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Two-dimensional magnets based on van der Waals materials are currently fostering great expectations for the advancement of spin-orbitronics, which aims to exploit the spin-orbit coupling in non-centrosymmetric magnetic heterostructures to enable current-driven magnetic torques and stabilize homochiral magnetic textures. Van der Waals magnets are particularly appealing for this purpose as their properties can be tuned by surface engineering at the atomic level. In this talk, I will present our investigation of the spin-orbitronics properties of selected highly promising van der Waals candidates, both in pristine and Janus configurations, from first principles and effective tight-binding models. I will first discuss the spin-orbit torque that emerges from inversion symmetry breaking in magnetic transition metal dichalcogenide monolayers [1] and demonstrate that sizable torques can be obtained, whose magnitude is controlled by the electric dipole due to the chalcogen elements. Most importantly, I will show the existence of a unique spin-orbit torque component that allows for field-free current-driven switching, of highest interest for applications. Then, I will discuss the nature of Dzyaloshinskii-Moriya interaction in these systems, and how they can stabilize magnetic skyrmions, but also magnetic bimerons depending on the magnetic anisotropy properties [2]. Finally, I will discuss the spin-orbitronics properties of Fe3Ge2Te2 and show that in spite of its high symmetry, its inherent mirror symmetry breaking enables the onset of an in-plane Dzyaloshinskii-Moriya interaction that can stabilize planar chiral textures [3].

[1] Smaili et al., arXiv:2007.07579
[2] Laref et al., arXiv:2011.07813 
[3] Laref et al., Physical Review B 102, 060402(R) (2020)


MATERIALS FOR HUMANITY (MH 21)

Theory of spin-orbit torque and Dzyaloshinskii-Moriya interaction in van der Walls magnets

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MH 21 is arranged around 6 themes that focus attention on pressing needs that should be addressed to enhance the well-being of communities and provide a forum for presenting breakthrough discoveries.

The discovery of the spin Hall effect (SHE) enabled the efficient generation and manipulation of the spin current. The magnetic spin Hall effect provides a unique opportunity to control the spin current and relevant device performance with controllable magnetization. In this talk, we report the magnetic spin Hall effect both in non-collinear antiferromagnet Mn3Pt and a collinear antiferromagnet Mn2Au. We generate tiny out-of-plane polarized spin current when the charge current is applied along the axis perpendicular to the magnetic mirror plane of Mn3Pt/permalloy bilayers, but robust when the current is parallel to the magnetic mirror plane in all of the Mn3Pt films with different orientations. In Mn2Au, the spin currents are generated at two spin sublattices with broken spatial symmetry, and the antiparallel antiferromagnetic moments play an important role. Therefore, we term the Néel vector-dependent spin Hal effect the ‘antiferromagnetic spin Hall effect’. The out-of-plane spins from the antiferromagnetic spin Hall effect are favourable for the efficient switching of perpendicular magnetized devices, which is required for high-density applications. The antiferromagnetic spin Hall effect adds another twist to the atomic-level control of spin currents via the antiferromagnetic spin structure.

Antiferromagnetic spin Hall effect

In this presentation, microscopic structures and magnetic properties of the Fe5−xGeTe2 single crystal, recently discovered as a promising van der Waals (vdW) ferromagnet, are introduced. Our study demonstrate that the √3 × √3 superstructures have two different phases due to the symmetry of Fe(1) ordering. Intriguingly, the observed √3 × √3 ordering breaks the inversion symmetry of crystal, resulting in substantial antisymmetric exchange interaction. The temperature dependence of magnetization reveals a sharp magnetic anomaly suggesting helical magnetism of the Fe5−xGeTe2 due to its non‐centrosymmetricity. Analytical study also supports that the observed ordering can give rise to the helimagnetism. The work will provide essential information to understand the complex magnetic properties of the new vdW ferromagnet, Fe5−xGeTe2 for future topology‐based spin devices.

