Current-driven magnetic domain-wall logic.

Spin-based logic architectures provide nonvolatile data retention, near-zero leakage, and scalability, extending the technology roadmap beyond complementary metal-oxide-semiconductor logic1-13. Architectures based on magnetic domain walls take advantage of the fast motion, high density, non-volatility and flexible design of domain walls to process and store information1,3,14-16. Such schemes, however, rely on domain-wall manipulation and clocking using an external magnetic field, which limits their implementation in dense, large-scale chips. Here we demonstrate a method for performing all-electric logic operations and cascading using domain-wall racetracks. We exploit the chiral coupling between neighbouring magnetic domains induced by the interfacial Dzyaloshinskii-Moriya interaction17-20, which promotes non-collinear spin alignment, to realize a domain-wall inverter, the essential basic building block in all implementations of Boolean logic. We then fabricate reconfigurable NAND and NOR logic gates, and perform operations with current-induced domain-wall motion. Finally, we cascade several NAND gates to build XOR and full adder gates, demonstrating electrical control of magnetic data and device interconnection in logic circuits. Our work provides a viable platform for scalable all-electric magnetic logic, paving the way for memory-in-logic applications.

Orbital Torque in Rare-Earth Transition-Metal Ferrimagnets.

Orbital currents have recently emerged as a promising tool to achieve electrical control of the magnetization in thin-film ferromagnets. Efficient orbital-to-spin conversion is required in order to torque the magnetization. Here, we show that the injection of an orbital current in a ferrimagnetic Gd_{y}Co_{100-y} alloy generates strong orbital torques whose sign and magnitude can be tuned by changing the Gd content and temperature. The effective spin-orbital Hall angle reaches up to -0.25 in a Gd_{y}Co_{100-y}/CuO_{x} bilayer compared to +0.03 in Co/CuO_{x} and +0.13 in Gd_{y}Co_{100-y}/Pt. This behavior is attributed to the local orbital-to-spin conversion taking place at the Gd sites, which is about 5 times stronger and of the opposite sign relative to Co. Furthermore, we observe a manyfold increase in the net orbital torque at low temperature, which we attribute to the improved conversion efficiency following the magnetic ordering of the Gd and Co sublattices.

Field-Free Spin-Orbit Torque Driven Switching of Perpendicular Magnetic Tunnel Junction through Bending Current.

Current-induced spin-orbit torques (SOTs) enable fast and efficient manipulation of the magnetic state of magnetic tunnel junctions (MTJs), making them attractive for memory, in-memory computing, and logic applications. However, the requirement of the external magnetic field to achieve deterministic switching in perpendicularly magnetized SOT-MTJs limits its implementation for practical applications. Here, we introduce a field-free switching (FFS) solution for the SOT-MTJ device by shaping the SOT channel to create a "bend" in the SOT current. The resulting bend in the charge current creates a spatially nonuniform spin current, which translates into inhomogeneous SOT on an adjacent magnetic free layer enabling deterministic switching. We demonstrate FFS experimentally on scaled SOT-MTJs at nanosecond time scales. This proposed scheme is scalable, material-agnostic, and readily compatible with wafer-scale manufacturing, thus creating a pathway for developing purely current-driven SOT systems.

Asynchronous current-induced switching of rare-earth and transition-metal sublattices in ferrimagnetic alloys.

Ferrimagnetic alloys are model systems for understanding the ultrafast magnetization switching in materials with antiferromagnetically coupled sublattices. Here we investigate the dynamics of the rare-earth and transition-metal sublattices in ferrimagnetic GdFeCo and TbCo dots excited by spin-orbit torques with combined temporal, spatial and elemental resolution. We observe distinct switching regimes in which the magnetizations of the two sublattices either remain synchronized throughout the reversal process or switch following different trajectories in time and space. In the latter case, we observe a transient ferromagnetic state that lasts up to 2 ns. The asynchronous switching of the two magnetizations is ascribed to the master-agent dynamics induced by the spin-orbit torques on the transition-metal and rare-earth sublattices and their weak antiferromagnetic coupling, which depends sensitively on the alloy microstructure. Larger antiferromagnetic exchange leads to faster switching and shorter recovery of the magnetization after a current pulse. Our findings provide insight into the dynamics of ferrimagnets and the design of spintronic devices with fast and uniform switching.

