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The spin orbit torque is one of the most promising effects for inducing magnetization dynamics and switching in a thin ferromagnetic (FM) layer and is at the base of several advancements in the field of spintronic memory devices [1,2]. The effect is caused by the spin current electrically generated by the spin Hall effect in a adjacent heavy metal (HM) layer. The description of the spin orbit torque effects on the magnetization of FM requires the introduction of two torque components in the magnetization dynamic equation: the field-like (FL) and the damping-like (DL), both proportional to intensity of the spin Hall effect [3]. By projecting all the vectors into the plane perpendicular to the magnetization, one finds the DL in the direction of the projected spin current and the FL in the perpendicular direction. The harmonic Hall method permits a detailed characterization of the two components [4] and reveals that the FL is much smaller than the DL and that they both have a non obvious dependence upon the thicknesses of the layers. &lt;br/&gt;&lt;br/&gt;In the literature, the two torque terms are derived by the introduction of the spin mixing conductance of the interface, whose real and imaginary parts give rise to the two torque terms [3]. However the spin mixing conductance has a difficult physical interpretation and justification. We propose here an alternative approach which is based on the definition of the spin current at the interface of a ferromagnet.&lt;br/&gt;&lt;br/&gt;To derive the torque terms we allow for the presence of a spin current at the interface of a FM and therefore we extend the boundary conditions of micromagnetism, therefore replacing the classical Brown&#39;s boundary conditions. The analysis reveals that by using the continuity of the spin current at the interface between the FM and the HM, one is able to derive two torque components. As a result the ratio between the DL and the FL is proportional to the damping constant of the FM and depends on thicknesses of the two layers. In the present paper we will present the derivation and the properties of the DL and FL torque terms and we will compare the outcome with experimental results from the literature [5].

2022 Joint MMM-INTERMAG

Spin currents at the interface and spin Hall torque

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

The spin orbit torque is one of the most promising effects for inducing magnetization dynamics and switching in a thin ferromagnetic (FM) layer and is at the base of several advancements in the field of spintronic memory devices [1,2]. The effect is caused by the spin current electrically generated by the spin Hall effect in a adjacent heavy metal (HM) layer. The description of the spin orbit torque effects on the magnetization of FM requires the introduction of two torque components in the magnetization dynamic equation: the field-like (FL) and the damping-like (DL), both proportional to intensity of the spin Hall effect [3]. By projecting all the vectors into the plane perpendicular to the magnetization, one finds the DL in the direction of the projected spin current and the FL in the perpendicular direction. The harmonic Hall method permits a detailed characterization of the two components [4] and reveals that the FL is much smaller than the DL and that they both have a non obvious dependence upon the thicknesses of the layers. In the literature, the two torque terms are derived by the introduction of the spin mixing conductance of the interface, whose real and imaginary parts give rise to the two torque terms [3]. However the spin mixing conductance has a difficult physical interpretation and justification. We propose here an alternative approach which is based on the definition of the spin current at the interface of a ferromagnet. To derive the torque terms we allow for the presence of a spin current at the interface of a FM and therefore we extend the boundary conditions of micromagnetism, therefore replacing the classical Brown's boundary conditions. The analysis reveals that by using the continuity of the spin current at the interface between the FM and the HM, one is able to derive two torque components. As a result the ratio between the DL and the FL is proportional to the damping constant of the FM and depends on thicknesses of the two layers. In the present paper we will present the derivation and the properties of the DL and FL torque terms and we will compare the outcome with experimental results from the literature [5].

