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We studied the effect of inserting 0.5-nm-thick spacer layers (Ti, V, Cr, Mo, W) at the Pt/Co interface on the spin-orbit torques, the Hall effect, magnetoresistance, saturation magnetization, and magnetic anisotropy. We find that the dampinglike spin-orbit torque decreases substantially for all samples with a spacer layer compared to the reference Pt/Co bilayer, consistently with the opposite sign of the atomic spin-orbit coupling constant of the spacer elements relative to Pt. The reduction of the dampinglike torque is monotonic with atomic number for the isoelectronic 3d,4d, and 5d elements, with the exception of V that has a stronger effect than Cr. The fieldlike spin-orbit torque almost vanishes for all spacer layers irrespective of their composition, suggesting that this torque predominantly originates at the Pt/Co interface. The anomalous Hall effect, magnetoresistance, and saturation magnetization are also all reduced substantially, whereas the sheet resistance is increased in the presence of the spacer layer. Finally, we evidence a correlation between the amplitude of the spin-orbit torques, the spin-Hall-like magnetoresistance, and the perpendicular magnetic anisotropy. These results highlight the significant influence of ultrathin spacer layers on the magnetotransport properties of heavy-metal/ferromagnetic systems., Swiss National Science Foundation (Grant 200020-172775), National Science Foundation (U.S.) (Grant ECCS-6938765)

Ferrimagnetic iron garnets are promising materials for spintronics applications, characterized by ultralow damping and zero current shunting. It has recently been found that few nm-thick garnet films interfaced with a heavy metal can also exhibit sizable interfacial spin-orbit interactions, leading to the emergence, and efficient electrical control, of one-dimensional chiral domain walls. Two-dimensional bubbles, by contrast, have so far only been confirmed in micrometer-thick films. Here, we show by high resolution scanning transmission x-ray microscopy and photoemission electron microscopy that submicrometer bubbles can be nucleated and stabilized in ∼25-nm-thick thulium iron garnet films via short heat pulses generated by electric current in an adjacent Pt strip, or by ultrafast laser illumination. We also find that quasistatic processes do not lead to the formation of a bubble state, suggesting that the thermodynamic path to reaching that state requires transient dynamics. X-ray imaging reveals that the bubbles have Bloch-type walls with random chirality and topology, indicating negligible chiral interactions at the garnet film thickness studied here. The robustness of thermal nucleation and the feasibility demonstrated here to image garnet-based devices by x-rays both in transmission geometry and with sensitivity to the domain wall chirality are critical steps to enabling the study of small spin textures and dynamics in perpendicularly magnetized thin-film garnets., US Defense Advanced Research Projects Agency (DARPA) under Project No. HR0011834375, NSF Grant No. DMR1808190

The Dzyaloshinskii-Moriya interaction (DMI) is responsible for exotic chiral and topological magnetic states such as spin spirals and skyrmions. DMI manifests at metallic ferromagnet/heavy-metal interfaces, owing to inversion symmetry breaking and spin-orbit coupling by a heavy metal such as Pt. Moreover, in centrosymmetric magnetic oxides interfaced by Pt, DMI-driven topological spin textures and fast current-driven dynamics have been reported, though the origin of this DMI is unclear. While in metallic systems, spin-orbit coupling arises from a proximate heavy metal, we show that in perpendicularly-magnetized iron garnets, rare-earth orbital magnetism gives rise to an intrinsic spin-orbit coupling generating interfacial DMI at mirror symmetry-breaking interfaces. We show that rare-earth ion substitution and strain engineering can significantly alter the DMI. These results provide critical insights into the origins of chiral magnetism in low-damping magnetic oxides and identify paths toward engineering chiral and topological states in centrosymmetric oxides through rare-earth ion substitution., National Science Foundation (Award DMR-1808190)

© 2020 American Chemical Society. Voltage control of interfacial magnetism has been greatly highlighted in spintronics research for many years, as it might enable ultralow power technologies. Among a few suggested approaches, magneto-ionic control of magnetism has demonstrated large modulation of magnetic anisotropy. Moreover, the recent demonstration of magneto-ionic devices using hydrogen ions presented relatively fast magnetization toggle switching, tsw ∼100 ms, at room temperature. However, the operation speed may need to be significantly improved to be used for modern electronic devices. Here, we demonstrate that the speed of proton-induced magnetization toggle switching largely depends on proton-conducting oxides. We achieve ∼1 ms reliable (>103 cycles) switching using yttria-stabilized zirconia (YSZ), which is ∼100 times faster than the state-of-the-art magneto-ionic devices reported to date at room temperature. Our results suggest that further engineering of the proton-conducting materials could bring substantial improvement that may enable new low-power computing scheme based on magneto-ionics., Korea Institute of Science and Technology Institutional Program (Grant 2E29410, 2E30220), National Research Councilof Science and Technology (Korea) (Grant CAP-16-01-KIST), National Science Foundation (U.S.) (Awards DMR-1419807, ECCS-1808828)

