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Identifying orbital textures and their effects on the electronic properties of quantum materials is a critical element in developing orbitronic devices. However, orbital effects are often entangled with the spin degree of freedom, making it difficult to uniquely identify them in charge transport phenomena. Here, we present a combination of scanning superconducting quantum interference device (SQUID) current imaging, global transport measurements, and theoretical analysis, that reveals a direct contribution of orbital textures to the linear charge transport of 2D systems. Specifically, we show that in the LaAlO$_3$/SrTiO$_3$ interface, which lacks both rotation and inversion symmetries, an anisotropic orbital Rashba coupling leads to conductivity anisotropy in zero magnetic field. We experimentally demonstrate this result by locally measuring the conductivity anisotropy, and correlating its appearance to the non-linear Hall effect, showing that the two phenomena have a common origin. Our results lay the foundations for an all--electrical probing of orbital currents in two-dimensional systems., Comment: 22 pages, 15 figures

One of the key elements in spintronics research is the spin Hall effect, allowing to generate spin currents from charge currents. A large spin Hall effect is observed in materials with strong spin orbit coupling, e.g., Pt. Recent research suggests the existence of an orbital Hall effect, the orbital analogue to the spin Hall effect, which also arises in weakly spin orbit coupled materials like Ti, Mn or Cr. In Pt both effects are predicted to coexist. In any of these materials, a magnetic field perpendicular to the spin or orbital accumulation leads to additional Hanle dephasing and thereby the Hanle magnetoresistance (MR). To reveal the MR behavior of a material with both spin and orbital Hall effect, we thus study the MR of Pt thin films over a wide range of thicknesses. Careful evaluation shows that the MR of our textured samples is dominated by the ordinary MR rather than by the Hanle effect. We analyze the intrinsic properties of Pt films deposited by different groups and show that next to the resistivity also the structural properties of the film influence which MR dominates. We further show that this correlation can be found in both spin Hall active materials like Pt and orbital Hall active materials, like Ti. For both materials, the crystalline samples shows a MR attributed to the ordinary MR, whereas we find a large Hanle MR for the samples without apparent structural order. We then provide a set of rules to distinguish between the ordinary and the Hanle MR. We conclude that in all materials with a spin or orbital Hall effect the Hanle MR and the ordinary MR coexist and the purity and crystallinity of the thin film determine the dominating effect.

Quantum materials are characterized by electromagnetic responses intrinsically linked to the geometry and topology of the electronic wavefunctions. These properties are encoded in the quantum metric and Berry curvature. While Berry curvature-mediated transport effects such as the anomalous and nonlinear Hall effects have been identified in several magnetic and nonmagnetic systems, quantum metric-induced transport phenomena remain limited to topological antiferromagnets. Here we show that spin-momentum locking -- a general characteristic of the electronic states at surfaces and interfaces of spin-orbit coupled materials -- leads to a finite quantum metric. This metric activates a nonlinear in-plane magnetoresistance that we measure and electrically control in 111-oriented LaAlO$_3$/SrTiO$_3$ interfaces. These findings demonstrate the existence of quantum metric effects in a vast class of materials and provide new strategies to design functionalities based on the quantum geometry., Comment: Revised manuscript

Slow magnetization relaxation processes are an important time-dependent property of many magnetic materials. We show that magnetotransport measurements based on a well-established current-reversal method can be utilized to implement a simple and robust screening scheme for such relaxation processes. We demonstrate our approach considering the anomalous Hall effect in a Pt/Co/AlOx trilayer model system, and then explore relaxation in {\tau} -MnAl films. Compared to magnetotransport experiments based on ac lock-in techniques, we find that the dc current-reversal method is particulary sensitive to relaxation processes with relaxation time scales on the order of seconds, comparable to the current-reversal measurement time scales.

Taking advantage of the anomalous Hall effect, we electrically probe low-frequency magnetization fluctuations at room temperature in a thin ferromagnetic Pt/Co/AlO$_x$ layer stack with perpendicular magnetic anisotropy. We observe a strong enhancement of the Hall voltage fluctuations within the hysteretic region of the magnetization loop. Analyzing both the temporal evolution of the anomalous Hall voltage and its frequency-dependent noise power density, we identify two types of magnetic noise: abrupt changes in the magnetic domain configuration, evident as Barkhausen-like steps in the Hall voltage time trace, yield a noise power density spectrum scaling with frequency as $1/f^{\beta}$ with $\beta\approx 1.9$. In contrast, quasi-stationary magnetization configurations are connected with a magnetic noise power density with an exponent $\beta\approx 0.9$. The observation of Barkausen steps and relaxation effects shows that the magnetic system is in a non-stationary state in the hysteresis region, such that the fluctuation-dissipation theorem cannot be expected to hold. However, the time-dependent change in the Hall voltage for constant magnetic field strength resembles the integrated noise power.

