the transfer of the angular momentum in solids between the lattice, the local magnetic moment, and the electron’s spin and orbital, and successfully implemented it within the density functional theory framework [4]. This enables us to understand the microscopic nature of the OT and quantify different competing contributions. Finally, I will also discuss unique qualitative features of the OT mechanisms: significant dependence of the interface orbital transparency on the crystallinity and long-range transport and dephasing in a ferromagnet [5].

symposium

Hybrid magnonic systems incorporating superconducting systems have recently emerged as a new promising direction for coherent information processing by exploiting magnon excitations and high quality factor superconducting resonators [1]. Magnons are fundamental excitations of magnetic systems with a frequency band which can be adapted in microwave superconducting quantum circuits. In particular, magnons possess large dipolar magnon-photon coupling and wide frequency tunability, which may find new potentials in quantum information. Superconducting resonators serve as coherent data buses of many quantum circuits with long microwave coherence time. Superconducting-circuit-based cavity magnonics may provide a convenient circuit platform that bridges magnonics and quantum information. In this tutorial, we will discuss recent progresses of cavity magnonics built on superconducting circuits. We will start from the original idea of coupling spin ensembles with superconducting resonators, and how magnetic spins are involved to replace spin ensembles. Then we will examine different magnetic materials and superconducting resonator designs for building superconducting cavity magnonics. Last, we will discuss future opportunities and challenges in scaling up such hybrid magnonic systems on superconducting circuits, with an emphasis on maintaining coherence time of magnons and photons, as well as utilizing superconducting properties such as vortices for empowering magnonics.

Emerging Opportunities for Coherent Information Processing at the Intersection of Superconductivity and Magnetism

The past years have witnessed an increasing interest in the field of quantum materials (QM), not only thanks to their fascinating properties as a macroscopic manifestation of quantum mechanics (high-temperature superconductivity, quantum Hall effect, giant magnetoelectric effect, etc...), but also for the opportunities that these materials can offer towards the next generation of electronic devices. Understanding the physics behind quantum materials is thus a primary goal of condensed matter physics, both from a fundamental point of view as well for gaining control over the QM functional properties. Among all the experimental observables, excitations in QMs can provide unique information about the key-interactions at play in the system (magnetic interactions, electron-phonon coupling, spin-orbit coupling, topology, multiferroicity, etc...) and the nature of the excitations themselves (magnon, phonon, intra-band electronic excitations, orbiton, exotic modes, etc...). In this talk, I will focus on soft Resonant Inelastic X-ray Scattering (RIXS), as an emergent technique for the study of excitations and their momentum dependence. I will present recent results achieved on ferromagnetic thin films to investigate the evolution of the spin dynamics as a function of thickness [1]. Our work reveals an asymmetric evolution of the spin dynamics between the in-plane and out-of-plane directions: while the spin excitations remain invariant along the in-plane direction, in the out-of-plane direction a dampening is observed as a function of thickness. Such result is interpreted as an effect of confinement, enabling the use of the thickness as a “knob” to control the spin excitation energies.

Tuning Spin Excitations in Magnetic Films by Confinement

Significant attention has recently been attracted by phases that spontaneously break real-space symmetries in addition to spin, phase, or gauge symmetries. These phases include, for example, the charge-density wave or stripe phases in the cuprate superconductors, the Ising-nematic phases in the iron pnictides, and the valence-bond-solids in certain quantum magnets. We discuss the interplay between the broken real-space symmetries and vacancies, impurities and other types of quenched disorder that are inevitable in real materials. Specifically, we demonstrate that spinless impurities in a frustrated Ising magnet give rise to a random-field mechanism that can destroy the stripe-ordered phase. The strength of the emerging random fields is governed by the spatial impurity distribution. Moreover, the mechanism can be tuned very efficiently by weak exchange anisotropies that explicitly break the real-space symmetry, providing a way of controlling the phase diagram of this many-particle system. This work was supported in part by the National Science Foundation under Grant Nos. DMR-1828489 and OAC-1919789.

