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Antiferromagnetic (AF) spintronics received an enormous impulse after the first demonstrations of electrical switching of the AF order [1]. However, a lot of these observations can equally well be explained by non-magnetic, parasitic effects caused by the same electrical current pulses that are intended to manipulate the magnetic state of the AF [2].&lt;br/&gt;While it is possible to distinguish between magnetic and non-magnetic effects using imaging techniques that can resolve the AF order [3], these techniques are usually very complex. Moreover, since they require access to the AF layer, they are not suitable for systems where the AF is buried beneath other layers. Our approach is to distinguish between the magnetic and non-magnetic effects by suppressing the magnetic effects using high magnetic fields.&lt;br/&gt;In this contribution, we study the high magnetic field behavior of the electrical switching of thin-film AFs NiO and CoO, using the devices shown in Fig. 1. We perform switching experiments in magnetic fields up to 16 Tesla (Fig. 2). The measurements show that these high magnetic fields indeed suppress the current-induced switching of the AF order, whereas the thermal effects remain unaffected. Hence, this technique allows to irrefutably separate the magnetic and non-magnetic effects. These results are corroborated by a model accounting for the multi-domain character of the AF.&lt;br/&gt;Finally, the experiments with CoO yield an unexpected dependence of the magnetic configuration on the direction of the high magnetic fields. This indicates an unexpectedly complex magnetic anisotropy in CoO that depends on the magnetic field strength and orientation, most likely due to unquenched orbital momentum.&lt;br/&gt;These results both demonstrate that combining electrical methods with strong magnetic fields can be a valuable tool for AF spintronics, and give invaluable insight into the interplay of spin-Hall magnetoresistance and thermal effects as well as the domain structure and complex anisotropy of thin-film antiferromagnets.

![](https://assets.underline.io/uploads/markdown_image/1/image/1fb212d0af0688a1f81826c7b8bf2f9a.jpg)

Fig. 1: Micrograph of the device used for the experiments.

![](https://assets.underline.io/uploads/markdown_image/1/image/e89ac11416c899724e28149f7ee39cf4.jpg)

Fig. 2: Switching amplitude as a function of magnetic field. The lines are calculated with the model; the pie charts represent the modeled domain distribution.


2022 Joint MMM-INTERMAG

Suppressing Electrical Switching of Antiferromagnets with High Magnetic Fields

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.

The 2022 Joint Conference will offer both in-person and prerecorded on-demand content.

For tickets to the event, please register at the following link: https://magnetism.org/register

Please register for the Joint MMM-Intermag conference to join the event.

This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

Antiferromagnetic (AF) spintronics received an enormous impulse after the first demonstrations of electrical switching of the AF order [1]. However, a lot of these observations can equally well be explained by non-magnetic, parasitic effects caused by the same electrical current pulses that are intended to manipulate the magnetic state of the AF [2]. While it is possible to distinguish between magnetic and non-magnetic effects using imaging techniques that can resolve the AF order [3], these techniques are usually very complex. Moreover, since they require access to the AF layer, they are not suitable for systems where the AF is buried beneath other layers. Our approach is to distinguish between the magnetic and non-magnetic effects by suppressing the magnetic effects using high magnetic fields. In this contribution, we study the high magnetic field behavior of the electrical switching of thin-film AFs NiO and CoO, using the devices shown in Fig. 1. We perform switching experiments in magnetic fields up to 16 Tesla (Fig. 2). The measurements show that these high magnetic fields indeed suppress the current-induced switching of the AF order, whereas the thermal effects remain unaffected. Hence, this technique allows to irrefutably separate the magnetic and non-magnetic effects. These results are corroborated by a model accounting for the multi-domain character of the AF. Finally, the experiments with CoO yield an unexpected dependence of the magnetic configuration on the direction of the high magnetic fields. This indicates an unexpectedly complex magnetic anisotropy in CoO that depends on the magnetic field strength and orientation, most likely due to unquenched orbital momentum. These results both demonstrate that combining electrical methods with strong magnetic fields can be a valuable tool for AF spintronics, and give invaluable insight into the interplay of spin-Hall magnetoresistance and thermal effects as well as the domain structure and complex anisotropy of thin-film antiferromagnets.