Perpendicularly magnetized thin films with a strong Dzyaloshinskii-Moriya interaction (DMI) exhibit chiral spin structures such as Néel domain walls and skyrmions. These structures are promising candidates for next-generation magnetic memory devices. Determining the magnitude of the DMI accurately is key to engineering materials for such applications. Existing approaches are based on quantities extracted either from magnetization dynamics, which present experimental and theoretical challenges, or from measurements of quasistatic domain spacing, which so far have been analyzed using incomplete models or prohibitively slow micromagnetic simulations. Here, we use a recently developed analytical model of stripe domain widths in perpendicularly magnetized multilayers to extract the DMI from domain images combined with magnetometry data. Our approach is tested on micromagnetically simulated domain patterns, where we achieve a 1% agreement of the extracted DMI with the DMI used to run the simulation. We then apply our method to determine the thickness-dependent DMI in two experimental materials, one with ([Pt(2.5-7.5nm)/Co60Fe20B20(0.8nm)/MgO(1.5nm)]13) and one without ([Pt(2.5-7.5nm)/Co(0.8nm)/Pt(1.5nm)]13) inversion symmetry breaking. We discuss the means to obtain realistic error bars with our method. Our results demonstrate that analytical domain spacing analysis is a powerful tool to extract the DMI from technologically relevant multilayer materials., United States. Department of Energy. Office of Basic Energy Sciences (Award #DE-SC0012371), National Science Foundation (U.S.) (Awards DMR-1419807, 1541959)

Current-induced dynamics of twisted domain walls and skyrmions in ferromagnetic perpendicularly magnetized multilayers is studied through three-dimensional micromagnetic simulations and analytical modeling. It is shown that such systems generally exhibit a Walker-breakdown-like phenomenon in the presence of a current-induced dampinglike spin-orbit torque. Above a critical current threshold, corresponding to typical velocities of the order of tens of m/s, domain walls in some layers start to precess with frequencies in the gigahertz regime, which leads to oscillatory motion and a significant drop in mobility. This phenomenon originates from complex stray field interactions and occurs for a wide range of multilayer materials and structures that include at least three ferromagnetic layers and finite Dzyaloshinskii-Moriya interaction. An analytical model is developed to describe the precessional dynamics in multilayers with surface-volume stray field interactions, yielding qualitative agreement with micromagnetic simulations.

Magnetic properties in ferrimagnetic GdCo alloy films with bulk perpendicular magnetic anisotropy (PMA) are investigated as a function of annealing temperature (T anneal ) and annealing time for several capping layers. Magnetic properties in films capped by TaO x vary markedly with T anneal ; the saturation magnetization and coercivity vary progressively with increasing T anneal up to 300°C, and above that temperature, PMA is lost abruptly. By comparing the annealing temperature dependence for Co-dominated and Gd-dominated compositions close to the magnetization compensation point, the data are readily explained by preferential oxidation of Gd during annealing. When films are capped by a Ta/Pt bilayer, the film properties are stable up T anneal = 300 °C, indicating that oxidation at high temperatures is effectively blocked, but the abrupt loss of PMA for T anneal > 300 °C is still observed. X-ray diffraction measurement reveals that the amorphous structure of the films remains the same after high-temperature annealing that is sufficient to remove PMA, indicating that crystallization from the amorphous phase is not responsible for the lack of PMA. Instead, our results suggest that high annealing temperatures may cause segregation of Co and Gd atoms in the films, which reduces anisotropic pair-pair correlations responsible for the observed bulk PMA in the as-grown state. ©2018 Author(s)., NSF (DMR-14-19807), NSF (NSF-ECCS-1408172)

Electrical control of magnetic order in antiferromagnetic insulators (AFIs) using a Pt overlayer as a spin current source has been recently reported, but detecting and understanding the nature of current-induced switching in AFIs remain a challenge. Here, we examine the origin of spin Hall magnetoresistance-like signals measured in a standard Hall bar geometry, which have recently been taken as evidence of current-induced switching of the antiferromagnetic order in Pt/AFI bilayers. We show that transverse voltage signals consistent with both the partial switching and toggle switching of the Néel vector in epitaxial Pt/NiO bilayers on Al2O3 are also present in Pt/Al2O3 in which the AFI is absent. We show that these signals have a thermal origin and arise from (i) transient changes in the current distribution due to nonuniform Joule heating and (ii) irreversible changes due to electromigration at elevated current densities, accompanied by long-term creep. These results suggest that more sophisticated techniques that directly probe the magnetic order are required to reliably exclude transport artifacts and thus infer information about the antiferromagnetic order in such systems. Keywords: Magnetic ordering; Transition metal oxides; Magnetism; Spintronics; Hall effect; Epitaxy; Spin Hall effect; Scanning electron microscopy; Magnetron sputtering; Electromigration, National Science Foundation. MRSEC Program (Grant DMR-1419807)

We demonstrate a conceptually new mechanism to generate an in-plane spin current with out-of-plane polarization in a nonmagnetic metal, detected by nonlocal thermoelectric voltage measurement. We generate out-of-plane (∇T_{OP}) and in-plane (∇T_{IP}) temperature gradients, simultaneously, acting on a magnetic insulator-Pt bilayer. When the magnetization has a component oriented perpendicular to the plane, ∇T_{OP} drives a spin current into Pt with out-of-plane polarization due to the spin Seebeck effect. ∇T_{IP} then drags the resulting spin-polarized electrons in Pt parallel to the plane against the gradient direction. This finally produces an inverse spin Hall effect voltage in Pt, transverse to ∇T_{IP} and proportional to the out-of-plane component of the magnetization. This simple method enables the detection of the perpendicular magnetization component in a magnetic insulator in a nonlocal geometry., National Science Foundation (U.S.) (Grant 1808190), National Science Foundation (U.S.). Materials Research Science and Engineering Centers (Program) (Grant DMR1419807)