We study the incubation and transition times that characterize the magnetization switching induced by spin-orbit torques in nanomagnets with perpendicular anisotropy. We present a phenomenological model to interpret the dependence of the incubation time on the amplitude of the voltage pulse and assisting magnetic field and estimate the volume of the seed domain that triggers the switching. Our measurements evidence a correlation between the incubation and transition times that is mediated by the temperature variation during the electric pulse. In addition, we discuss the stochastic distributions of the two times in terms of the energy barriers opposing the nucleation and expansion of the seed domain. We propose two models based on the log-normal and gamma functions to account for the different origin of the variability of the incubation and transition times, which are associated with a single nucleation barrier and multiple pinning sites, respectively.

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.

Light transition metals have recently emerged as a sustainable material class for efficient spin-charge interconversion. We report measurements of current-induced spin-orbit torques generated by Ni$_{1-x}$Cu$_{x}$ alloys in perpendicularly magnetized ferrimagnetic Gd/Fe multilayers. We show that the spin-orbit torque efficiency of Ni$_{1-x}$Cu$_{x}$ increases with the Ni/Cu atomic ratio, reaching values comparable to those of Pt for Ni$_{55}$Cu$_{45}$. Furthermore, we demonstrate magnetization switching of a 20-nm-thick Gd/Fe multilayer with a threshold current that decreases with increasing Ni concentration, similar to the spin-orbit torque efficiency. Our findings show that Ni$_{1-x}$Cu$_{x}$$-$based magnetic heterostructures allow for efficient control of the magnetization by electric currents.

The orbital Hall effect provides an alternative means to the spin Hall effect to convert a charge current into a flow of angular momentum. Recently, compelling signatures of orbital Hall effects have been identified in 3d transition metals. Here, we report a systematic study of the generation, transmission, and conversion of orbital currents in heterostructures comprising 3d, 5d, and 4f metals. We show that the orbital Hall conductivity of Cr reaches giant values of the order of 5*10^5 Ohm^{-1} m^{-1} and that Pt presents a strong orbital Hall effect in addition to the spin Hall effect. Measurements performed as a function of thickness of nonmagnetic Cr, Mn, and Pt layers and ferromagnetic Co and Ni layers reveal how the orbital and spin currents compete or assist each other in determining the spin-orbit torques acting on the magnetic layer. We further show how this interplay can be drastically modulated by introducing 4 f spacers between the nonmagnetic and magnetic layers. Gd and Tb act as very efficient orbital-to-spin current converters, boosting the spin-orbit torques generated by Cr by a factor of 4 and reversing the sign of the torques generated by Pt. To interpret our results, we present a generalized drift-diffusion model that includes both spin and orbital Hall effects and describes their interconversion mediated by spin-orbit coupling.

The manipulation of antiferromagnetic order by means of spin-orbit torques opens unprecedented opportunities to exploit the dynamics of antiferromagnets in spintronic devices. In this work, we investigate the current-induced switching of the magnetic octupole vector in the Weyl antiferromagnet Mn$_3$Sn as a function of pulse shape, field, temperature, and time. We find that the switching behavior can be either bistable or tristable depending on the temporal structure of the current pulses. Time-resolved Hall effect measurements reveal that Mn$_3$Sn switching proceeds via a two-step demagnetization-remagnetization process caused by self-heating over a timescale of tens of ns followed by cooling in the presence of spin-orbit torques. Our results shed light on the switching dynamics of Mn$_3$Sn and prove the existence of extrinsic limits on its switching speed., Comment: Rectified wrong order of MS and Supplement

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 monotonously 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.

We use three-terminal magnetic tunnel junctions (MTJs) designed for field-free switching by spin-orbit torques (SOTs) to systematically study the impact of dual voltage pulses on the switching performances. We show that the concurrent action of an SOT pulse and an MTJ bias pulse allows for reducing the critical switching energy below the level typical of spin transfer torque while preserving the ability to switch the MTJ on the sub-ns time scale. By performing dc and real-time electrical measurements, we discriminate and quantify three effects arising from the MTJ bias: the voltage-controlled change of the perpendicular magnetic anisotropy, current-induced heating, and the spin transfer torque. The experimental results are supported by micromagnetic modeling. We observe that, depending on the pulse duration and the MTJ diameter, different effects take a lead in assisting the SOTs in the magnetization reversal process. Finally, we present a compact model that allows for evaluating the impact of each effect due to the MTJ bias on the critical switching parameters. Our results provide input to optimize the switching of three-terminal devices as a function of time, size, and material parameters.

