Orbital Currents Research Articles

Orbitronics: light-induced orbital currents in Ni studied by terahertz emission experiments

Orbitronics is based on the use of orbital currents as information carriers. Orbital currents can be generated from the conversion of charge or spin currents, and inversely, they could be converted back to charge or spin currents. Here we demonstrate that orbital currents can also be generated by femtosecond light pulses on Ni. In multilayers associating Ni with oxides and nonmagnetic metals such as Cu, we detect the orbital currents by their conversion into charge currents and the resulting terahertz emission. We show that the orbital currents extraordinarily predominate the light-induced spin currents in Ni-based systems, whereas only spin currents can be detected with CoFeB-based systems. In addition, the analysis of the time delays of the terahertz pulses leads to relevant information on the velocity and propagation length of orbital carriers. Our finding of light-induced orbital currents and our observation of their conversion into charge currents opens new avenues in orbitronics, including the development of orbitronic terahertz devices.

Variation of magnetic properties with current in ferrimagnetic semiconductor Mn3Si2Te6

Orbital currents play a fundamental role in a wide range of transport phenomena. Recently, the discovery of a novel chiral orbital current state in the ferrimagnetic nodal-line semiconductor Mn3Si2Te6 has attracted significant interest, supported by anomalous I–V characteristics and time-dependent bistable switching. However, the direct experimental verifications, combining electrical transport and magnetic measurement, that detect the variation of the magnetic properties vs the current are still rare. Here, we investigate the transport properties of Mn3Si2Te6 and track the current-induced dynamics of the magnetic moment. Reflective magnetic circular dichroism reveals that significant alterations in Mn3Si2Te6 magnetoresistance in response to an electric field are necessarily coupled with a magnetic phase transition, establishing a rare correlation. Our findings indicate the predominance of magnetic chiral orbital currents in the colossal angular magnetoresistance effect, offering a unique platform for advanced studies in orbital magnetism.

Orbital Rashba Effect as a Platform for Robust Orbital Photocurrents.

Orbital current has emerged over the past years as one of the key novel concepts in magnetotransport. Here, we demonstrate that laser pulses can be used to generate large and robust nonrelativistic orbital currents in systems where the inversion symmetry is broken by the orbital Rashba effect. By referring to model and first principles tools, we demonstrate that orbital Rashba effect, accompanied by crystal field splitting, can mediate robust orbital photocurrents without a need for spin-orbit interaction even in metallic systems. We show that such nonrelativistic orbital photocurrents are translated into derivative photocurrents of spin when relativistic effects are taken into account. We thus promote orbital photocurrents as a promising platform for optical generation of currents of angular momentum, and discuss their possible applications.

Correlated order at the tipping point in the kagome metal CsV3Sb5

Spontaneously broken symmetries are at the heart of many phenomena of quantum matter and physics more generally. However, determining the exact symmetries that are broken can be challenging due to imperfections such as strain, in particular when multiple electronic orders are competing. This is exemplified by charge order in some kagome systems, where evidence of nematicity and flux order from orbital currents remains inconclusive due to contradictory measurements. Here we clarify this controversy by fabricating highly symmetric samples of a member of this family, CsV3Sb5, and measuring their transport properties. We find that a measurable anisotropy is absent at any temperature in the unperturbed material. However, a pronounced in-plane transport anisotropy appears when either weak magnetic fields or strains are present. A symmetry analysis indicates that a perpendicular magnetic field can indeed lead to in-plane anisotropy by inducing a flux order coexisting with more conventional bond order. Our results provide a unifying picture for the controversial charge order in kagome metals and highlight the need for materials control at the microscopic scale in the identification of broken symmetries.