![](https://assets.underline.io/uploads/markdown_image/1/image/28c2747899a50f243b196002129a9945.jpg)

Domains of horizontal and vertical stripes in the diluted J1-J2 Ising model.

Controlling the Stripe Order in a Diluted Frustrated Magnet

Microwave detectors based on the spin-torque diode effect are among the key emerging spintronic devices (see ref.[1] and references therein). By utilizing the spin of electrons in addition to their charge, they have the potential to overcome the theoretical performance limits of their semiconductor (Schottky) counterparts. Those devices realized with magnetic tunnel junctions and in active regime exhibit high-detection sensitivity &gt;200kV/W at room temperature and zero bias field, thanks to the injection locking mechanism, and for low-input power (micro-Watts or lower). Those performance can be improved with the bolometric effect or when coupled properly in arrays. Here, I will discuss our recent results in the field of microwave detectors based on spin diodes and possible implementations of THz detectors based on antiferromagnets working in linear and parametric excitation regime. I will point out how those devices can impact the IoT market and can be used for implement hardware multiplication by using the concept of degree of rectification and as dual band detectors in frequency shifting keying demodulation schemes in which the information is coded in two discrete values of the frequency in a carrier signal. In particular, the frequency response of spin-torque diodes and their current tunability can be also used as building blocks of the hardware realization of neurons and synapses in neuromorphic applications. Another application of spintronic diodes, when they have a broadband frequency response, is as electromagnetic energy harvesting, which offers an attractive energy source for applications in self-powered portable electronics in the “internet of things” era. Here I will show the development of a bias-field-free spin-torque diodes based on a magnetic tunnel junction having a canted magnetization in the free layer, and demonstrate that those devices could be an efficient harvester of broadband ambient RF radiation, capable to efficiently harvest microwave powers of microWatt and below and to power a black phosphorous nanodevice. I will also review recent idea on spintronic detectors in presence of nonuniform ground states such as skyrmions.

Challenges in microwave and THz spintronic diodes

There is a great interest to generate electricity using ambient RF energy. We addressed this using two different approaches. We first use the intrinsic quantum property of the Weyl semimetal to convert the RF energy into electricity [1]. The nonlinear Hall effect (NLHE) can produce a dc transverse voltage in zero magnetic field. However, it requires NLHE to be detected at room temperature. Despite of several studies of NLHE in topological materials and 2D materials, the room-temperature NLHE has not yet been achieved. We find the room-temperature NLHE in a type-II Weyl semimetal TaIrTe4, which hosts a robust NLHE due to broken inversion symmetry and large band overlapping at the Fermi level. The NLHE is present only when the electric field is applied along the axis of the mirror plane (a-axis of the crystal). Based on the observed room-temperature NLHE in TaIrTe4 we demonstrate the wireless RF rectification with zero external bias and magnetic field. An incident electric field along the a-axis (Ea) generates a rectified voltage along the b-axis (Vb), whereas, there is no rectification when the incident electric field is along the b-axis (Eb) in consistent with the symmetry constraints of NLHE. This work opens a door to realizing room temperature rectification applications based on the NLHE in Weyl semimetals. The other approach is to use the spin-torque diode effect of spin-torque oscillators (STOs) [2]. For the application in rectification and energy harvesting, the spin-diode effect is demonstrated by measuring the rectified dc voltage. Due to the canted anisotropy, the free layer of the individual STOs shows a large RF sensitivity as a result of non-linear dynamics. We demonstrate series connections have an advantage for rectification due to the additive effect of the diode voltages from STOs. Using eight oscillators in series, the rectified voltage is enhanced and we have achieved a rectification efficiency of 6% at -20 dBm, which outperforms the Schottky diode capability at sub µW power. By integrating the electrically connected eight STOs with conventional electronics, we demonstrate the battery-free energy-harvesting system by utilizing the wireless RF energy to power electronic devices such as LEDs. We also demonstrate the capability of this energy harvesting system in holding dc power using a time-varying signal, which is useful in harvesting energy from discrete commercial sources such as a WiFi router. Our results highlight the significance of electrical topology (series vs. parallel) while designing an on-chip STOs system.