poster

Room temperature magnetic skyrmions have the potential of enabling compact and energetically-efficient storage such as racetrack memories, albeit with two fundamental challenges: 1) Not being able to restrict their motion along straight paths, leading to skyrmions being lost at the device edge; one possible solution is the use of antiferromagnetically-coupled skyrmions [1]; and 2) Not having stable inter-skyrmion distances, leading to fluctuating distances among bits; a potential solution was revealed with the experimental observation of coexisting skyrmions and chiral bobbers [2], opening the possibility that a chain of binary data bits could be encoded by the two states. However, these observations were in B20-type crystalline materials and at low temperatures. In our previous work [3], we developed a ferro/ferri/ferromagnetic (FM/FI/FM) trilayer system that can host two distinct skyrmions at room temperature and can serve as a solution to the second challenge. The two phases represent a tubular skyrmion (running through the entire trilayer) and an incomplete skyrmion (existing in the FM layers only), as revealed from magnetic force microscopy (MFM) data and micromagnetic simulations. Such a two-skyrmion phase system exists for specific magnetic parameters of the individual sublayers. By exploring this parameter space, in this new study we reveal that the densities of the two skyrmions can be tuned via different routes: either by changing the magnetic properties of the FI or those of the FM. More specifically, we investigate the trilayer system when changing the thickness of the FM multilayers by using a combination of MFM, vibrating sample magnetometry and Brillouin light scattering experiments together with micromagnetic simulations. We show how the competition between different energies allows for the stabilization of either incomplete-only skyrmions, combination of both or mainly tubular skyrmions (Figure 1). Having a good understanding of the interplay between different magnetic properties can lead to better-tailored systems and possibly bring skyrmions a step closer to applications.

![](https://assets.underline.io/uploads/markdown_image/1/image/5ed95347749731b8a51d650ec9a59f11.jpg)

Fig. 1: Sample schematics and MFM images of three FM/FI/FM samples with varying Fe-layer thickness.

Tuning the Density of Incomplete and Tubular Skyrmions in Ferro/ferri/ferromagnetic Trilayers

The spin-momentum locking of surface states in topological quantum materials can produce a resistance that scales linearly with magnetic and electric fields and also depends on the current direction relative to the crystalline axes1,2. Such a bilinear magneto-electric resistance (BMER) effect offers a completely new approach for magnetic storage and magnetic field sensing applications. The effects demonstrated so far, however, are relatively weak or only for low temperatures1-3. In this presentation, we report a strong room-temperature BMER effect in topological Dirac semimetal α-Sn thin films4. The epitaxial α-Sn films were grown by magnetron sputtering on single-crystal silicon substrates at room temperature. They showed room-temperature BMER responses that are 106 times larger than previously reported at room temperature,2 and also larger than that previously reported at low temperatures.1,3 These results represent a major advance toward realistic BMER applications. Our experimental data also made possible the first characterization of the three-dimensional, Fermi-level spin texture of topological surface states in α-Sn thin films.

Large Magneto-Electric Resistance in the Topological Dirac Semimetal α-Sn

Magnetic two-dimensional (2D) van der Waals (vdWs) materials are receiving increased attention due to their exceptional properties and potential applications in spintronic devices. Because exchange bias and spin-orbit torque (SOT)-driven magnetization switching are basic ingredients for spintronic devices, it is of pivotal importance to demonstrate these effects in the 2D vdWs material-based magnetic heterostructures. In this work, we employ a vacuum exfoliation approach to fabricate Fe3GeTe2 (FGT)/Ir22Mn78 (IrMn) and FGT/Pt bilayers, which have high-quality interfaces. An out-of-plane exchange bias of up to 895 Oe is obtained in the former bilayer, which is larger than that of the previously studied bilayers. In the latter bilayer, the SOT switching of the perpendicularly magnetized FGT is realized, which exhibits higher SOT-driven switching performance compared to the previously studied FGT/Pt bilayer devices with interfacial oxidation. The minimum of SOT efficiency is further determined to be 0.18 ± 0.04, comparable to the previously reported values for Pt/Co and Pt/CoFeB bilayers. This work highlights the importance of the high-quality interface for the exchange bias and SOT effect and may pave the way for implementing 2D vdWs in spintronic devices.

![](https://assets.underline.io/uploads/markdown_image/1/image/acc94c8690514d4c33c542dacf41d203.jpg)

Magnetic properties and SOT-driven perpendicular magnetization switching in the FGT/Pt bilayer device. (a) Hall resistance as a function of the out-of-plane field at different temperatures. (b) Arrott plots of the Hall resistance for the FGT/Pt device. The extracted Tc is about 208 K. (c) RAHE as a function of in-plane (IP) and out-of-plane (OOP) magnetic field at 100 K. (d) Current-driven perpendicular magnetization switching for in-plane magnetic fields of +2000 Oe and −2000 Oe at 100 K with clockwise and anticlockwise switching polarity, respectively. The dashed lines mark the RAHE at saturated magnetization states.