Orbital Hanle Magnetoresistance in a 3d Transition Metal.

The Hanle magnetoresistance is a telltale signature of spin precession in nonmagnetic conductors, in which strong spin-orbit coupling generates edge spin accumulation via the spin Hall effect. Here, we report the existence of a large Hanle magnetoresistance in single layers of Mn with weak spin-orbit coupling, which we attribute to the orbital Hall effect. The simultaneous observation of a sizable Hanle magnetoresistance and vanishing small spin Hall magnetoresistance in BiYIG/Mn bilayers corroborates the orbital origin of both effects. We estimate an orbital Hall angle of 0.016, an orbital relaxation time of 2 ps and diffusion length of the order of 2 nm in disordered Mn. Our findings indicate that current-induced orbital moments are responsible for magnetoresistance effects comparable to or even larger than those determined by spin moments, and provide a tool to investigate nonequilibrium orbital transport phenomena.

Erratum: Orbital Hanle Magnetoresistance in a 3d Transition Metal [Phys. Rev. Lett. 131, 156703 (2023)].

This corrects the article DOI: 10.1103/PhysRevLett.131.156703.

Electron Paramagnetic Resonance of Alkali Metal Atoms and Dimers on Ultrathin MgO.

Electron paramagnetic resonance (EPR) can provide unique insight into the chemical structure and magnetic properties of dopants in oxide and semiconducting materials that are of interest for applications in electronics, catalysis, and quantum sensing. Here, we demonstrate that EPR in combination with scanning tunneling microscopy (STM) allows for probing the bonding and charge state of alkali metal atoms on an ultrathin magnesium oxide layer on a Ag substrate. We observe a magnetic moment of 1 µB for Li2, LiNa, and Na2 dimers corresponding to spin radicals with a charge state of +1e. Single alkali atoms have the same charge state and no magnetic moment. The ionization of the adsorbates is attributed to charge transfer through the oxide to the metal substrate. Our work highlights the potential of EPR-STM to provide insight into dopant atoms that are relevant for the control of the electrical properties of surfaces and nanodevices.

Correlation between Electronic Configuration and Magnetic Stability in Dysprosium Single Atom Magnets.

Single atom magnets offer the possibility of magnetic information storage in the most fundamental unit of matter. Identifying the parameters that control the stability of their magnetic states is crucial to design novel quantum magnets with tailored properties. Here, we use X-ray absorption spectroscopy to show that the electronic configuration of dysprosium atoms on MgO(100) thin films can be tuned by the proximity of the metal Ag(100) substrate onto which the MgO films are grown. Increasing the MgO thickness from 2.5 to 9 monolayers induces a change in the dysprosium electronic configuration from 4f9 to 4f10. Hysteresis loops indicate long magnetic lifetimes for both configurations, however, with a different field-dependent magnetic stability. Combining these measurements with scanning tunneling microscopy, density functional theory, and multiplet calculations unveils the role of the adsorption site and charge transfer to the substrate in determining the stability of quantum states in dysprosium single atom magnets.

Chiral Coupling between Magnetic Layers with Orthogonal Magnetization.

We report on the occurrence of strong interlayer Dzyaloshinskii-Moriya interaction (DMI) between an in-plane magnetized Co layer and a perpendicularly magnetized TbFe layer through a Pt spacer. The DMI causes a chiral coupling that favors one-handed orthogonal magnetic configurations of Co and TbFe, which we reveal through Hall effect and magnetoresistance measurements. The DMI coupling mediated by Pt causes effective magnetic fields on either layer of up to 10-15 mT, which decrease monotonically with increasing Pt thickness. Ru, Ta, and Ti spacers mediate a significantly smaller coupling compared to Pt, highlighting the essential role of Pt in inducing the interlayer DMI. These results are relevant to understand and maximize the interlayer coupling induced by the DMI as well as to design spintronic devices with chiral spin textures.