WiFi Band Energy Harvesting using Spin-Torque Diode and Nonlinear Hall Effects

A key challenge of neuromorphic computing is to build hardware neural networks with dense connectivity between nanoscale synapses and neurons, approaching the brain’s thousands of synapses per neuron (1). In this talk, I will show that spin diodes are microwave nano-synapses that naturally and densely interface with neurons made of spin-torque nano-oscillators (2). I will describe the principle of these novel synapses and explain how their microwave features can be harnessed to achieve the multiply-and-accumulate operations at the core of neural networks, with over 500 synapses/neuron. I will show that they implement all-to-all connections as well as convolutional operations in a fully parallel way with high density and speed. I will describe our experiments highlighting these functionalities (3), and show that they open the path to radio-frequency deep learning.

Radio-Frequency Spintronic Neural Networks

Antiferromagnets are prospective materials for spintronic applications due to their internal ultrafast dynamics, robustness with respect to the external magnetic fields, and high sensitivity to spin-torques of different nature. Moreover, in contrast to ferromagnets, spin-torques can induce steady precession of the Néel vector at THz frequencies whose values can be controlled by the current. Hence, antiferromagnets can be considered as tunable current controlled auto-oscillators, which is the main component of phase-controlling devices. An auto-oscillation regime is supported solely by antidamping torques that compensate the internal energy losses. However, the frequency of the precession, threshold value, the type of dynamics etc can be effectively manipulated by applying the field-like torques. In this presentation we review recent developments in the field of antiferromagnetic spin-torque oscillators and discuss new functionalities stemming from the combining effect of the field-like and antidamping-like torques. To demonstrate the effects of different torques we start from the dynamics of ultrafast switching and discuss various mechanisms including the Néel spin-orbit torques [1], thermomagnetoelastic mechanism [2], and optically-induced spin-transfer torques [3]. We illustrate possible applications of nontrivial antiferromagnetic dynamics for the detection and emission of teraherz radiation in altermagnets CuMnAs and Mn2Au in which electrical current can induce simultaneously the ac Néel spin-orbit torque and dc spin-orbit torque [1]. Using NiO antiferromagnet as an example, we discuss and compare various scenarios of ultrafast dynamics, such as: i) reorientation of the Néel vector due to the field-like torques of magnetoelastic nature and spin-orbit torques due to spin-pumping [4]; ii) fast switching and stable precession induced by the ac spin-transfer torques whose frequency coinsides with the frequency of antiferromagnetic resonance. We also analyse the chaotic regimes of an antiferromagnetic oscillator that appear at certain combination of field-like and damping-like torques (see Fig.1) and and discuss possible applications for neuromorphic computations [5]. As an outline of future development, we discuss influence of the magnetoelastic and thermal effects and combination of different stimulus for the effective control and manipulation of the antiferromagnet-based devices.

![](https://assets.underline.io/uploads/markdown_image/1/image/b59399d9c1fc0e1b590576e4fe529e56.jpg)

Current-induced transition to chaos traced by variation of the largest of three Lyapunov's exponents. Red lines on the spheres show trajectories of the Neel vector. From [5].

Antiferromagnetic Spin-torque Oscillators: Ultrafast Dynamics and Possible Applications