Exchange bias and spin-orbit torque in the Fe3GeTe2-based heterostructures prepared by vacuum exfoliation approach

The spin to charge interconversion has been intensively studied in 5d materials such as platinum. In these non-magnetic systems, the relation between the charge current, the spin current and its polarization is strongly constrained by symmetries. Recently, a strong spin to charge interconversion efficiency has been obtained in 3d ferromagnets with strong spin orbit interactions such as NiCu. In ferromagnetic materials, the symmetry breaking induced by the presence of the magnetization lifts the geometrical constraints on the relation between charge and spin currents. However, the link between the ferromagnetic order and spin to charge interconversion remains unclear. By using spin pumping measurements, we injected a spin current from a CoFeB layer into the weak ferromagnets Ni60Cu40 and Ni50Cu50. The charge current generated by the spin to charge interconversion was subsequently measured across the Curie temperatures (Tc) of these alloys. A change of sign of the generated spin current was observed across the Tc when the CoFeB and NiCu layers are in direct contact. However, this sign change disappears when inserting a copper layer between the two. This indicates that two ferromagnetic materials can be coupled and influence each other at the Ferromagnetic Resonance (FMR), thus questioning the results of studies claiming the observation of spin fluctuation and spin-charge interconversion using FMR measurements. Most importantly, the fact that the generated charge current does not change across the Curie temperature of NiCu alloys indicates that the spin-charge interconversion does not depend on the magnetic phase [1]. The independence of the interconversion on the magnetic phase shows either that the band structure of NiCu is not affected, or that its change across the Tc does not influence the spin-charge interconversion. These results consequently provide an important contribution to both the experimental and theoretical understanding of the spin to charge interconversion in ferromagnetic materials.

Independence of the Inverse Spin Hall Effect with the Magnetic Phase in Thin NiCu Films

Magnonics is an emergent frontier of magnetism, which aims at using magnons as spin information carriers to avoid the Joule heating and electron scattering in current electron-based spintronics. In general, magnon currents can be excited both thermally and electrically in magnetic insulators, by applying charge currents in an adjacent metallic layer. Here, the magnon junctions (MJs) are studied in the Y3Fe5O12/CoO/Y3Fe5O12 heterostructure composed by ferrimagnetic insulator Y3Fe5O12(YIG) and antiferromagnetic insulator CoO. The temperature gradient driven magnon current transmission could be effectively controlled by the relative orientations of bottom and top YIG layers, i.e., high transmission for the parallel state and low transmission for the antiparallel state, demonstrating the spin transistor-like functions based on magnons. The electrical spin Hall injected magnon current could also be controlled by the MJs, contributing to a magnon junction effect in the magnetoresistance (MR) signals. This work demonstrates the building block of magnonic devices, which sheds light on the future applications of magnon-based memory, logic and computing, etc

![](https://assets.underline.io/uploads/markdown_image/1/image/0ee76393b0704c3d54a175b1865b38f3.jpg)

Magnon Junction Effect in Y3Fe5O12/CoO/Y3Fe5O12 Insulating Heterostructures

Spin-orbitronics exploits the interplay between charge and spin currents enabled by the spin-orbit coupling in non-magnetic systems. This spin-orbit coupling is indeed the phenomenon at the origin of spin-charge interconversions in bulk materials, via the spin Hall effect, and at surfaces presenting a broken inversion symmetry, via the Rashba-Edelstein effect. Recently, spin-to-charge conversion studies in Metal/SrTiO3-based two-dimensional (2D) electron gases have revealed a high conversion efficiency via the inverse Rashba-Edelstein effect [1]. The following demonstration of non-volatile electric-control of the spin-to-charge conversion further brings to light the great potential of these quantum materials for novels ultra-low power spintronics applications [2]. Achieving a metal barrier thickness study is thus desirable to gain insight on the different contributions to the charge-to-spin conversion in metal/SrTiO3-based 2D electron gases. Here, we report spin-orbit torques results obtained by spin-torque ferromagnetic resonance (ST-FMR) in Metal/SrTiO3-based 2D electron gases, for different metal barrier thicknesses. A demonstration of charge-to-spin conversion at the metal/oxide interface is firstly achieved by ST-FMR on both Ta and Mg barrier-based heterostructures. The spin-orbit torques are further investigated for different temperatures, revealing temperature-dependent symmetric and antisymmetric ST-FMR signals. We further achieve the non-volatile electric-control of the sheet resistance of the 2D electron gas in ST-FMR devices, which makes it possible to investigate the gate dependence of the charge-to-spin conversion via ST-FMR techniques. Finally, the dependence of the charge-to-spin conversion with the metallic barrier thickness is discussed, providing routes to improve the spin-orbit torques, and opening the way to optimized spintronics devices based on Metal/SrTiO3 2D electron gases.