Field‐Free and Energy‐Efficient Switching of a Ferrimagnetic Insulator Through Orbital Currents of Copper

AbstractElectrically manipulating the magnetization of insulators presents exciting opportunities for fast and energy‐efficient spintronic devices. However, the existing approaches, which rely on spin‐orbit torque (SOT), invariably require an auxiliary field. Here field‐free current‐induced magnetization switching in perpendicularly magnetized Tm3Fe5O12 films is demonstrated. This is achieved through a magnetic hybrid structure, Tm3Fe5O12/Co40Fe40B20/Cu/SiO2, where the Cu layer acts as the source of orbital current, and the in‐plane magnetized Co40Fe40B20 layer functions as the converter of orbital‐to‐spin current. The interplay between the insulating and metallic magnetic layers not only yields a significant anomalous Hall signal for monitoring the Tm3Fe5O12 magnetization states, but also enables field‐free switching that is immune to the magnetic history of the structure. It also observes similar Tm3Fe5O12 switching in stacks with different spin/orbital current sources, with the SOT‐driven switching consuming substantially more power. This work establishes a pathway for achieving energetically efficient all‐electrical manipulation of insulator spins through orbital currents.

Anomalous Hall effect in naturally oxidized normal-metal Al/Cu double films

An unexpectedly larger current-induced spin–orbit torque in oxidized Cu (CuO x )/ferromagnet (FM) than heavy-metal/FM has recently attracted intense attention in spintronic studies. Although the two mechanisms, interfacial Rashba Edelstein effect and spin-vorticity coupling, have been put forward based on the two different conductive features of CuO x , i.e. electrical insulator and gradient of electrical mobility, the detailed investigation of transport of CuO x is still lacking. Here we experimentally report the positive and negative anomalous Hall effect (AHE) in naturally oxidized normal-metal Al/Cu double films. We found that the onset temperature of AHE corresponds to magnetic transition temperature of CuO x . Furthermore, by comparing Hall resistance of the crystalline and amorphous Cu/Al double films, we identify that the positive anomalous Hall resistance attributes to magnetic moment of CuO x itself, while the negative anomalous Hall resistance can originate from the spin or orbital currents generated at the CuO x /AlO x interface interact with magnetization of CuO x and its inverse process.

Electromagnetic signatures of a chiral quantum spin liquid

Quantum spin liquids (QSL) have emerged as a captivating subject within interacting spin systems that exhibit no magnetic ordering even at the lowest temperature accessible experimentally. However, definitive experimental evidence remains elusive. In light of the recent surge in theoretical and experimental interest in the half-filled Hubbard model on a triangular lattice, which offers the potential for stabilizing a chiral QSL, we investigate the electromagnetic signatures of this phase to facilitate experimental detection. Utilizing a combination of parton mean-field theory and unbiased density-matrix renormalization group calculations, we systematically examine the electrical charge and orbital electrical current associated with a spinon excitation in the chiral QSL. Additionally, we calculate the longitudinal and transverse optical conductivities below the Mott gap. Furthermore, employing quantum field theory analysis, we unravel the connection between spinon excitations and emergent as well as physical gauge fields. Our results demonstrate that the chiral QSL phase exhibits a distinct electromagnetic response, even within a Mott insulator regime. This finding holds great potential for enabling the experimental detection of this long-sought-after phase.

Electric current distribution induced by applied magnetic field in a bent graphene nanoribbon cantilever

Graphene exhibits diamagnetism, and its origin is the orbital electric currents induced on the surface by an applied magnetic field. The magnetic response of a graphene cantilever in the presence of a magnetic field is mainly determined by the diamagnetic electric current, and spin paramagnetism, which suppresses the diamagnetism. We elucidate the change in the electric current distribution caused by the large bending of the graphene cantilever using the tight-binding model. The electric current almost disappears when the position of the graphene cantilever transitions from perpendicular to parallel to the magnetic field and reverses when the graphene cantilever is folded in half. Furthermore, the temporal change in the magnetic energy of the vibrating graphene cantilever is calculated using the molecular dynamics simulation. The strong dependence of the magnetization of a graphene cantilever on its position relative to the magnetic field can be utilized for actuating and controlling the cantilever.

Paramagnetic Singularities of the Orbital Magnetism in Graphene with a Moiré Potential.