Rare-earth iron garnet thin films with perpendicular magnetic anisotropy (PMA) have recently attracted a great deal of attention for spintronic applications. Thulium iron garnet (TmIG) has been successfully grown and TmIG/Pt heterostructures have been characterized. However, TmIG is not the only rare-earth iron garnet that can be grown with PMA. We report the growth, magnetic, and spintronic properties of epitaxial terbium iron garnet (TbIG) and europium iron garnet (EuIG) thin films with PMA. Reciprocal space mapping shows the films are lattice matched to the substrate without strain relaxation, even for films up to 56 nm thick. The lattice strain and magnetostriction coefficient produce PMA in certain cases. TbIG grows on (111) gadolinium gallium garnet (GGG) with PMA due to the in-plane compressive strain, whereas TbIG on (111) substituted GGG (SGGG) is in tension and has an in-plane easy axis. EuIG grows with PMA on (100) and (111) GGG substrates, which facilitates the investigation of spintronic properties as a function of orientation. Both garnets have excess rare earth, which is believed to occupy Fe octahedral sites and in the case of TbIG is associated with an increase in the compensation temperature to 330 K, higher than the bulk value. Anomalous Hall effect (AHE) measurements of Pt/EuIG Hall crosses show that the spin mixing conductance of Pt/ (111) and (100) EuIG is similar. AHE measurements of Pt/TbIG Hall crosses reveal a sign change in the AHE amplitude at the compensation point analogous to all-metallic systems., National Science Foundation (U.S.) (Grant 1122374)

Magnetic skyrmions are topological quasiparticles of great interest for data storage applications because of their small size, high stability, and ease of manipulation via electric current. However, although models exist for some limiting cases, there is no universal theory capable of accurately describing the structure and energetics of all skyrmions. The main barrier is the complexity of non-local stray field interactions, which are usually included through crude approximations. Here we present an accurate analytical framework to treat isolated skyrmions in any material, assuming only a circularly-symmetric 360° domain wall profile and a homogeneous magnetization profile in the out-of-plane direction. We establish the first rigorous criteria to distinguish stray field from DMI skyrmions, resolving a major dispute in the community. We discover new phases, such as bi-stability, a phenomenon unknown in magnetism so far. We predict materials for sub-10 nm zero field room temperature stable skyrmions suitable for applications. Finally, we derive analytical equations to describe current-driven dynamics, find a topological damping, and show how to engineer materials in which compact skyrmions can be driven at velocities > 1000 m/s., United States. Department of Energy. Office of Basic Energy Sciences (Award DE-SC0012371)

This article reviews static and dynamic interfacial effects in magnetism, focusing on interfacially driven magnetic effects and phenomena associated with spin-orbit coupling and intrinsic symmetry breaking at interfaces. It provides a historical background and literature survey, but focuses on recent progress, identifying the most exciting new scientific results and pointing to promising future research directions. It starts with an introduction and overview of how basic magnetic properties are affected by interfaces, then turns to a discussion of charge and spin transport through and near interfaces and how these can be used to control the properties of the magnetic layer. Important concepts include spin accumulation, spin currents, spin-transfer torque, and spin pumping. An overview is provided to the current state of knowledge and existing review literature on interfacial effects such as exchange bias, exchange-spring magnets, the spin Hall effect, oxide heterostructures, and topological insulators. The article highlights recent discoveries of interface-induced magnetism and noncollinear spin textures, nonlinear dynamics including spin-transfer torque and magnetization reversal induced by interfaces, and interfacial effects in ultrafast magnetization processes., United States. Department of Energy. Division of Materials Sciences and Engineering (DE-SC0012371)

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., Gordon and Betty Moore Foundation (PiQS Initiative through Grant GBMF4531), National Science Foundation (U.S.). Graduate Research Fellowship (grant no. DGE1144152), National Science Foundation (U.S.) (NSF award no. 1541959), United States. Department of Energy. Office of Basic Energy Science (Award no. DE-SC0012371 (sample fabrication and magnetic properties characterization))

Recent studies have shown that material structures, which lack structural inversion symmetry and have high spin-orbit coupling can exhibit chiral magnetic textures and skyrmions which could be a key component for next generation storage devices. The Dzyaloshinskii-Moriya Interaction (DMI) that stabilizes skyrmions is an anti-symmetric exchange interaction favoring non-collinear orientation of neighboring spins. It has been shown that materials systems with high DMI can lead to very efficient domain wall and skyrmion motion by spin-orbit torques. To engineer such devices, it is important to quantify the DMI for a given material system. Here, we extract the DMI at the Heavy Metal/Ferromagnet interface using two complementary measurement schemes, namely, asymmetric domain wall motion and the magnetic stripe annihilation. By using the two different measurement schemes, we find for W(5 nm)/Co₂₀Fe₆₀B₂₀(0.6 nm)/MgO(2 nm) the DMI to be 0.68 ± 0.05 mJ/m² and 0.73 ± 0.5 mJ/m², respectively. Furthermore, we show that this DMI stabilizes skyrmions at room temperature and that there is a strong dependence of the DMI on the relative composition of the CoFeB alloy. Finally, we optimize the layers and the interfaces using different growth conditions and demonstrate that a higher deposition rate leads to a more uniform film with reduced pinning and skyrmions that can be manipulated by spin orbit torques., United States. Department of Energy. Office of Basic Energy Sciences (Award DE-SC0012371)