Control of Nonlocal Magnon Spin Transport via Magnon Drift Currents.

Spin transport via magnon diffusion in magnetic insulators is important for a broad range of spin-based phenomena and devices. However, the absence of the magnon equivalent of an electric force is a bottleneck. In this Letter, we demonstrate the controlled generation of magnon drift currents in heterostructures of yttrium iron garnet and platinum. By performing electrical injection and detection of incoherent magnons, we find magnon drift currents that stem from the interfacial Dzyaloshinskii-Moriya interaction. We can further control the magnon drift by the orientation of the magnetic field. The drift current changes the magnon propagation length by up to ±6% relative to diffusion. We generalize the magnonic spin transport theory to include a finite drift velocity resulting from any inversion asymmetric interaction and obtain results consistent with our experiments.

Chiral Domain Wall Injector Driven by Spin-Orbit Torques.

Memory and logic devices that encode information in magnetic domains rely on the controlled injection of domain walls to reach their full potential. In this work, we exploit the chiral coupling, which is induced by the Dzyaloshinskii-Moriya interaction, between in-plane and out-of-plane magnetized regions of a Pt/Co/AlOx trilayer in combination with current-driven spin-orbit torques to control the injection of domain walls into magnetic conduits. We demonstrate that the current-induced domain nucleation is strongly inhibited for magnetic configurations stabilized by the chiral coupling and promoted for those that have the opposite chirality. These configurations allow for efficient domain wall injection using current densities of the order of 4 × 1011 A m-2, which are lower than those used in other injection schemes. Furthermore, by setting the orientation of the in-plane magnetization using an external field, we demonstrate the use of a chiral domain wall injector to create a controlled sequence of alternating domains in a racetrack structure driven by a steady stream of unipolar current pulses.

Origins of the Unidirectional Spin Hall Magnetoresistance in Metallic Bilayers.

Recent studies evidenced the emergence of asymmetric electron transport in layered conductors owing to the interplay between electrical conductivity, magnetization, and the spin Hall or Rashba-Edelstein effects. Here, we investigate the unidirectional magnetoresistance (UMR) caused by the current-induced spin accumulation in Co/Pt and CoCr/Pt bilayers. We identify three competing mechanisms underpinning the resistance asymmetry, namely, interface and bulk spin-dependent electron scattering and electron-magnon scattering. Our measurements provide a consistent description of the current, magnetic field, and temperature dependence of the UMR and show that both positive and negative UMR can be obtained by tuning the interface and bulk spin-dependent scattering.

Magnetic Properties of Metal⁻Organic Coordination Networks Based on 3d Transition Metal Atoms.

The magnetic anisotropy and exchange coupling between spins localized at the positions of 3d transition metal atoms forming two-dimensional metal⁻organic coordination networks (MOCNs) grown on a Au(111) metal surface are studied. In particular, we consider MOCNs made of Ni or Mn metal centers linked by 7,7,8,8-tetracyanoquinodimethane (TCNQ) organic ligands, which form rectangular networks with 1:1 stoichiometry. Based on the analysis of X-ray magnetic circular dichroism (XMCD) data taken at T = 2.5 K, we find that Ni atoms in the Ni⁻TCNQ MOCNs are coupled ferromagnetically and do not show any significant magnetic anisotropy, while Mn atoms in the Mn⁻TCNQ MOCNs are coupled antiferromagnetically and do show a weak magnetic anisotropy with in-plane magnetization. We explain these observations using both a model Hamiltonian based on mean-field Weiss theory and density functional theory calculations that include spin⁻orbit coupling. Our main conclusion is that the antiferromagnetic coupling between Mn spins and the in-plane magnetization of the Mn spins can be explained by neglecting effects due to the presence of the Au(111) surface, while for Ni⁻TCNQ the metal surface plays a role in determining the absence of magnetic anisotropy in the system.

Perpendicular switching of a single ferromagnetic layer induced by in-plane current injection.