The recent detection of the singular diamagnetism of Dirac electrons in a single graphene layer paved a new way of probing 2D quantum materials through the measurement of equilibrium orbital currents which cannot be accessed in usual transport experiments. Among the theoretical predictions is an intriguing orbital paramagnetism at saddle points of the dispersion relation. Here we present magnetization measurements in graphene monolayers aligned on hexagonal boron nitride crystals. Besides the sharp diamagnetic McClure response at the Dirac point, we detect extra diamagnetic singularities at the satellite Dirac points of the moiré lattice. Surrounding these diamagnetic satellite peaks, we also observe paramagnetic peaks located at the chemical potential of the saddle points of the graphene moiré band structure and relate them to the presence of vanHove logarithmic singularities in the density of states. These findings reveal the long ago predicted anomalous paramagnetic orbital response in 2D systems when the Fermi energy is tuned to the vicinity of saddle points.

Models of the Formation of Doppler Spectrum of Surface Reverberation for Sound Waves of the Meter Range

Narrowband spectra of sound scattered on the surface wave in the frequency range from 500 to 3000 Hz have been analyzed. Experimental results and theoretical models are reviewed. Previously published work by the authors is reviewed and new results are presented. The first characteristic case considered is forward scattering, where the sound transmitter and receiver are substantially separated from each other in space, and a continuous emission of a sinusoidal signal is produced. For this case, it is shown that the modulation spectrum of the scattered signal repeats the frequency spectrum of the surface wave with a certain coefficient and small corrections. The second considered characteristic case is a monostatic location, where the receiver and transmitter are combined and tone-pulse signals are emitted. Previously, for this case, it was implicitly expected that the reverberation spectrum would be generated by Bragg scattering on surface waves corresponding to half of the sound wavelength, and hence the spectrum of the scattered signal would be discrete. However, the experimental results indicate that the monostatic scattering spectra have a smooth bell-shape. Explaining this requires taking the effects of modulation of short surface waves by the long-wave component into account. Additionally, to explain the experimental phenomenon, the authors include a model of sound scattering on air bubbles, which are located in the near-surface layer of water and make oscillatory movements in the field of orbital currents of surface waves.

Inverse orbital Hall effect and orbitronic terahertz emission observed in the materials with weak spin-orbit coupling

The Orbital Hall effect, which originates from materials with weak spin-orbit coupling, has attracted considerable interest for spin-orbitronic applications. Here, we demonstrate the inverse effect of the orbital Hall effect and observe orbitronic terahertz emission in the Ti and Mn materials. Through spin-orbit transition in the ferromagnetic layer, the generated orbital current can be converted to charge current in the Ti and Mn layers via the inverse orbital Hall effect. Furthermore, the inserted W layer provides an additional conversion of the orbital-charge current in the Ti and Mn layers, significantly enhancing the orbitronic terahertz emission. Moreover, the orbitronic terahertz emission can be manipulated by cooperating with the inverse orbital Hall effect and the inverse spin Hall effect in the different sample configurations. Our results not only discover the physical mechanism of condensed matter physics but also pave the way for designing promising spin-orbitronic devices and terahertz emitters.

Theory of nematic charge orders in kagome metals

Kagome metals $A$V$_3$Sb$_5$ ($A=$K, Rb, Cs) exhibit an exotic charge order (CO), involving three order parameters, with broken translation and time-reversal symmetries compatible with the presence of orbital currents. The properties of this phase are still intensely debated, and it is unclear if the origin of the CO is mainly due to electron-electron or electron-phonon interactions. Most of the experimental studies confirm the nematicity of this state, a feature that might be enhanced by electronic correlations. However, it is still unclear whether the nematic CO becomes stable at a temperature equal to ($T_{\text{nem}} = T_\text{C}$) or lower than ($T_{\text{nem}} < T_\text{C}$) the one of the CO itself. Here, we systematically characterize several CO configurations, some proposed for the new member of the family ScV$_6$Sn$_6$, by combining phenomenological Ginzburg-Landau theories, valid irrespective of the specific ordering mechanism, with mean-field analysis. We find a few configurations for the CO that are in agreement with most of the experimental findings to date and that are described by different Ginzburg-Landau potentials. We propose to use resonant ultrasound spectroscopy to experimentally characterize the order parameters of the CO, such as the number of their components and their relative amplitude, and provide an analysis of the corresponding elastic tensors. This might help understand which mean-field configuration found in our study is the most representative for describing the CO state of kagome metals, and it can provide information regarding the nematicity onset temperature $T_\text{nem}$ with respect to $T_\text{C}$.