We present an analytical theory to describe three-dimensional magnetic textures in perpendicularly magnetized magnetic multilayers that arise in the presence of magnetostatic interactions and the Dzyaloshinskii-Moriya interaction (DMI). We demonstrate that domain walls in multilayers develop a complex twisted structure, which persists even for films with strong DMI. The origin of this twist is surface-volume stray field interactions that manifest as a depth-dependent effective field whose form mimics the DMI effective field. We find that the wall twist has a minor impact on the equilibrium skyrmion or domain size but can significantly affect current-driven dynamics. Our conclusions are based on the derived analytical expressions for the magnetostatic energy and confirmed by micromagnetic simulations., United States. Department of Energy. Office of Basic Energy Sciences (Award DE-SC0012371)

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 skyrmions are topologically protected spin textures that exhibit fascinating physical behaviours and large potential in highly energy-efficient spintronic device applications. The main obstacles so far are that skyrmions have been observed in only a few exotic materials and at low temperatures, and fast current-driven motion of individual skyrmions has not yet been achieved. Here, we report the observation of stable magnetic skyrmions at room temperature in ultrathin transition metal ferromagnets with magnetic transmission soft X-ray microscopy. We demonstrate the ability to generate stable skyrmion lattices and drive trains of individual skyrmions by short current pulses along a magnetic racetrack at speeds exceeding 100 m s-1as required for applications. Our findings provide experimental evidence of recent predictions and open the door to room-temperature skyrmion spintronics in robust thin-film heterostructures., United States. Department of Energy. Office of Basic Energy Sciences (Award DE-SC0012371)

We report fast and efficient current-induced switching of a perpendicular anisotropy magnetic insulator thulium iron garnet by using spin-orbit torques (SOT) from the Pt overlayer. We first show that, with quasi-DC (10 ms) current pulses, SOT-induced switching can be achieved with an external field as low as 2 Oe, making TmIG an outstanding candidate to realize efficient switching in heterostructures that produce moderate stray fields without requiring an external field. We then demonstrate deterministic switching with fast current pulses (≤20 ns) with an amplitude of ∼10¹²A/m², similar to all-metallic structures. We reveal that, in the presence of an initially nucleated domain, the critical switching current is reduced by up to a factor of five with respect to the fully saturated initial state, implying efficient current-driven domain wall motion in this system. Based on measurements with 2 ns-long pulses, we estimate the domain wall velocity of the order of ∼400 m/s per j = 10¹²A/m².

We report on a memory device concept based on the recently discovered unidirectional spin Hall magnetoresistance (USMR), which can store multiple bits of information in a single ferromagnetic heterostructure. We show that the USMR with possible contribution of Joule heating-driven magnetothermal effects in ferromagnet/normal metal/ferromagnet (FM/NM/FM) trilayers gives rise to four different 2nd harmonic resistance levels corresponding to four magnetization states (¶, ⇄, ⇆, ¶) in which the system can be found. Combined with the possibility of controlling the individual FMs by spin-orbit torques, we propose that it is possible to build an all-electrical lateral two-terminal multi-bit-per-cell memory device.

The spin-Hall effect induced modification of the attenuation of propagating exchange-mode spin waves (SWs) is studied micromagnetically and analytically in heavy-metal/ferromagnet bilayers. Micromagnetic simulations of spin-wave propagation in Pt/NiFe show that at a relatively low current density of ∼ 6 × 10¹¹A/m², Gilbert damping is exactly balanced by the spin-Hall torque and long-distance SW transmission is possible. An analytical model is developed to explain the micromagnetic results and relate the current density to the characteristic attenuation length. The results suggest that the spin Hall effect can be used as an effective means to control the attenuation length of propagating spin waves in nanostructures.

Directed transport of biological species across the surface of a substrate is essential for realizing lab-on-chip technologies. Approaches that utilize localized magnetic fields to manipulate magnetic particles carrying biological entities are attractive owing to their sensitivity, selectivity, and minimally disruptive impact on biomaterials. Magnetic domain walls in magnetic tracks produce strong localized fields and can be used to capture, transport, and detect individual superparamagnetic microbeads. The dynamics of magnetic microbead transport by domain walls has been well studied. However, demonstration of more complex functions such as selective motion and sorting using continuously driven domain walls in contiguous magnetic tracks is lacking. Here, a junction architecture is introduced that allows for branching networks in which superparamagnetic microbeads can be routed along dynamically-selected paths by a combination of rotating in-plane field for translation, and a pulsed out-of-plane field for path selection. Moreover, experiments and modeling show that the select-field amplitude is bead-size dependent, which allows for digital sorting of multiple bead populations using automated field sequences. This work provides a simple means to implement complex routing networks and selective transport functionalities in chip-based devices using magnetic domain wall conduits.

We report the effect of the rare earth metal Gd on current-induced spin-orbit torques (SOTs) in perpendicularly magnetized Pt/Co/Gd heterostructures, characterized using harmonic measurements and spin-torque ferromagnetic resonance (ST-FMR). By varying the Gd metal layer thickness from 0 nm to 8 nm, harmonic measurements reveal a significant enhancement of the effective fields generated from the Slonczewski-like and field-like torques. ST-FMR measurements confirm an enhanced effective spin Hall angle and show a corresponding increase in the magnetic damping constant with increasing Gd thickness. These results suggest that Gd plays an active role in generating SOTs in these heterostructures. Our finding may lead to spin-orbitronics device application such as non-volatile magnetic random access memory, based on rare earth metals., National Science Foundation (U.S.) (NSF-ECCS-1408172)

The current-induced domain wall motion along a thin cobalt ferromagnetic strip sandwiched in a multilayer (Pt/Co/AlO) is theoretically studied with emphasis on the roles of the Rashba field, the spin Hall effect, and the Dzyaloshinskii-Moriya interaction. The results point out that these ingredients, originated from the spin-orbit coupling, are consistent with recent experimental observations in three different scenarios. With the aim of clarifying which is the most plausible the influence of in-plane longitudinal and transversal fields is evaluated.