The spin-torque magnetic diode (STMD) effect [1] is a quadratic rectification effect of the input microwave current IRF(t) in a magnetoresistive nano-junction, which is commonly observed in the traditional regime of operation of an STMD, when the magnetization of the “free” layer (FL) lies in-plane, and when the frequency fs of the current IRF(t) is close to the ferromagnetic resonance (FMR) frequency f0 of the junction. In this case, the induced resonance oscillations of the junction resistance R(t) can mix with the oscillations of the input microwave current IRF(t) , and produce an output DC voltage UDC = &lt;IRF(t)R(t)&gt; (where "&lt;&gt;" denotes time averaging) across the junction. It was demonstrated theoretically in [2] that in an STMD, biased by an out-of-plane static magnetic field, a different dynamical regime of the STMD operation characterized by large-angle out-of-plane magnetization precession can be realized. The excitation of the large-angle precession has a threshold character, and is possible only for input microwave currents exceeding a certain frequency-dependent critical value, and sufficiently low frequency. In this regime of the out-of-plane precession the output DC voltage of an STMD increases with the frequency of the input signal, but is virtually independent of its power. An STMD working in the regime of large-amplitude out-of-plane precession functions as a non-resonant threshold detector of low frequency microwave signals, due to the large nonlinear shift of its operating frequency. Therefore, this precession regime is particularly suitable for applications in the microwave energy harvesting. It was demonstrated experimentally in [3] that the out-of-plane magnetization precession regime in an STMD operation predicted in [2] can be realized without any bias magnetic field, if an STMD FL has a perpendicular magnetic anisotropy. In such a regime an STMD has the rectification properties that are independent of the input microwave frequency, and the performance of the STMD-based energy harvesting device is comparable to the performance of the state-of-the-art Schottky diode for low-power rectification. It was further shown in [3] that the developed bias-free STMD provides sufficient dc voltage to power a practical nanodevice − a black phosphorus photosensor. Here we present an analytical and numerical theory explaining the performance of a bias-free STMD with perpendicular magnetic anisotropy [4]. We show that in an STMD, having a magnetic FL with perpendicular magnetic anisotropy of the first and second order, and no external bias magnetic field, the out-of-plane regime of magnetization precession can be excited by sufficiently large (exceeding a certain threshold) RF signals with the frequencies smaller than 250 MHz . We also show that such a device can operate as a broadband energy harvester capable of converting incident RF power into a DC power with a conversion efficiency of ∼5%. The developed analytical theory of the bias-free STMD operation can be used for the optimization of high-efficiency RF detectors and energy harvesters based on STMDs. Our results are paving a way for use of spintronic detectors and harvesters as building blocks for self-powered nano-systems, such as implantable biomedical devices, wireless sensors, and portable electronics.

Signal Detector and RF Energy Harvester Based On A Spintronic Diode With Perpendicular Anisotropy

Experimental methods allowing for the detection of single spins in the solid-state, which were initially developed for quantum information science, open new avenues for the development of highly sensitive quantum sensors [1]. In that context, the electronic spin of a single nitrogen-vacancy (NV) defect in diamond can be used as an atomic-sized magnetometer, providing an unprecedented combination of spatial resolution and magnetic sensitivity under ambient conditions [2]. In this talk, I will illustrate how scanning-NV magnetometry can be used as a powerful tool for exploring condensed-matter physics, focusing on chiral spin textures in antiferromagnetic materials [3-5].

Exploring antiferromagnetic order at the nanoscale with a single spin microscope

Hydrodynamic electron flow, where electrons in a conductor flow collectively - akin to a fluid, is a unique signature of strong electron interactions in a material. This effect has been observed in 2D materials, but observations in bulk materials are intriguing as high-carrier density should screen the interactions. In this talk, I will discuss a recent measurement of hydrodynamic flow in the semimetal WTe2, allowing us to gain insight into the microscopic origin of its electron interactions. We image the spatial profile of the electric current by using a nitrogen-vacancy scanning tip. Using coherent quantum sensing, we obtain magnetic field resolution of ~10nT and spatial resolution of ~100nm. The current pattern we observe differs substantially from the flat profile of a normal metal, and indicates correlated flow through the semimetal. The pattern also shows non-monotonic temperature dependence, with hydrodynamic effects peaking at ~20 K. We compare our results to a model which combines ab initio electron scattering rates and the electronic Boltzmann transport equation. The model shows quantitative agreement with our measurement, allowing us to extract the strength of electron-electron interactions in our material. Furthermore, we conclude that electron interactions are phonon-mediated. This result opens a path for hydrodynamic flow and strong interactions in a variety of new materials.

Theory of Orbital Hall Effect and Current-Induced Torques by Orbital Current

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Theory of Orbital Hall Effect and Current-Induced Torques by Orbital Current

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Emerging Opportunities for Coherent Information Processing at the Intersection of Superconductivity and Magnetism

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Competition between orbital and spin angular momenta of the THz beams at the antiferromagnetic resonances and Landau level transitions

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