Modern computing technology is based on writing, storing and retrieving information encoded as magnetic bits. Although the giant magnetoresistance effect has improved the electrical read out of memory elements, magnetic writing remains the object of major research efforts. Despite several reports of methods to reverse the polarity of nanosized magnets by means of local electric fields and currents, the simple reversal of a high-coercivity, single-layer ferromagnet remains a challenge. Materials with large coercivity and perpendicular magnetic anisotropy represent the mainstay of data storage media, owing to their ability to retain a stable magnetization state over long periods of time and their amenability to miniaturization. However, the same anisotropy properties that make a material attractive for storage also make it hard to write to. Here we demonstrate switching of a perpendicularly magnetized cobalt dot driven by in-plane current injection at room temperature. Our device is composed of a thin cobalt layer with strong perpendicular anisotropy and Rashba interaction induced by asymmetric platinum and AlOx interface layers. The effective switching field is orthogonal to the direction of the magnetization and to the Rashba field. The symmetry of the switching field is consistent with the spin accumulation induced by the Rashba interaction and the spin-dependent mobility observed in non-magnetic semiconductors, as well as with the torque induced by the spin Hall effect in the platinum layer. Our measurements indicate that the switching efficiency increases with the magnetic anisotropy of the cobalt layer and the oxidation of the aluminium layer, which is uppermost, suggesting that the Rashba interaction has a key role in the reversal mechanism. To prove the potential of in-plane current switching for spintronic applications, we construct a reprogrammable magnetic switch that can be integrated into non-volatile memory and logic architectures. This device is simple, scalable and compatible with present-day magnetic recording technology.

Spin tuning of electron-doped metal-phthalocyanine layers.

The spin state of organic-based magnets at interfaces is to a great extent determined by the organic environment and the nature of the spin-carrying metal center, which is further subject to modifications by the adsorbate-substrate coupling. Direct chemical doping offers an additional route for tailoring the electronic and magnetic characteristics of molecular magnets. Here we present a systematic investigation of the effects of alkali metal doping on the charge state and crystal field of 3d metal ions in Cu, Ni, Fe, and Mn phthalocyanine (Pc) monolayers adsorbed on Ag. Combined X-ray absorption spectroscopy and ligand field multiplet calculations show that Cu(II), Ni(II), and Fe(II) ions reduce to Cu(I), Ni(I), and Fe(I) upon alkali metal adsorption, whereas Mn maintains its formal oxidation state. The strength of the crystal field at the Ni, Fe, and Mn sites is strongly reduced upon doping. The combined effect of these changes is that the magnetic moment of high- and low-spin ions such as Cu and Ni can be entirely turned off or on, respectively, whereas the magnetic configuration of MnPc can be changed from intermediate (3/2) to high (5/2) spin. In the case of FePc a 10-fold increase of the orbital magnetic moment accompanies charge transfer and a transition to a high-spin state.

Site- and orbital-dependent charge donation and spin manipulation in electron-doped metal phthalocyanines.

Chemical doping offers promise as a means of tailoring the electrical characteristics of organic molecular compounds. However, unlike for inorganic semiconductors used in electronics applications, controlling the influence of dopants in molecular complexes is complicated by the presence of multiple doping sites, electron acceptor levels, and intramolecular correlation effects. Here we use scanning tunnelling microscopy to analyse the position of individual Li dopants within Cu- and Ni-phthalocyanine molecules in contact with a metal substrate, and probe the charge transfer process with unprecedented spatial resolution. We show that individual phthalocyanine molecules can host at least three distinct stable doping sites and up to six dopant atoms, and that the ligand and metal orbitals can be selectively charged by modifying the configuration of the Li complexes. Li manipulation reveals that charge transfer is determined solely by dopants embedded in the molecules, whereas the magnitude of the conductance gap is sensitive to the molecule-dopant separation. As a result of the strong spin-charge correlation in confined molecular orbitals, alkali atoms provide an effective way for tuning the molecular spin without resorting to magnetic dopants.

Observation of different Li intercalation states and local doping in epitaxial mono- and bilayer graphene on SiC(0001).