We investigate the inversion process of magnetic domain walls (DWs) propagating through synthetic noncollinear magnetic textures, whereby an up/down DW can be transformed into a down/up DW and vice versa. We exploit the lateral coupling between out-of-plane and in-plane magnetic regions induced by the interfacial Dzyaloshinskii-Moriya interaction in Pt/Co/AlOx trilayers to realize both field-driven and current-driven magnetic DW inverters. The inverters consist of narrow in-plane magnetic regions embedded in out-of-plane DW racetracks. Magnetic imaging and micromagnetic simulations provide insight into the DW inversion mechanism, showing that DW inversion proceeds by annihilation of the incoming domain on one side of the in-plane region and nucleation of a reverse domain on the opposite side. By changing the shape of the in-plane magnetic region, we show that the DW inversion efficiency can be tuned by adjusting the ratio between the chiral coupling energy at the inverter boundary and the energy cost of nucleating a reverse domain. Finally, we realize an asymmetric DW inverter that has nonreciprocal inversion properties and demonstrate that such a device can operate as a DW diode. Our results provide input for the versatile manipulation of DWs in magnetic racetracks and the design of efficient DW devices for nonvolatile magnetic logic schemes.

We report on the combination of current-induced spin-orbit torques and giant magnetoresistance in a single device to achieve all-electrical write and read out of the magnetization. The device consists of perpendicularly magnetized TbCo and Co layers separated by a Pt or Cu spacer. Current injection through such layers exerts spin-orbit torques and switches the magnetization of the Co layer while the TbCo magnetization remains fixed. Subsequent current injection of lower amplitude senses the relative orientation of the magnetization of the Co and TbCo layers, which results in two distinct resistance levels for parallel and antiparallel alignment due to the current-in-plane giant magnetoresistance effect. We further show that the giant magnetoresistance of devices including a single TbCo/spacer/Co trilayer can be improved from 0.02% to 6% by using a Cu spacer instead of Pt. This type of devices offers an alternative route to a two terminal spintronic memory that can be fabricated with moderate effort., Comment: 18 pages, 5 figures

Current-induced spin-transfer torques (STT) and spin-orbit torques (SOT) enable the electrical switching of magnetic tunnel junctions (MTJs) in nonvolatile magnetic random access memories. In order to develop faster memory devices, an improvement of the timescales underlying the current driven magnetization dynamics is required. Here we report all-electrical time-resolved measurements of magnetization reversal driven by SOT in a three-terminal MTJ device. Single-shot measurements of the MTJ resistance during current injection reveal that SOT switching involves a stochastic two-step process consisting of a domain nucleation time and propagation time, which have different genesis, timescales, and statistical distributions compared to STT switching. We further show that the combination of SOT, STT, and voltage control of magnetic anisotropy (VCMA) leads to reproducible sub-ns switching with a spread of the cumulative switching time smaller than 0.2 ns. Our measurements unravel the combined impact of SOT, STT, and VCMA in determining the switching speed and efficiency of MTJ devices.

Magnonics is gaining momentum as an emerging technology for information processing. The wave character and Joule heating-free propagation of spin-waves hold promises for highly efficient analog computing platforms, based on integrated magnonic circuits. Miniaturization is a key issue but, so far, only few examples of manipulation of spin-waves in nanostructures have been demonstrated, due to the difficulty of tailoring the nanoscopic magnetic properties with conventional fabrication techniques. In this Letter, we demonstrate an unprecedented degree of control in the manipulation of spin-waves at the nanoscale by using patterned reconfigurable spin-textures. By space and time-resolved scanning transmission X-ray microscopy imaging, we provide direct evidence for the channeling and steering of propagating spin-waves in arbitrarily shaped nanomagnonic waveguides based on patterned domain walls, with no need for external magnetic fields or currents. Furthermore, we demonstrate a prototypic nanomagnonic circuit based on two converging waveguides, allowing for the tunable spatial superposition and interaction of confined spin-waves modes., Comment: 16 pages, 5 figures