The temperature dependence of spin-orbit torques (SOTs) and spin-dependent transport parameters is measured in bilayer Ta/TbCo ferrimagnetic alloy films with bulk perpendicular magnetic anisotropy. We find that the dampinglike (DL)-SOT effective field diverges as temperature is swept through the magnetic compensation temperature (T[subscript M]), where the net magnetization vanishes due to the opposing contributions from the Tb and Co sublattices. We show that DL-SOT scales with the inverse of the saturation magnetization (M[subscript s]), whereas the spin-torque efficiency is independent of the temperature-dependent M [subscript s]. Our findings provide insight into spin transport mechanisms in ferrimagnets and highlight low-M [subscript s] rare-earth/transition-metal alloys as promising candidates for SOT device applications., National Science Foundation (U.S.) (NSF-ECCS-1408172)

A solid-state three-terminal resistive switch based on gate-voltage-tunable reversible oxidation of a thin-film metallic channel is demonstrated. The switch is composed of a cobalt wire placed under a GdOx layer and a Au top electrode. The lateral resistance of the wire changes with the transition between cobalt and cobalt oxide controlled by a voltage applied to the top electrode. The kinetics of the oxidation and reduction process are examined through time- and temperature-dependent transport measurements. It is shown that that reversible voltage induced lateral resistance switching with a ratio of 10 3 can be achieved at room temperature. The reversible non-volatile redox reaction between metal and metal oxide may provide additional degrees of freedom for post-fabrication control of properties of solid-state materials. This type of three-terminal device has potential applications in neuromorphic computing and multilevel data storage, as well as applications that require controlling a relatively large current., National Science Foundation (U.S.) (Grant DMR-1419807)

We develop an accurate analytical model for the stray field energy of parallel stripe domains in multilayer films with perpendicular magnetic anisotropy, taking into account the effects of finite domain wall width and variable domain wall angle. By minimizing the total energy, we predict the domain width, the domain wall width, and the domain wall angle for given material parameters. We show how the domain wall width depends on the film thickness and the domain size. We explore the domain wall angle as a function of Dzyaloshinskii-Moriya interaction (DMI) and derive a threshold value D[subscript thr] beyond which the system is in a Néel state. We find that thicker films require larger values of DMI to stabilize the Néel state. Finally, we test the effective medium theory, which allows treating multilayers as effective single layer films, and provide criteria for the applicability of the model in the presence of both surface and volume stray fields. Our results are supported by micromagnetic simulations, which indicate that the predictions are still precise even if the system is in a labyrinthine domain state. Using our model, otherwise inaccessible magnetic parameters, such as the DMI constant or the exchange constant, can now be obtained straightforwardly from static measurements of the stripe domain width in such films.

Thermally activated domain-wall (DW) motion driven by magnetic field and electric current is investigated experimentally in out-of-plane magnetized Pt(Co/Pt)3 multilayers. We directly extract the thermal activation energy barrier for DW motion and observe the dynamic regimes of creep, depinning, and viscous flow. Further analysis reveals that the activation energy must be corrected with a factor dependent on the Curie temperature, and we derive a generalized Arrhenius-like equation governing thermally activated motion. By using this generalized equation, we quantify the efficiency of current-induced spin torque in assisting DW motion. Current produces no effect aside from Joule heating in the multilayer with 7-Å thick Co layers, whereas it generates a finite spin torque on DWs in the multilayer with atomically thin 3-Å Co layers. These findings suggest that conventional spin-transfer torques from in-plane spin-polarized current do not drive DWs in ultrathin Co/Pt multilayers.

We characterize the spin Hall magnetoresistance (SMR), spin Seebeck effect (SSE), and dampinglike spin-orbit torque (SOT) in thulium iron garnet/platinum bilayers with perpendicular magnetic anisotropy by using harmonic Hall effect measurements. By consecutive annealing steps followed by measurements on a single device, we reveal that the spin-dependent effects gradually decrease in amplitude as the annealing temperature increases. We attribute this behavior primarily to the changes in the spin-mixing conductance, which sensitively depends on the interface quality. However, further analysis demonstrates that although the SSE scales closely with the SMR, the dampinglike SOT shows a significantly different trend upon annealing, contrary to theoretical expectations. By comparing the dampinglike SOT with the field-induced Hall effect, we found evidence that scattering from Fe impurities in the Pt at the interface might be responsible for the distinct annealing temperature dependence of the dampinglike SOT., Deutsche Forschungsgemeinschaft, United States. Defense Advanced Research Projects Agency (C-SPIN, a SRC STARnet Center), Microelectronics Advanced Research Corporation (MARCO) (C-SPIN, a SRC STARnet Center)

In this paper, we show that applying a hard axis field reduces the energy barrier for the spontaneous formation of a multi-domain state in magnetic ultrathin films sandwiched between a heavy metal and an oxide. This provides a simple technique to generate a metastable multi-domain state in magnetic films where the ground state is uniform. This approach could be particularly interesting in materials with strong Dzyaloshinskii-Moriya interaction as a means to realize metastable chiral textures., National Science Foundation (U.S.) (NSF-CCS-1408172)