Helimagnetism of the Fe5GeTe2 crystal

The rising demand for computing power driven by real-world applications is driving significant research and development effort into discovery of new device technologies (e.g., mem-transistor, spintronics, etc.) that better meet the requirements of novel computing paradigms (e.g., bio-inspired neural networks, Ising machines, etc.). In this talk, we will present an overview of our research in exploring emerging non-volatile computing device technologies for novel computing paradigms from a devices-to-algorithms perspective. We will be highlighting some of the research gaps that need to be closed to enable architecture-level simulations that better capture the effects of stochasticity in emerging device technologies, and discussing the exploitation of physical phenomena in novel device technologies for enabling alternative computing paradigms.

A Devices-to-Algorithms Perspective on Non-volatile Computing Device Technologies

Inspired by the success in switching FM magnetization by various electrical means, AFM spintronics has received a great deal of attention in recent years. While most efforts have focused on electrical manipulations of a bulk AFM, interfacial effects between FM and AFM layers are also vitally important for spintronic devices.
Here we demonstrate that applying current pulses to Pt/Co/IrMn trilayers causes concurrent switching of FM magnetization and perpendicular exchange bias (EB)1. This implies that the FM magnetization and EB can be manipulated independently. When comparing with the conventional field-annealing approach to generate EB, SOT determines the FM magnetization direction and further provides effective disturbance to align the interfacial spins between the FM/AFM layers to the FM magnetization. We further develop a time-resolved resistance measurement technique to eliminate the possibility of EB reversal due to joule heating effects. Not only the direction of the exchange bias can be reversed, but its strength can also be controlled by electric current pulses. 
For manipulating in-plane exchange bias, we applied an anisotropic magneto-resistance (AMR) effect for studying the spin-orbit torque (SOT)-driven magnetization switching in PtMn/Co bilayer, under y-type SOT geometry2. The tailorable magneto-structural ordering of PtMn provides an additional dimension for the SOT switching. The results reveal the effective field generated by current in PtMn can be enhanced via forming L10 (antiferromagnetic) phase after annealing. On the other hand, the critical current for the y-type SOT switching is strongly associated with the PtMn/Co interfacial spin configuration. The lowest (highest) critical current is yielded when Co is antiferromagnetically (ferromagnetically) coupled to PtMn through the exchange bias. 
With further investigation and optimization along this direction, the current-pulse-induced EB shall have significant impacts on the SOT-MRAM and other spintronic devices.

1P.H. Lin, B. Y. Yang, M. H. Tsai, H. H. Lin, C.H. Lai, Nat. Mater. 18, 335, (2019)
2 C. Y Yang, L. C. He, Y. S. Yen, P. C. Chen, J. C. Chiu, S. D. Huang, C. H Tseng, and C. H. Lai, Appl. Phys. Lett. 118, 102403 (2021)