![](https://assets.underline.io/uploads/markdown_image/1/image/c24dfd85212876a78c60e1c793e05850.jpg)

Fig.1: ST-FMR signals in Mg/SrTiO3 heterostructure at 77K

Spin-Orbit Torques Dependence on the Metal Barrier Thickness in Metal/SrTiO3-based Two-Dimensional Electron Gases Studied by Spin-Torque Ferromagnetic Resonance

The dynamics of magnetization generates a spin current, which is referred to as spin pumping [1]. The spin pumping has been intensively studied because it can be utilized in quantifying spin related parameters, such as spin Hall angle, spin diffusion length and spin mixing conductance [2, 3]. In ferromagnet (FM) / heavy metal (HM) layers, which has been a central focus of research during last decade [2-4], the magnetization dynamics of FM generates a spin current in the HM layer, and the spin current is converted into the tangible charge current via inverse spin Hall effect (ISHE) [2-4]. However, the spin pumping efficiency is still low to be used directly for spintronic applications. Here we demonstrate a giant spin pumping induced by a phase transition of FeRh. FeRh is metallic alloy with CsCl structure which undergoes a phase transition from antiferromagnetic to ferromagnetic phase near 370 K [5]. We measured the transient ISHE voltage in FeRh/Pt bi-layer and found that the spin pumping signal appears during the phase transition of FeRh. Notably, the observed spin pumping signal is at least 2 orders of magnitude larger than those of previous reports [6, 7], suggesting that the spin pumping can be utilized in spintronic applications, e.g., magnetization switching [8]. The large transient spin pumping signal is ascribed to the total angular momentum change between antiferromagnet and ferromagnet during the phase transition, which accompanies the sign change of the exchange interaction. Our work provides a novel method to generate a large spin current, which could be utilized in spintronics application.

Direct Detection of Transient Spin Pumping during Phase Transition of FeRh

Magnetite (Fe3O4) is a unique half-metallic magnetic material for longitudinal spin Seebeck effect (LSSE) investigations because of its characteristic Verwey transition (TV ≈ 125 K). Since Fe3O4 is metallic above TV, the measured LSSE signal is contaminated by the anomalous Nernst effect (ANE) arising from the Fe3O4 layer. Earlier study on the LSSE in Fe3O4/Pt [1] did not disentangle the LSSE and ANE signals as a function of temperature above and below TV. To address this, we have performed a comprehensive study of the temperature dependence of ANE and LSSE in Fe3O4 thin films (80 nm) grown on Si and Al2O3 substrates. We find that while both effects are present in Fe3O4/Pt at T &gt; TV, the ANE signal is much smaller compared to the intrinsic LSSE signal. Below TV, the total signal across Fe3O4/Pt is completely dominated by the LSSE. Through a comprehensive analysis of temperature dependent LSSE and ANE, we decouple their contributions that allow us, for the first time, to observe an anomalous temperature dependence of the intrinsic LSSE signal in Fe3O4/Pt around TV. A comparative study of the intrinsic LSSE in Si/Fe3O4/Pt and Al2O3/Fe3O4/Pt points to the important role of the ordering and density of spins on the Fe3O4 surface on the spin transport and spin-charge conversion efficiency [2,3]. The LSSE voltage measured at 300 K in Si/Fe3O4/Pt is about two times greater than that of Al2O3/Fe3O4/Pt. This finding is fully supported by the magnetic force microscopy study that reveals the higher density of magnetic domains on the surface of the Fe3O4 film grown on Si compared to the Fe3O4 film grown on Al2O3. Our study not only provides deeper insights into the LSSE and its temperature evolution in magnetic oxides like Fe3O4 but also an effective way for improving the spin-charge conversion efficiency in magnetic films through surface magnetism engineering.