We report on large modifications of current-induced spin-orbit torques in a gated Pt/Co/Gd-oxide microstrip due to voltage-driven O[superscript 2]−migration. The Slonczewski-like and field-like torques are quantified using a low-frequency harmonic technique based on the polar magneto-optical Kerr effect. Voltage-induced oxidation of Co enhances the Slonczewski-like torque by as much as an order of magnitude and simultaneously reduces the anisotropy energy barrier by a factor of ~5. Such magneto-ionic tuning of interfacial spin-orbit effects may significantly enhance the efficiency of magnetization switching and provide additional degrees of freedom in spintronic devices., National Science Foundation (U.S.) (NSF-CCS-1408172)

Spin-orbit torques (SOTs) are studied in perpendicularly magnetized ultrathin Co films sandwiched between two heavy metals, Pt and Ta. A significant enhancement of the Slonczewski-like torque is achieved by placing dissimilar metals with opposite spin Hall angles on opposite sides of the ferromagnet. SOTs were characterized through harmonic measurements and the contribution by the Ta overlayer was isolated by systematically varying its thickness. An effective spin Hall angle of up to 34% is observed, along with a sizable field-like torque that increases with increasing Ta layer thickness. Current-induced switching measurements reveal a corresponding increase in switching efficiency, suggesting that by engineering both interfaces in trilayer structures, the SOTs can be significantly improved., National Science Foundation (U.S.) (NSF-ECCS-1408172)

Current-induced domain wall motion in the presence of the Dzyaloshinskii-Moriya interaction (DMI) is experimentally and theoretically investigated in heavy-metal/ferromagnet bilayers. The angular dependence of the current-induced torque and the magnetization structure of Dzyaloshinskii domain walls are described and quantified simultaneously in the presence of in-plane fields. We show that the DMI strength depends strongly on the heavy metal, varying by a factor of 20 between Ta and Pa, and that strong DMI leads to wall distortions not seen in conventional materials. These findings provide essential insights for understanding and exploiting chiral magnetism for emerging spintronics applications., National Science Foundation (U.S.) (NSF-ECCS-1128439), National Science Foundation (U.S.). Graduate Research Fellowship

The dynamics of fluid-borne superparamagnetic bead transport by field-driven domain walls (DWs) in submicrometer ferromagnetic tracks is studied experimentally together with numerical and analytical modeling. A combination of micromagnetic modeling and numerical calculation is used to determine the strength of bead-DW interaction for a range of track geometries and bead sizes. The maximum DW velocity for continuous bead transport is predicted from these results and shown to be supported by experimental measurements. Enhancement of the maximum velocity by appropriate material selection or field application is demonstrated, and an analysis of the source of statistical variation is presented. Finally, the dynamics of bead-DW interaction and bead transport above the maximum DW velocity for continuous DW-mediated bead transport is characterized., Massachusetts Institute of Technology. Center for Materials Science and Engineering, National Science Foundation (U.S.) (DMR-0819762), Deshpande Center for Technological Innovation (Massachusetts Institute of Technology. School of Engineering)

The influence of a gate voltage on magnetic anisotropy is investigated in a thin Fe film epitaxially grown on a Ag(1,1,10) substrate and covered by MgO. Oscillations in step-induced magnetic anisotropy due to quantum well states (QWS) confined in the Fe film are observed and shown to persist up to room temperature at low Fe thicknesses. By systematically examining the voltage and thickness dependence of the magnetic hysteresis loop characteristics, we identify two distinct effects by which an applied voltage modifies the magnetic anisotropy. The first effect is due to voltage-induced changes to interfacial perpendicular magnetic anisotropy which, due to the vicinal geometry, leads to changes in the effective in-plane uniaxial magnetic anisotropy. A second effect is observed at lower film thicknesses and shows nonmonotonic voltage-induced effects on magnetic anisotropy. This nonmonotonic behavior coincides with the onset of significant QWS-induced effects on magnetic anisotropy and suggests a link between QWS- and voltage-induced anisotropy changes., National Science Foundation (U.S.) (Grant NSF-ECCS-1128439)

A method of patterning magnetic metallic thin films is presented using a bilayer polymethyl methacrylate and hydrogen silsesquioxane electron beam lithography resist mask combined with ion beam etching. The bilayer resist process allows for the combination of a high-resolution resist mask with easy postprocess removal of the mask without damage to the magnetic quality of the film. Co60Fe20B20 and Co/Ni multilayer films were patterned with electron beam lithography at 10–125 keV down to 25 nm wide features with 2 nm average root-mean square edge roughness. Both the in-plane and out-of-plane magnetic anisotropies of the respective film types were preserved after patterning., Skolkovo Institute of Science and Technology, Microelectronics Advanced Research Corporation (MARCO) (C-SPIN, a STARnet center)), United States. Defense Advanced Research Projects Agency (C-SPIN, one of the six SRC STARnet Centers)

In most ferromagnets the magnetization rotates from one domain to the next with no preferred handedness. However, broken inversion symmetry can lift the chiral degeneracy, leading to topologically rich spin textures such as spin spirals and skyrmions through the Dzyaloshinskii–Moriya interaction (DMI). Here we show that in ultrathin metallic ferromagnets sandwiched between a heavy metal and an oxide, the DMI stabilizes chiral domain walls (DWs) whose spin texture enables extremely efficient current-driven motion. We show that spin torque from the spin Hall effect drives DWs in opposite directions in Pt/CoFe/MgO and Ta/CoFe/MgO, which can be explained only if the DWs assume a Néel configuration with left-handed chirality. We directly confirm the DW chirality and rigidity by examining current-driven DW dynamics with magnetic fields applied perpendicular and parallel to the spin spiral. This work resolves the origin of controversial experimental results and highlights a new path towards interfacial design of spintronic devices., Castilla y León (Spain). Junta (SA163A12), Spain (project MAT2011-28532-C03-01), National Science Foundation (U.S.) (NSF Graduate Research Fellowship Program), National Science Foundation (U.S.) (NSF-ECCS-1128439)