![](https://assets.underline.io/uploads/markdown_image/1/image/1fb212d0af0688a1f81826c7b8bf2f9a.jpg)

Fig. 1: Micrograph of the device used for the experiments.

![](https://assets.underline.io/uploads/markdown_image/1/image/e89ac11416c899724e28149f7ee39cf4.jpg)

Fig. 2: Switching amplitude as a function of magnetic field. The lines are calculated with the model; the pie charts represent the modeled domain distribution.

technical paper

The application of gate voltages in ferromagnet/Oxide/Heavy metal thin film multilayer has been identified as one possible candidate to manipulate their anisotropy at will [3], [1], [4]. Unfortunately, this method has proven to be unreliable in terms of the reversibility: e.g, the application of a gate voltage onMgO/CoFeB/Ta [3] causes an irreversible change of the magnetic anisotropy axis from in plane to out-of-plane, while HfO2/CoFeB/Ta stacks display a more complicated behavior, with different regimes characterized by different reversibility behaviors [2]. The microscopic origin of these phenomena remains unclear and is the object of our inquiry. In this work we performed ab-initio simulations on 6 setups comprising Fe/O, HfO2/Fe, MgO/Fe interfaces each one with frontal and interstitial oxygen atomic configurations (fig.1). The pure Fe/O interface prefers interstitial oxygen configurations while the addition of oxides seems to switch this trend around. In particular, HfO2/Fe displays a strong preference for the frontal oxygen arrangement, leading us to identify a possible hypothesis for the phenomenon of the multiple magneto-ionic regimes displayed. In it’s as grown form, HfO2/CoFeB is characterized by an underoxidized ferromagnet interface [2]. The application of a gate voltage on HfO2/CoFeB pushes some of the oxygen species in proximity of the interface where they occupy the stable frontal site. Further application of a gate voltage pushes other oxygen atoms toward the still free and more unstable interstitial sites. The occupation of these interstitial sites has the effect of destroying perpendicular magnetic anisotropy as seen both in experiments and simulations [5] [1]. Once these more mobile interstitial sites are occupied, magnetic anisotropy can be switched reversibly by inverting the gate voltage and adjusting the interstitial site occupation (fig.2)

![](https://assets.underline.io/uploads/markdown_image/1/image/40c593503d5a4f3ee9c27db4ad2dc04d.jpg)

Comparison of the different interfacial configurations in the differentsamples. The bar plots represent the ground state energies and highlight themore stable configuration

![](https://assets.underline.io/uploads/markdown_image/1/image/f5dc5807d0f4552079d7a39375420a9e.jpg)

Hypothesis for the mechanism governing magneto-ionic regimes inHfO2/FM stacks. The text highlights the magnetic properties of the interface under different oxidation conditions.

Reversible anisotropy manipulation via gate voltages in ferromagnet/oxide multilayers

Magnetoionics (MI) is a much-in-demand feature for spintronics devices due to its great potential for improving energy efficiency in memory devices. The main feature of MI is to allow for the nonvolatile modulation of magnetic properties [1–5], making MI reversibility a fundamental quality for high device performance. Various studies have addressed issues impacting reversibility such as the presence of different types of ions, oxides and the degree of oxidation at the oxide/ferromagnetic interface [3, 5–8], while the influence of annealing temperature on reversibility has been largely overlooked. Annealing is commonly used to induce crystallization in CoFeB layers leading to the enhancement of perpendicular magnetic anisotropy (PMA), interfacial Dzyaloshinskii-Moriya interaction (iDMI), and tunnel magnetoresistance [9–11], therefore its impact on MI is of great interest. In this study, we show that W/CoFeB/HfO2 thin films annealed at 350°C and 390°C show a significant but irreversible dependence of PMA and DMI on gate voltage. However, an annealing program using a slow ramp that minimizes the exposure to the highest temperatures allows to induce PMA and iDMI while also showing a MI reversibility of 71% in remanence with respect to PMA. This dependence of MI reversibility on annealing profiles and temperatures could be related to the different degrees of crystallinity obtained under different annealing conditions. Such structural differences, such as size and distribution of crystallites, can greatly impact the ion mobility inside the stack and be responsible for observed modulation of the MI reversibility. Our results therefore show that annealing parameters need to be optimized to obtain enhanced magnetic properties without compromising MI performance.