Manipulating exchange bias by spin–orbit torque

The precession of magnetization in a ferromagnet (FM) can transmit pure spin current into an adjacent heavy metal (HM) via spin pumping. This pure spin current gets converted to a charge current due to high spin orbit coupling (SOC) of the HM due to the inverse spin Hall effect (ISHE). I will discuss recent ISHE results on Co2Fe0.4Mn0.6Si/Pt bilayers, where Co2Fe0.4Mn0.6Si is a full Heusler alloy. Damping analysis indicates the presence of significant spin pumping at the interface of Co2Fe0.4Mn0.6Si and Pt [1]. I will also discuss ISHE experiments on some other combinations such as CoFeB/IrO2 and manganite based La0.66Sr0.34MnO3/Pt bilayers [2-3]. Recently AFM materials having high SOC have been found to be a good replacement of HM in spin current based study. We have performed the ISHE study of CoFeB (10 nm)/ AFM (d nm) where we considered various AFM such as Mn2Au, Mn3Ga, IrMn etc. The systematic angle dependent ISHE measurements have been carried out to disentangle the different spin rectification effects viz. anisotropic magnetoresistance and anomalous Hall effect [4-6]. Further I will show the ISHE study on topological insulator (TI)/ferromagnetic Bi2Se3/CoFeB films [7,8]. ISHE experiments have also been performed to demonstrate that TIs are potential candidates to replace HM as they possess high spin-orbit coupling. In the second part of my talk, I will discuss about magnetic skyrmion. Skyrmions in ultrathin films are believed to offer large performance advantages in the development of novel spintronics technologies [9]. Recent studies have shown that skyrmions can be stabilized by interfacial Dzyaloshinskii-Moriya Interaction (iDMI). The controlled nucleation, stabilization, smaller size and efficient motion of skyrmions at room temperature and low magnetic field are the major challenges for R&D purpose. In this context, I will discuss the generation of skyrmions from triangular antidot structure in a ferromagnetic nanotrack using local Oersted field [10]. The dependency of skyrmion size and shape for variable Dzyaloshinskii–Moriya interaction and uniaxial anisotropy will also be discussed [11]. Sometimes the shape of skyrmions is not perfectly circled which is explained by the presence of different local anisotropy energy [12] using micromagnetic simulations. I will discuss the effect of the interlayer exchange interaction on between skyrmion-antiskymion pair [13]. I will also discuss the current induced motion of skyrmions in Pt/CoFeB thin films. The presence of low pinning sites in the Pt/CoFeB thin films helps skyrmions to move with a low threshold current density [14].

Acknowledgement: I like to sincerely thank my group members and collaborators for their hardwork and kind cooperation. I also acknowledge the funding agencies. 

References: 
[1] B. B. Singh et al., NPG Asia Materials, 13, 9 (2021)
[2] B. Sahoo et al. arXiv:2102.03624
[3] P. Gupta et al., Nanoscale, 13, 2714-2719, (2021)
[4] B. B. Singh et al., Phy. Rev. Appl. 13, 044020 (2020)
[5] Koustuv Roy et al., arXiv:2102.03624
[6] B. B. Singh et al., Phys. Rev. B 102, 174444 (2020). 
[7] B. B. Singh et al., PSS Rapid 2018, 1800492 (2018) 
[8] B. B. Singh et al., ACS Applied Material & Interfaces 12, 53409 (2020).
[9] A. Fert et al., Nat. Rev. Mater. 2, 17031 (2017)
[10] A. K. Behera et al., J. Phys. D: Appl. Phys. 54 025001 (2021)
[11] A. K. Behera et al., J. Phys. D: Appl. Phys. 51, 285001 (2018)
[12] G. Pradhan et al., J. Magn. Magn. Mater. 528, 167805 (2021)
[13] M. M. M. Bhukta et al., arXiv:2010.07328
[14] B. Ojha et al., (unpublished).

Spintronics with heavy metals, topological insulators and antiferromagnets

We examine interfacial magnetic properties of ultra-thin 3d transition metal alloys deposited on a Pt underlayer. The interfacial Dzyaloshinskii-Moriya interaction (iDMI) and the interfacial perpendicular magnetic anisotropy (iPMA) are measured as a function of the average valence electron number per atom in 3d alloys from 25 (Mn) to 28 (Ni). Interestingly, both iDMI and iPMA exhibit the Slater-Pauling-like dependence on the electron number as the saturation magnetization does, and the three quantities are strongly correlated with each other. The iPMA and saturation magnetizations are calculated by virtual crystal approximation for FM monolayer alloys. We also calculated the iDMI, iPMA, and spin mixing conductance by employing tight binding single band model, by which the Slater-Pauling curve-like behaviors of iPMA and iDMI can be explained. Based on our finding, we claim that the strong correlation among the saturation magnetization, iPMA, and iDMI is manifested in a wide range of electron numbers.