Decoupling anomalous Nernst and longitudinal spin Seebeck effects in Fe3O4/Pt thin films around the Verwey transition

Spin-orbit torques (SOTs) provide an electrical way to manipulate the magnetization of magnetic films, which is promising for their application in magnetic random-access memory (MRAM) with high speed and long endurance [1,2]. SOT is usually observed in magnetic-heavy-metal bilayers and casued by the spin Hall effect (SHE) in the heavy metal and as-induced spin current. Restricted by the symmetry of the SHE, the spin current is normally polarized in plane, which can only determinstically switch a magnetic film with in-plane magnetic anisotropy (IMA). To switch a magnetic film with perpendicular magnetic anisotropy (PMA), which is desired for high-density memory applications, an in-plane symmetry-breaking field is indispensable. The field can be provided directly by a sourcing current via the Ostered mechanism or from the exchange-bias or coupling effects [3]. Here, we demonstrate through both theory and experiments that an effective perpendicular field scaling with SOT can inherently result from a magnetic trilayer, which consists of a magnetic film with PMA, another magnetic film with IMA, and a spacer in between to mediate their coupling. More importantly, when the two magnetic films experience two SOTs with the same (opposite) polarity, the effective perpendicular field can favor (hamper) SOT switching of the perpendicular film. This special magentic trilayer can guide the design of efficient and versatile SOT MRAM devices. In our work, a macrospin model is employed to explain the generation of effective perpendicular field. And after a seris of experiments of SOT switching under different in-plane fields, the efficiency to produce the perpendicular field reaches 2.1 Oe/1010 Am-2[4].

![](https://assets.underline.io/uploads/markdown_image/1/image/130bf5ae1259f90b28ef46b38ebb0c93.jpg)

Fig.1. Physics scenario to create Hz1eff and predicted dependence of Mz of the perpendicular layer on applied torque.

![](https://assets.underline.io/uploads/markdown_image/1/image/75788d4c598295b4d3750d6ee5817573.jpg)

Fig. 2. Direct measurement of Hz1eff and dependence of SOT efficiency χ on applied field Hy.

Efficient Spin-Orbit-Torque Switching Assisted by an Effective Perpendicular Field in a Magnetic Trilayer

GdFeCo, a rare-earth/transition-metal composition, is a competitive candidate for practical applications on GMR devices [1,2], magneto-optical recording medium [3,4], and ultrafast magnetic switching [5,6]. Particularly, the ability to control magnetic coercivity (Hc) is one of the most important parameters for the advantage in magnetic data storage technologies. It is well known that the coercivity of the GdFeCo compound can be tuned by varying content of Gd or FeCo component [7]. Although these methods can effectively alter the magnetic properties of a sample, the changes are permanent, thus, one may expect a further increase in the flexible ability to manipulate Hc will be explored. Here, we reveal that the coercive field of GdFeCo adjacent to heavy metal Hf can be effectively modulated by electric current. The stack structure of Gd28.5(Fe80Co20)71.5 (7nm)/Hf(4nm)/MgO(4nm), as illustrated in Fig.1(a), is prepared by means of a RF magnetron co-sputtering, and then characterized by the X-Ray Fluorescence (XRF) spectroscopy technique and the Alternating Gradient Magnetometer (AGM). A 5 μm-width and 100 μm-length Hall bar is fabricated using standard photolithography, E-beam lithography, and Ar ion-beam etching technique. We perform a measurement by injecting a DC current along the Hall channel in the presence of an external magnetic field which is swept perpendicularly to the sample plane, as illustrated in Fig.1(b). Interestingly, we observe that in the early stage of measurement, the Hc reduces drastically while at a higher current level coercivity is able to recover back to its initial value, as shown in Fig. 2. Such dependence of Hc on electric current can be explained by the competing interplay of the spin-orbit torque (SOT) that arises from heavy metal layer Hf and the Joule heating effects. This finding is a supplement for researchers and engineers who are working on spintronics materials

![](https://assets.underline.io/uploads/markdown_image/1/image/08b9c854f08b49452e0f1b365d6455ba.jpg)

(a) Schematic illustrations of stacked structure for thin films; (b) Optical microscopy image of the Hall bar device and the schematic of the experimental setup for the magneto-transport measurement.


![](https://assets.underline.io/uploads/markdown_image/1/image/693fba0be8e46cdfc523beab4832c892.jpg)

Hc variation as a function of input DC obtained from the anomalous hall effect (AHE) measurements.

Spin currents at the interface and spin Hall torque

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