![](https://assets.underline.io/uploads/markdown_image/1/image/54d50bab8c546ddbc8fd33ecfea28690.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/bf6e6dbd3a0f9277642eaa6aab5dd034.jpg)

Effect of Annealing on Magnetoionics in W/CoFeB/HfO2

Effect of Annealing on Magnetoionics in W/CoFeB/HfO2

The Ising machine is an unconventional computing architecture that can be used to solve NP-hard combinatorial optimization problems more efficiently than traditional von Neumann architectures. GHz spin Hall nano-oscillators (SHNOs) are a particularly attractive technology for building fast, energy-efficient, and scalable Ising machines; however, electrical coupling mechanisms which allow for full programmability among different oscillator nodes have not yet been fully demonstrated in such a network. Here, we develop a general analytical framework that can describe injection locking of SHNOs with arbitrary oscillation orbits at both the fundamental frequency and harmonics. With this compact analytical framework, we integrate the SHNO into a Verilog-A device model that can emulate the oscillator’s injection locking behavior in circuit simulations, where the dynamics of coupled oscillator networks are simulated together with conventional electronic components (Fig. 1). While our abstract circuit simulations achieve similar accuracy as full micromagnetic simulations, the device model we developed leads to more than 100 times improvement in simulation efficiency and allows us to evaluate the performance using realistic circuits. Using circuit-level simulations, we further study the effects of phase noise and scalability in networks of up to hundreds of coupled oscillators to show that the SHNO-based Ising machine can be operated robustly at room temperature. Compared with existing technologies, SHNO networks exhibit orders of magnitude improvement in time, space, and energy efficiency (Table 1). Our results provide analytical tools and design insights that will be useful for the realization of a CMOS-integrated SHNO Ising machine.

![](https://assets.underline.io/uploads/markdown_image/1/image/a0dab57c9a06319f78760697037422fd.jpg)

Fig. 1: (a) Electrical coupling circuit linking two SHNOs in the oscillator-based Ising machine. (b) Phases of oscillators in a 4-node coupled network solving the Ising model in circuit simulations (HSPICE) using our abstract device model and in micromagnetic simulations (MuMax3).

![](https://assets.underline.io/uploads/markdown_image/1/image/56041ec137cf8fc9052b69c276e29915.jpg)

Table 1: Comparison of speed, energy, and space metrics between the SHNO Ising machine and existing technologies. Values are standardized to a 100-node network.