Nonlocal orbital torques in magnetic multilayers

We investigate current-induced torques in Ni/Ti/Fe/Ti multilayers. In the multilayers, we find that the damping-like torque acting on the Ni magnetization increases with the thickness of the bottom Ti layer, despite the negligible spin Hall conductivity of Ti and the presence of the Fe interlayer that effectively absorbs the transverse spins. The nonlocal nature of the observed torque is consistent with the orbital torque arising from the orbital Hall effect in the Ti layer and orbital transport through the Fe layer. This observation highlights the unique features of the orbital currents, offering enhanced flexibility in the design of spintronic devices.

ENERGETIC POWER ESTIMATION OF SWELLS AND ORBITAL MARINE CURRENTS IN BENIN COASTAL ZONE (GULF OF GUINEA)

The announced depletion of fossil energy resources is fueling some speculation. It is therefore urgent to explore the different renewable energy sources available to Benin. In the ocean, in addition to swells, there are also orbital marine currents generated by them. An advantageous solution for the countries located in the Gulf of Guinea is the recovery and transformation of the energy of the swell and its orbital marine currents into electrical energy. Swells are adult waves that propagate freely at the atmosphere-ocean interface. In this work, based on measurements made by the Millenium Challenge Account (MCA-Benin) as part of the extension of the Autonomous Port of Cotonou, we have shown that the swells at the Autonomous Port of Cotonou are Airy swells or of Stokes. We have identified the modified Boussinesq equations, proposed by Peregrine in 1967, as the theory for characterizing the evolution of these swells during their formation in the coastal zone. The variations of the different wave parameters (height, wavelength, period, phase and group velocities) are characterized from the shoaling zone to the breaking point. With this theory the results obtained are in agreement with the experimental measurements made, they perfectly describe the amplification of the height of these waves and show that these swells become very energetic when they approach the coast.

Effect of Internal Waves on Moving Small Vessels in the Sea

Internal waves are responsible for many important processes in the ocean environment (ocean ventilation, energy transfer from large-scale processes to turbulence, etc.). Our goal is to draw attention to the relatively little studied effect of internal waves on ships at sea. We encountered this effect many times while working on the study of internal waves in the shelf zone. The work was carried out from a yacht equipped with the “Rio Grande 600 kHz” ADCP, which makes it possible to measure both the parameters of internal waves and other important parameters of the medium. Two typical examples of the impact of internal waves on a yacht are given. One, when the yacht was at anchor and a train of soliton-like internal waves passed under it. The second, when the yacht was moving and passing over a train of internal waves. Internal waves passing under the moored yacht shifted its position synchronously with the periods of passing waves. A uniformly moving yacht, passing over a package of internal waves synchronously with the period of waves, alternately increased and decreased the speed of its movement. The described effect is explained by the impact on the vessel of the orbital currents of internal waves. Under our conditions, at heights of internal waves reaching 10–15 m, the ship’s speed fluctuations reached 0.30 m/s, which was more than 10% of the ship’s speed.

Observation of long-range orbital transport and giant orbital torque

Modern spintronics relies on the generation of spin currents through spin-orbit coupling. The spin-current generation has been believed to be triggered by current-induced orbital dynamics, which governs the angular momentum transfer from the lattice to the electrons in solids. The fundamental role of the orbital response in the angular momentum dynamics suggests the importance of the orbital counterpart of spin currents: orbital currents. However, evidence for its existence has been elusive. Here, we demonstrate the generation of giant orbital currents and uncover fundamental features of the orbital response. We experimentally and theoretically show that orbital currents propagate over longer distances than spin currents by more than an order of magnitude in a ferromagnet and nonmagnets. Furthermore, we find that the orbital current enables electric manipulation of magnetization with efficiencies significantly higher than the spin counterpart. These findings open the door to orbitronics that exploits orbital transport and spin-orbital coupled dynamics in solid-state devices.