Li intercalation is commonly used to enhance the carrier density in epitaxial graphene and mitigate coupling to the substrate. So far, the understanding of the intercalation process, particularly how Li penetrates different layers above the substrate, and its impact on electron transport remains incomplete. Here, we report different phases of Li intercalation and their kinetic processes in epitaxial mono- and bilayer graphene grown on SiC. The distinct doping effects of each intercalation phase are characterized using scanning tunneling spectroscopy. Furthermore, changes in the local conduction regimes are directly mapped by scanning tunneling potentiometry and attributed to different charge transfer states of the intercalated Li. The stable intercalation marked by the formation of Li-Si bonds leads to a significant 56% reduction in sheet resistance of the resulting quasi-free bilayer graphene, as compared to the pristine monolayer graphene.

Spin torque-driven electron paramagnetic resonance of a single spin in a pentacene molecule.

Control over quantum systems is typically achieved by time-dependent electric or magnetic fields. Alternatively, electronic spins can be controlled by spin-polarized currents. Here, we demonstrate coherent driving of a single spin by a radiofrequency spin-polarized current injected from the tip of a scanning tunneling microscope into an organic molecule. With the excitation of electron paramagnetic resonance, we established dynamic control of single spins by spin torque using a local electric current. In addition, our work highlights the dissipative action of the spin-transfer torque, in contrast to the nondissipative action of the magnetic field, which allows for the manipulation of individual spins based on controlled decoherence.

Spin-Orbit Torques and Spin Hall Magnetoresistance Generated by Twin-Free and Amorphous Bi0.9 Sb0.1 Topological Insulator Films.

Topological insulators have attracted great interest as generators of spin-orbit torques (SOTs) in spintronic devices. Bi1-x Sbx is a prominent topological insulator that has a high charge-to-spin conversion efficiency. However, the origin and magnitude of the SOTs induced by current-injection in Bi1-x Sbx remain controversial. Here, the investigation of the SOTs and spin Hall magnetoresistance resulting from charge-to-spin conversion in twin-free epitaxial layers of Bi0.9 Sb0.1 (0001) coupled to FeCo are investigated, and compared with those of amorphous Bi0.9 Sb0.1 . A large charge-to-spin conversion efficiency of 1 in the first case and less than 0.1 in the second is found, confirming crystalline Bi0.9 Sb0.1 as a strong spin-injector material. The SOTs and spin Hall magnetoresistance are independent of the direction of the electric current, indicating that charge-to-spin conversion in single-crystal Bi0.9 Sb0.1 (0001) is isotropic despite the strong anisotropy of the topological surface states. Further, it is found that the damping-like SOT has a non-monotonic temperature dependence with a minimum at 20 K. By correlating the SOT with resistivity and weak antilocalization measurements, charge-spin conversion is concluded to occur via thermally excited holes from the bulk states above 20 K, and conduction through the isotropic surface states with increasing spin polarization due to decreasing electron-electron scattering below 20 K.

Electrically programmable magnetic coupling in an Ising network exploiting solid-state ionic gating.

Two-dimensional arrays of magnetically coupled nanomagnets provide a mesoscopic platform for exploring collective phenomena as well as realizing a broad range of spintronic devices. In particular, the magnetic coupling plays a critical role in determining the nature of the cooperative behavior and providing new functionalities in nanomagnet-based devices. Here, we create coupled Ising-like nanomagnets in which the coupling between adjacent nanomagnetic regions can be reversibly converted between parallel and antiparallel through solid-state ionic gating. This is achieved with the voltage-control of the magnetic anisotropy in a nanosized region where the symmetric exchange interaction favors parallel alignment and the antisymmetric exchange interaction, namely the Dzyaloshinskii-Moriya interaction, favors antiparallel alignment of the nanomagnet magnetizations. Applying this concept to a two-dimensional lattice, we demonstrate a voltage-controlled phase transition in artificial spin ices. Furthermore, we achieve an addressable control of the individual couplings and realize an electrically programmable Ising network, which opens up new avenues to design nanomagnet-based logic devices and neuromorphic computers.