Using Machine Based on Electrically Coupled Spin Hall Nano-Oscillators

In order to go beyond the traditional CMOS logic technology, novel spin-based logic architectures are being developed to provide nonvolatile data retention, near-zero leakage, and scalability. In particular, architectures based on magnetic domain walls take the advantage of the fast motion, high density, non-volatility and flexible design of domain walls to process and store information in three dimensions [1,2]. Such logic schemes have so far relied on domain wall manipulation and clocking using an external magnetic field, which hinders their industrial implementation. Here we demonstrate a method for performing all-electric logic operations and cascading using domain wall racetracks [3]. Our concept is based on the recently developed chiral coupling mechanism between adjacent magnets where the magnetic anisotropy competes with the interfacial Dzyaloshinskii–Moriya interaction (DMI) in Pt/Co/AlOx trilayers [4,5]. When a narrow in-plane (IP) magnetized region is incorporated into an out-of-plane (OOP) magnetized track, it couples to its surrounding, leading to the antiferromagnetic alignment of the OOP magnetization on the left and right of the IP region. This is enforced by interfacial DMI favouring a fixed magnetization winding direction, which is left-handed in our Pt/Co/AlOx trilayers. When a current-driven domain wall propagating in the track encounters such a region, the magnetization of the IP regions flips, leading to the annihilation of the incoming domain wall and the nucleation of a new domain wall of opposite polarity on the other side of the IP region (Fig. 1a). The chiral OOP-IP-OOP structure therefore serves as a domain wall inverter, the essential building block for all implementations of Boolean logic. Based on this principle, we fabricated reconfigurable NAND and NOR logic gates, making our concept for current-driven DW logic functionally complete. We also cascaded several NAND gates to build XOR and full adder gates, demonstrating electrical control of magnetic data and device interconnection in logic circuits (Fig. 1b). The functionality of logic circuits can be also expanded by the realization of a domain wall diode based on a geometrically tailored inverter [7]. We also broadened the application of chiral coupling towards dynamic computation with oscillators [8]. By imprinting the magnetic configuration of an IP magnetized disk in an OOP magnetized slab containing sizeable DMI, a chiral polar vortex texture can be established as a ground state in the patterned region (Fig. 2a). By means of micromagnetic calculations, we show that such an oscillator can be driven and manipulated by an injected spin current. We investigated the mutual synchronization of such oscillators via spin wave and dipolar interactions (Fig. 2b) and demonstrated their potential for neuromorphic computing with a neural network of six oscillators.

![](https://assets.underline.io/uploads/markdown_image/1/image/28a28fb12e8a66f07e883d8cc0fb0ebe.jpg)

Fig. 1. Current-driven DW logic. (a) Schematic of current-driven DW inversion, occurring as the DW moves across the in-plane region. After selective oxidization, the magnetizations of neighboring OOP and IP regions align with a left-handed chirality in Pt/Co/AlOx. Here a down│up DW is inverted to an up│down DW. (b) Left panel: Schematic of a full adder gate obtained by cascading several NAND gates. Right panel: Full adder gate with “a=0” and “b=1” inputs resulting in “Sum=1” with a “Carry = 0”.

![](https://assets.underline.io/uploads/markdown_image/1/image/b552ddf811e6fdfc165e88837fcab20a.jpg)

Fig. 2. Computation with chiral oscillators. (a) Equilibrium magnetic texture in the DMI-based nano-oscillator with 100 nm diameter. The oscillator has two equivalent states, depending on the magnetization direction in the OOP region. Magnetization along the +z and –z direction is indicated in white and black, while the IP magnetization direction is given by the color wheel. (b) Synchronization pattern of two oscillators separated by 60 nm distance. The current density in the left oscillator is fixed (j1=0.8×109 A/m2), while the current density of the oscillator on the right (j2) is swept.

Computation with Domain Walls and Oscillators in Chirally Coupled Systems

Modern magnetic-memory technology requires all-electric control of perpendicular magnetization with low energy consumption. While spin-orbit torque (SOT) in heavy metal/ferromagnet (HM/FM) heterostructures holds promise for applications in magnetic random access memory, till today, it is limited to the in-plane direction. Such in-plane torque can switch perpendicular magnetization only deterministically with the help of additional symmetry breaking, e.g., through the application of an external magnetic field, an interlayer coupling or an asymmetric design. Instead, an out-of-plane spin-orbit torque could directly switch perpendicular magnetization. In current presentation, we report that we observe an out-of-plane spin-orbit torque in an HM/FM bilayer of L11-ordered CuPt/CoPt and demonstrate field-free switching of the perpendicular magnetization of the CoPt layer.1 The low symmetry point group (3m1) at the CuPt/CoPt interface gives rise to this spin torque, herein after referred as 3m torque, which strongly depends on the relative orientation of current flow and crystal symmetry. We observe a 3-fold angular dependence in both the field-free switching and the current-induced out-of-plane effective field as shown in Figure 1. Because of the intrinsic nature of the 3m torque, the field-free switching in CuPt/CoPt shows good endurance in cycling experiments. Experiments with the wide variety of SOT bilayers with low-symmetry point groups at the interface may uncover further unconventional spin-torques in future.