Inverse Orbital Torque via Spin-Orbital Intertwined States

Spin torque induced by orbital current has become of great interest, as it allows the use of lighter elements in the development of advanced spin-orbitronic devices. Meanwhile, the inverse orbital torque (IOT) effect, in which an orbital current creates a charge current, has been difficult to detect. This study uses pumped spin-orbital current in Y${}_{3}$Fe${}_{5}$O${}_{12}$/Pt/CuO${}_{x}$ heterostructures to investigate the IOT effect. Mixed spin-orbital states propagate to the Pt/CuO${}_{x}$ interface and create a much stronger transverse charge current than that created without the CuO${}_{x}$ coating. This inverse orbital Rashba-Edelstein effect can be used to advance applications in spintronics.

Enhanced spin-orbit torque and field-free switching in Au/TMDs/Ni hybrid structures.

Spin-orbit torque (SOT) plays a significant role in spintronic logic and memory devices. However, due to the limited spin Hall angle and SOT symmetry in a heavy-metal-ferromagnet bilayer, further improving SOT efficiency and all-electric magnetization manipulation remain a challenge. Here we report enhanced SOT efficiency and all-electric switching in Au based magnetic structures, by inserting two-dimensional transition metal dichalcogenides (2D TMDs) with large spin-orbit coupling. With the TMD spacer insert, both damping-like and field-like SOTs are improved, and an unconventional out-of-plane damping-like SOT is induced, due to the interface orbital hybridization, modified spin-mixing conductance and orbital current. Moreover, current induced field-free magnetization switching is demonstrated in Au/WTe2/Ni and Au/MoS2/Ni devices, and it shows multiple intermediate states and can be efficiently controlled by an electric current. Our results open a path for increasing torques and expand the application of 2D TMDs in spintronic devices for neuromorphic computing.

Local magnetic moments due to loop currents in metals

We present Hartree-Fock calculations on a simple model to obtain the conditions of formation of local magnetic moments due to loop currents ${L}_{o}$ and spin-loop currents ${L}_{s}$ and compare them to the conditions of formation of local spin moments $M$ which were given long ago in a similar approximation by Anderson. A model with three degenerate orbitals sitting on an equilateral triangle, with on-site and nearest-neighbor repulsions $U$ and $V$, respectively, and intersite kinetic energy, hybridizing with conduction electrons with a parameter $\mathrm{\ensuremath{\Delta}}$ is investigated. ${L}_{o}$ and ${L}_{s}$ are promoted by large $V/\mathrm{\ensuremath{\Delta}}$ and their magnitude is relatively unaffected by $U/\mathrm{\ensuremath{\Delta}}$. Spin-magnetic moments $M$ promoted by large $U/\mathrm{\ensuremath{\Delta}}$ on the other hand are adversely affected by $V/\mathrm{\ensuremath{\Delta}}$. In this model, ${L}_{o}$ for $V$ multiplied by the number of neighbors is approximately the same as the $M$ promoted by $U$ in Anderson's local model for $M$. ${L}_{o}$ and ${L}_{s}$ are degenerate if exchange interactions and Hund's rule are neglected but ${L}_{o}$ is favored when they are included. Many of the qualitative results are visible in an expression for the Hartree-Fock ground state energy derived as a function of small ${L}_{o}, {L}_{s}$, and $M$. Numerical minimization of the Hartree-Fock energy is presented for larger values. We also briefly discuss the connection and differences of the interaction-generated orbital currents and spin currents discussed here and generalized to a lattice with the topological states in metals and semiconductors.

Surface Cooper-Pair Spin Waves in Triplet Superconductors.

We study the electrodynamics of spin triplet superconductors including dipolar interactions, which give rise to an interplay between the collective spin dynamics of the condensate and orbital Meissner screening currents. Within this theory, we identify a class of spin waves that originate from the coupled dynamics of the spin-symmetry breaking triplet order parameter and the electromagnetic field. In particular, we study magnetostatic spin wave modes that are localized to the sample surface. We show that these surface modes can be excited and detected using experimental techniques such as microwave spin wave resonance spectroscopy or nitrogen-vacancy magnetometry, and propose that the detection of these modes offers a means for the identification of spin triplet superconductivity.