We study the effect of the Dzyaloshinskii-Moriya interaction (DMI) on current-induced magnetic switching of a perpendicularly magnetized heavy-metal/ferromagnet/oxide trilayer both experimentally and through micromagnetic simulations. We report the generation of stable helical magnetization stripes for a sufficiently large DMI strength in the switching region, giving rise to intermediate states in the magnetization and confirming the essential role of the DMI on switching processes. We compare the simulation and experimental results to a macrospin model, showing the need for a micromagnetic approach. The influence of the temperature on the switching is also discussed., National Science Foundation (U.S.) (NSF-ECCS-1128439), Spain (Project MAT2011-28532-C03-01), Junta de Castilla y Leon (Project SA163A12), Microelectronics Advanced Research Corporation (MARCO), Semiconductor Research Corporation. Center for Spintronic Materials, Interfaces, and Novel Architectures, United States. Defense Advanced Research Projects Agency

Current-induced domain wall motion along high perpendicular magnetocrystalline anisotropy multilayers is studied by means of full micromagnetic simulations and a one-dimensional model in the presence of in-plane fields. We consider domain wall motion driven by the spin Hall effect in the presence of the Dzyaloshinskii-Moriya interaction (DMI). In the case of relatively weak DMI, the wall propagates without significant tilting of the wall plane, and the full micromagnetic results are quantitatively reproduced by a simple rigid one-dimensional model. By contrast, significant wall-plane tilting is observed in the case of strong DMI, and a one-dimensional description including the wall tilting is required to qualitatively describe the micromagnetic results. However, in this strong-DMI case, the one-dimensional model exhibits significant quantitative discrepancies from the full micromagnetic results, in particular, when high longitudinal fields are applied in the direction of the internal domain wall magnetization. It is also shown that, even under thermal fluctuations and edge roughness, the domain wall develops a net tilting angle during its current-induced motion along samples with strong DMI., Castilla y León (Spain). Junta (Project SA163A12), Spain (project MAT2011-28532-C03-01), Microelectronics Advanced Research Corporation (MARCO) (C-SPIN), United States. Defense Advanced Research Projects Agency (C-SPIN, one of the six SRC STARnet Centers), National Science Foundation (U.S.) (NSF-ECCS-1128439)

In metal/oxide heterostructures, rich chemical electronic magnetic and mechanical properties can emerge from interfacial chemistry and structure. The possibility to dynamically control interface characteristics with an electric field paves the way towards voltage control of these properties in solid-state devices. Here, we show that electrical switching of the interfacial oxidation state allows for voltage control of magnetic properties to an extent never before achieved through conventional magneto-electric coupling mechanisms. We directly observe in situ voltage-driven O{superscript 2−] migration in a ​Co/metal-oxide bilayer, which we use to toggle the interfacial magnetic anisotropy energy by >0.75 erg cm[superscript −2] at just 2 V. We exploit the thermally activated nature of ion migration to markedly increase the switching efficiency and to demonstrate reversible patterning of magnetic properties through local activation of ionic migration. These results suggest a path towards voltage-programmable materials based on solid-state switching of interface oxygen chemistry., National Science Foundation (U.S.) (NSF-ECCS-1128439), National Science Foundation (U.S.). Materials Research Science and Engineering Centers (Program) (DMR-0819762), Samsung (Firm) (Samsung Global MRAM Innovation program)

The motion of domain walls (DWs), driven by magnetic field and spanning almost eight orders of magnitude in velocity, has been studied in a submicron-wide strip of Co/Pt with perpendicular magnetic anisotropy. A scanning magneto-optic Kerr effect (MOKE) system is used to conduct time-resolved measurements of DW dynamics in both the thermally activated and viscous flow regimes. MOKE signal transients in the thermally activated regime reveal distributions of stochastic DW propagation events. Transients in the viscous flow regime show deterministic DW motion with velocities ∼20 m/s. The transition between the two dynamic regimes is observed as the relationship between the DW velocity and the driving magnetic field changes from exponential to linear., National Science Foundation (U.S.). Graduate Research Fellowship Program

Ta oxide (TaOx) is investigated as a resistive buffer layer for the growth of high-quality Co/Pt multilayers with perpendicular magnetic anisotropy (PMA). The Pt/(Co/Pt)3 films grown on TaOx buffer layers exhibit stronger PMA than those grown on Pt buffer layers, and are of comparable quality to films grown on metallic Ta. The optimized multilayers with TaOx buffer layers remain out-of-plane magnetized for Co layer thicknesses up to 10 Å without introducing a metallic current-shunting path, making these films attractive for spintronic devices using spin-polarized current., National Science Foundation (U.S.) (Graduate Research Fellowship Program)