![](https://assets.underline.io/uploads/markdown_image/1/image/e032f3aa438f0424fd4d0cd491e3db92.jpg)

Figure 1| Symmetry-dependent magnetic field-free magnetization switching. a, Schematic of the CuPt/CoPt Hall bar for electrical transport measurement. The red arrow represents the magnetization (M). The grey arrow represents the current (I) flowing. b, The definition of current flowing direction (θI). The current is applied along the Hall bar, which has an azimuth angle of θI with respect to the [1-10] direction. c, Anomalous Hall effect of the bilayer for θI = 0°. d, Current angle dependence of the SOT induced magnetization switching. The solid line is a cosine fit to the data. e, Current-induced magnetization switching with different θI.

Symmetry Dependent Field-free Switching of Perpendicular Magnetization

A magnetic tunnel junction (MTJ) is one of the most important device structures in spintronic applications. However, significant improvement in the tunnel magnetoresistance (TMR) ratio at room temperature (RT) is necessary to establish novel spintronic applications. Even in a simple Fe/MgO/Fe(001) MTJ, the experimental TMR ratios (180-220% at RT [1]) are much smaller than the theoretical values &gt;1,000% [2, 3]. In addition, the origin of TMR oscillation with the barrier thickness in experiments is still an open question [1]. In this study, we revisited Fe/MgO/Fe(001) based structures to bridge the discrepancies between experiments and theories. We deposited Fe/MgO/Fe(001) MTJs on a Cr-buffered MgO(001) single crystal substrate. By combining sputtering and electron-beam evaporation, we improved the barrier interface crystallinity [4]. We further examined an MgAl2O4 (MAO) based barrier to reduce the lattice mismatch with Fe. An MAO composition of Mg:Al = 4:1 (Mg rich) was selected. Fig. 1 shows TMR ratios of Fe/MgO/Fe and Fe/MAO/Fe MTJs as a function of the barrier thickness at RT. The maximum TMR ratio of Fe/MgO/Fe is 417% at RT (917% at 5 K) [4], which is ~twice (~3 times) of the previous report [1]. The TMR ratio shows significant oscillatory behavior with the MgO thickness. The peak-to-peak of 80% is also much larger (~7 times) than the previous report [1]. A TMR ratio of 496% at RT was observed by CoFe insertion at the bottom Fe/MgO interface [4]. The use of an MAO barrier improved the TMR ratio and oscillation peak-to-peak of Fe/MgO/Fe; the maximum ratio (peak-to-peak) reaches 429% (120%) in Fe/MAO/Fe at RT, which may be due to reduced defects at barrier interfaces. This demonstration will be an important step to achieve much larger TMR ratios for widening the range of spintronic applications. This study was partly supported by the ImPACT Program of the Council for Science, Technology and innovation (Cabinet Office, Government of Japan), JSPS KAKENHI 16H06332, 21H01750, 21H01397, and project JPNP16007, commissioned by the New Energy and Industrial Technology Development Organization (NEDO).

![](https://assets.underline.io/uploads/markdown_image/1/image/6f165c2448768fb7457ce2e234352b60.jpg)

Fig.1 TMR ratio as a function of barrier thickness of Fe/MgO/Fe and Fe/MgAlO/Fe at RT.

Giant tunnel magnetoresistance ratio and oscillation in Fe/MgO/Fe(001) and Fe/MgAlO/Fe(001) magnetic tunnel junctions