Correlated interfacial magnetic properties of 3d transition metal alloys/Pt structures

The emergence of novel memories such as memristors or resistive memory (RRAM) opens the way to highly energy-efficient computation, near- or in-memory. However, this type of computation has to deal with the severe unreliability of emerging memories. To address this issue, inspired by the architecture of animal brains, we present a manufactured differential hybrid CMOS/RRAM memory architecture suitable for neural network implementation that functions without formal error correction. We also highlight that using highly error-prone programming conditions only slightly reduces network accuracy while bringing important benefits in energy efficiency. Then, we present a second approach where the probabilistic nature of RRAM, instead of being mitigated, can be fully exploited to implement a type of probabilistic learning. We show that the inherent variability in hafnium oxide RRAM can naturally implement the sampling step in the Metropolis-Hastings Markov Chain Monte Carlo algorithm and train experimentally an array of 16,384 RRAM cells to recognize images of cancerous tissues using this technique. These results highlight the interest in fully embracing the unreliable nature of emerging devices in neuromorphic designs.

Using Imperfect Nanodevices to Achieve Energy-Efficient Artificial Intelligence

In this talk, we show that the phenomenon known as "Valley Hall Effect", whereby a an electric field induces a transverse valley current, is better described as an instance of the Orbital Hall Effect (OHE), where the ambiguous ``valley'' indices are replaced by a physical quantity, the orbital magnetic moment, which can be defined uniformly over the entire Brillouin zone. This description removes ambiguities that are present in the definition of the valley Hall current, as the conductivity in the orbital Hall effect is unambiguously defined as the Brillouin zone integral of a new quantity, called the orbital Berry curvature. The reformulation in terms of OHE is illustrated in the case of gapped graphene, which has been previously proposed to be a good platform to observe the valley Hall effect. The new formulation provides a direct explanation to the orbital moments accumulated at the edges of the sample, which were observed in previous Kerr rotation measurements.


Orbital Hall effect as an alternative to valley Hall effect in gapped graphene

It is known that quantum phenomena become more pronounced in materials with reduced dimensionalities. The family of two-dimensional (2D) transition metal dichalcogenides (TMDs) exhibit a host of emergent quantum phenomena, such as valley-selective optical selection rules, the fractional quantum Hall effect and single photon emission. In this talk, we present insights from recent first principles calculations that map the atomic and electronic structure of 2D TMD materials to observable quantum phenomena. Using first principles calculations without any empirical parameters, we predict the Landau levels as well as single-band and exciton g-factors for 2D semiconducting H-phase TMDs, and elucidate the role of many-body interactions in the Zeeman effect [1]. We further present the optical properties of defect-induced localized excitons in these TMD materials, which are of relevance to single photon emission and quantum photonics applications [2]. Finally, we discuss how many-body interactions and interfacial hybridization can lead to spin-dependent tunneling barriers in cobalt pthalocyanine molecules adsorbed on the 2D TMD, VSe2 [3].

[1] Physical Review Research, 2, 033256 (2020)
[2] ACS Nano 13, 6050 (2019)
[3] J Phys Chem Lett 11, 9358 (2020)


Valleytronics, Quantum Photonics and Spintronics in Two-Dimensional Transition Metal Dichalcogenides

Electron emission from a surface or charge injection across an interface is a fundamental process in electronics and photonics. Depending on the energy involved, it can be broadly characterized into 3 different processes known as thermionic emission TE (by thermal energy), field emission FE (by quantum tunneling) and photoemission PE (by absorption of photons or optical tunneling). When the amount of charge is sufficient high, it will affect the space charge field that the process will saturated. With the development of new quantum materials including two-dimensional (2D) materials and 2D/3D Topological semi-metals, many classical laws or models will require revisions to account for new material properties, as well as novel operating regimes in nanometer dimensions and in ultrashort time scales. Thus the basic interaction of electrons between these quantum materials should be studied carefully before wrongly use the classical models directly. In this talk, some recent and self-consistent models will be presented, with applications related to electronics and photonics. These new models exhibit smooth transition to the classical models, report new findings to explain some experimental results, and to predict new operating regimes.

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Theory of spin-orbit torque and Dzyaloshinskii-Moriya interaction in van der Walls magnets