The effect of perpendicular magnetic anisotropy (PMA) on current-induced domain wall (DW) motion is investigated by micromagnetic simulations. The critical current density J[subscript C] to drive DWs into periodic transformation and continuous motion by adiabatic spin transfer torque decreases with increasing PMA. Also, with optimized PMA that almost exactly compensates the demagnetizing field, the adiabatic displacement of DWs driven by currents less than J[subscript C] is strongly enhanced. Since PMA can be controlled easily in magnetic multilayer films, this technique of enhancing current-induced DW motion may be practical for device applications., National Science Foundation (U.S.). Graduate Research Fellowship Program

Magnetic domain walls in ferromagnetic tracks can be used to trap and transport superparamagnetic beads for lab-on-a-chip applications. Here it is shown that the magnetostatic binding between a domain wall and a superparamagnetic bead suspended in a host fluid leads to a distinct magneto-mechanical resonance under application of a sinusoidal driving field. The characteristic resonant frequency depends on the ratio of the magnetostatic binding force to the viscous drag on the bead. This resonance has been experimentally detected for a single trapped superparamagnetic bead using an optical detection technique., National Science Foundation (U.S.). Materials Research Science and Engineering Centers (Program) (award number DMR 0819762), Deshpande Center for Technological Innovation

The influence of gate voltage, temperature, and magnetic field on domain wall (DW) creep dynamics is investigated in Pt/Co/gadolinium oxide (GdOx) films with perpendicular magnetic anisotropy and imaged by a scanning magneto-optical Kerr effect technique. The DW creep velocity can be controlled by an electric field applied to the Co/GdOx interface via a linear modulation of the activation energy barrier with gate voltage. At low speeds, the DW velocity can be changed significantly by a gate voltage, but the effect is diminished as the DW velocity increases, which limits electric field control of fast DW motion., National Science Foundation (U.S.) (NSF-ECCS-1128439), National Science Foundation (U.S.) (Graduate Research Fellowship Program)

The influence of a gate voltage on domain wall (DW) propagation is investigated in ultrathin Pt/Co/gadolinium oxide (GdOx) films with perpendicular magnetic anisotropy. The DW propagation field can be enhanced or retarded by an electric field at the Co/GdOx interface and scales linearly with gate voltage up to moderate bias levels. Higher gate voltage levels, corresponding to electric fields >0.2 V/nm, produce a large irreversible change to the magnetic anisotropy that can enable nonvolatile switching of the coercivity., National Science Foundation (U.S.) (Fellowship), National Science Foundation (U.S.) (NSF-ECCS-1128439)

Current-driven domain wall (DW) motion is investigated in Pt/Co/GdOx nanostrips with perpendicular magnetic anisotropy. Measurements of the propagation field and the energy barrier for thermally activated DW motion reveal a large current-induced torque equivalent to an out-of-plane magnetic field of ∼60 Oe per 10[superscript 11] A/m[superscript 2]. This same field-to-current scaling is shown to hold in both the slow thermally activated and fast near-flow regimes of DW motion. The current-induced torque decreases with 4 Å of Pt decorating the Co/GdOx interface and vanishes entirely with Pt replacing GdOx, suggesting that the Co/GdOx interface contributes directly to highly efficient current-driven DW motion., National Science Foundation (U.S.) (NSF-ECCS 1128439), National Science Foundation (U.S.) (NSF Graduate Research Fellowship Program)

Micromagnetic modeling shows that the placement of non-magnetic conductive pads on a ferromagnetic wire affects the current-induced velocity of a domain wall (DW) in the wire and can act as a DW chirality filter. The pads shunt the current, causing a non-uniform spin current distribution inside the ferromagnetic wire and an Oersted field transverse to the wire. This suppresses Walker breakdown allowing higher current densities to be imposed before breakdown occurs. The transverse Oersted field pins the DW under some regimes of current density and pad geometry, selectively allowing transmission of DWs of only one chirality., Korea Research Foundation (No. NRF-2009-352-D00127)

Interfacial magnetic anisotropy in Ta/Co[subscript x]Fe[subscript 100-x] (CoFe)/MgO films for alloy compositions spanning pure Co to pure Fe has been studied in order to investigate the role of chemical composition in the onset of perpendicular magnetic anisotropy at the CoFe/MgO interface. Out-of-plane magnetization is not observed in Ta/Fe/MgO (x = 0) and Ta/Co/MgO (x = 100), for all ranges of CoFe thickness (t), but a t-dependent crossover between in-plane and out-of-plane anisotropy is found for x = 20, 50, and 80. Interestingly, effective magnetic anisotropy K[subscript u] as well as interfacial anisotropy Ki are maximized for Co[subscript 50]Fe[subscript 50] at a fixed t = 0.8 nm. The results suggest that the degree of filling of valence bands in the CoFe adjacent to the interface, which determines the relative population of the anisotropic d-bands, plays an important role in the interfacial anisotropy brought on by CoFe-O hybridization at the metal/oxide interface., National Science Foundation (U.S.)

We formulate a local gauge-invariant theory for the electromotive force induced by domain-wall dynamics in a ferromagnet. We demonstrate that this emf generation is a real-space topological pumping effect. The integral of the emf over one pumping period is a quantized topological invariant which does not depend on the details of the domain-wall configuration nor on its detailed dynamics. Based on our theory, the full instantaneous electric potential distribution can be mapped out by standard electrostatic methods. We also provide further details on our recent experiments which confirmed the emf induced by domain-wall dynamics., National Science Foundation (U.S.) (Grant No. DMR-0906025), National Science Foundation (U.S.) (Grant No. DMR-0903812), Robert A. Welch Foundation, United States. Dept. of Energy. Division of Materials Sciences and Engineering, United States. Dept. of Energy (Grant No. DEFG03-02ER45958)