In a recent work [1], we investigated the spin transfer toque (STT) in epitaxial magnetic tunnel junctions (MTJs) based on ferrimagnetic tetragonal Mn3Ga [2] electrodes and MgO barrier (Fig.1a,b) from first principles ballistic non-collinear spin transport (NEGF + SDFT[LSDA]), using the Smeagol code [3]. We found a long-range spatial oscillation of the in-plane STT (defined as in Ref. [4]) decaying on a length scale of a few nm. We discussed how this STT oscillation can be anticipated from the bulk electronic structure of Mn3Ga and the spin-filtering properties of the MgO barrier, and it is robust against variations in the stack geometry. This is expected to result in a net in-plane torque which oscillates as a function of the Mn3Ga thickness, but stabilizes for sufficiently thick layers (&gt;40 MLs) at larger values than the net STT in conventional Fe/MgO/Fe MTJs [1]. We also discussed a novel all-ferrimagnetic MTJ in which the Fe electrode is substituted with Mn3Ga and found similar STT properties, particularly enhanced in the case of narrow MgO barrier (of 3 MLs), due to resonant interface states. Here we focus on the TMR effect in these MTJ stacks as a function of the applied bias voltage and find a maximum value of over 300%, asymmetry and multiple sign changes in the range ± 2V (Fig.1 c) for the Fe-based junction, in a noteworthy correspondence with experimental observations for similar ferrimagnetic junctions [5]. In the case of the fully symmetric novel ferrimagnetic MTJ, we find a symmetric TMR, peaking at 0 V. This is particularly enhanced for the thin barrier (3 ML) case due to the aforementioned interface resonances. We will discuss effects of geometry optimisation and possible Hubbard U corrections to the LSDA xc-functional on the transport properties, at computed bulk parameters of Mn3Ga closer to the experimental lattice constant and magnetic moments, as well as the role of different interface terminations. In view of the stronger TMR at finite bias for the Fe-based MTJs, our calculations suggest that further efforts are justified on the Fermi-level and interface engineering of ferrimagnetic electrodes, by means of both composition and substrate-induced strain, for demanding spintronic applications.

![](https://assets.underline.io/uploads/markdown_image/1/image/68696b51c4439eecb133e13652ee671a.jpg)

High bias TMR in ferrimagnetic MTJs based on Mn3Ga

Emerging phenomena, such as the spin-Hall effect (SHE), spin pumping, and spin-transfer torque (STT), allow for interconversion between charge and spin currents and the generation of magnetization dynamics that could potentially lead to faster, denser, and more energy efficient, non-volatile memory and logic devices. Present STT-based devices rely on ferromagnetic materials as their active constituents. However, the flexibility offered by the intrinsic net magnetization and anisotropy for detecting and manipulating the magnetic state of ferromagnets also translates into limitations in terms of density (neighboring elements can couple through stray fields), speed (frequencies are limited to the GHz range), and frequency tunability (external magnetic fields needed). A new direction in the field of spintronics is to employ antiferromagnetic materials. In contrast to ferromagnets, where magnetic anisotropy dominates spin dynamics, in antiferromagnets spin dynamics are governed by the interatomic exchange interaction energies, which are orders of magnitude larger than the magnetic anisotropy energy, leading to the potential for ultrafast information processing and communication in the THz frequency range, with broadband frequency tunability without the need of external magnetic fields. I will present the first evidence of sub-terahertz coherent spin pumping at the interface of a uniaxial insulating antiferromagnet MnF2 and a platinum thin film, measured by the ISHE voltage signal arising from spin-charge conversion in the platinum layer. The ISHE signal depends on the chirality of the dynamical modes of the antiferromagnet, which is selectively excited and modulated by the handedness of the circularly polarized sub-THz irradiation. Contrary to the case of ferromagnets, antiferromagnetic spin pumping exhibits a sign dependence on the chirality of dynamical modes, allowing for the unambiguous distinction between coherent spin pumping and the thermally-driven spin Seebeck effect. Our results open the door to the controlled generation of coherent pure spin currents with antiferromagnets at unprecedented high frequencies.

Coherent Sub-Terahertz Spin Pumping from an Insulating Antiferromagnet

The spin current with out-of-plane spin polarization (sigma-z) is favorable for the efficient switching of perpendicular magnetized devices, which is required for high-density memories [1,2]. Recently we observed sigma-z both in non-collinear antiferromagnets Mn3Pt [3] and Mn3SnN [4], as well as in collinear antiferromagnets Mn2Au [5,6] and RuO2 [7] thin films. Strong out-of-plane polarized spin current is generated when the charge current is applied along the magnetic mirror plane of non-collinear antiferromagnet, but tiny when perpendicular. With the aid of strong sigma-z, current induced spin-orbit torque (SOT) switching of adjacent perpendicular ferromagnet is realized without external magnetic field. In Mn2Au films, sigma-z is generated at two spin sublattices with broken spatial symmetry, and the antiparallel antiferromagnetic moments play an important role. The out-of-plane polarized spin current can be controlled by the current- and electric field-induced Néel vector switching. Thus this Néel vector-dependent spin Hal effect is termed as “antiferromagnetic spin Hall effect”, which adds another twist to the atomic-level control of spin currents via the antiferromagnetic spin tructure. RuO2 is a tetragonal itinerant collinear antiferromagnet with nonmagnetic atoms at noncentrosymmetric positions [8]. This particular crystal structure produces anisotropic band structure，enabling RuO2 a efficient spin source due to the spin splitting effect. Spin current generated by spin splitting effect do not meet conventional “cross product relationship”. The spin current flow direction is related to the crystal structure，while the spin polarization direction is related to the Néel vector. Spin splitting effect has more efficient spin-charge convention and more controllable spin polarization. The role of sigma-z for the field-free SOT switching is theoretically analyzed, and different roles of sigma-z and conventional in-plane spin polarization (sigma-y) are presented with different external magnetic field. Our findings would help to use out-of-plane polarization for efficient SOT-MRAM to combine the advantage of SOT and spin-transfer torque.

![](https://assets.underline.io/uploads/markdown_image/1/image/2cd5af1ecc73195bd6fc92b4627ec76c.jpg)

Fig. 1. Schematic of out-of-plane polarized spin current and field-free spin-orbit torque switching.

Out-of-plane spin polarization and antiferromagnetic spin Hall effect

The interplay between electronic transport and the antiferromagnetic order has attracted a surge of interest. Recent studies have shown that a moderate change in the spin orientation of a collinear antiferromagnet may significantly affect the electronic band structure and subsequently manifest itself in transport properties [1]. Among numerous electrical probes to read out such magnetic order, unidirectional magnetoresistance (UMR), where the resistance changes under the reversal of the current direction, can provide rich insights into the transport properties of spin-orbit coupled systems. However, UMR has never been observed in antiferromagnets before, given the absence of intrinsic spin-dependent scattering. Here, we report that a sizable UMR can emerge in an antiferromagnetic system, specifically in a collinear-antiferromagnet/heavy-metal bilayer. The observed UMR in the antiferromagnetic phase of a FeRh/Pt bilayer evolves nonlinearly with increasing magnetic field, persists to large values at high magnetic field and, most notably, exhibits a sign change at a critical field, which is in stark contrast with the UMRs observed in ferromagnetic and non-magnetic systems [2-3]. We attribute this UMR to the strong effective magnetic field due to spin canting in FeRh. Our results can motivate the growing fields of non-centrosymmetric and topological systems, and suggest a route to the development of tunable antiferromagnet-based spintronics devices. This research was primarily supported by the NSF through the University of Illinois at Urbana-Champaign Materials Research Science and Engineering Center DMR-1720633 and was carried out in part in the Materials Research Laboratory Central Research Facilities, University of Illinois. Thin-film growth at Argonne National Laboratory was supported by the U.S. Department of Energy, Office of Science, Materials Science and Engineering Division.

![](https://assets.underline.io/uploads/markdown_image/1/image/756eaf87bcd78eaae92bc5c59ee591d2.jpg)

Fig. 1: UMR in the antiferromagnetic phase of FeRh [110]/Pt (T = 10 K), as a function of field B at various current densities J.

![](https://assets.underline.io/uploads/markdown_image/1/image/71626e5a0aa513b3c7c5af64e05003bc.jpg)

Fig 2: Generation of a nonlinear charge current transverse to the applied B field (top left), which increases considerably in the presence of canting (bottom right).

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