A M was supported by the King Abdullah University of Science and Technology (KAUST) T J acknowledges support from the EU FET Open RIA Grant No 766566, the Ministry of Education of the Czech Republic Grant No LM2015087 and LNSM-LNSpin, and the Grant Agency of the Czech Republic Grant No 19-28375X J S acknowledges the Alexander von Humboldt Foundation, EU FET Open Grant No 766566, EU ERC Synergy Grant No 610115, and the Transregional Collaborative Research Center (SFB/TRR) 173 SPIN+X K G and P G acknowledge stimulating discussions with C O Avci and financial support by the Swiss National Science Foundation (Grants No 200021-153404 and No 200020-172775) and the European Commission under the Seventh Framework Program (spOt project, Grant No 318144) A T acknowledges support by the Agence Nationale de la Recherche, Project No ANR-17-CE24-0025 (TopSky) J Ž acknowledges the Grant Agency of the Czech Republic Grant No 19-18623Y and support from the Institute of Physics of the Czech Academy of Sciences and the Max Planck Society through the Max Planck Partner Group programme

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Current-induced spin-orbit torques in ferromagnetic and antiferromagnetic systems

The importance of global band topology is unequivocally recognized in condensed matter physics, and new states of matter, such as topological insulators, have been discovered. Owing to their bulk band topology, 3D topological insulators possess a massless Dirac dispersion with spin–momentum locking at the surface. Although 3D topological insulators were originally proposed in time-reversal invariant systems, the onset of a spontaneous magnetization or, equivalently, a broken time-reversal symmetry leads to the formation of an exchange gap in the Dirac band dispersion. In such magnetic topological insulators, tuning of the Fermi level in the exchange gap results in the emergence of a quantum Hall effect at zero magnetic field, that is, of a quantum anomalous Hall effect. Here, we review the basic concepts of magnetic topological insulators and their experimental realization, together with the discovery and verification of their emergent properties. In particular, we discuss how the development of tailored materials through heterostructure engineering has made it possible to access the quantum anomalous Hall effect, the topological magnetoelectric effect, the physics related to the chiral edge states that appear in these materials and various spintronic phenomena. Further theoretical and experimental research on magnetic topological insulators will provide fertile ground for the development of new concepts for next-generation electronic devices for applications such as spintronics with low energy consumption, dissipationless topological electronics and topological quantum computation. Magnetic topological insulators enable the investigation of the interplay between magnetism and topological electronic states. This Review summarizes the basic notions of magnetic topological insulators and the progress in the experimental realization of exotic topological phenomena.

Magnetic topological insulators

Review on spintronics: Principles and device applications

The rapid increase in information in the big-data era calls for changes to information-processing paradigms, which, in turn, demand new circuit-building blocks to overcome the decreasing cost-effectiveness of transistor scaling and the intrinsic inefficiency of using transistors in non-von Neumann computing architectures. Accordingly, resistive switching materials (RSMs) based on different physical principles have emerged for memories that could enable energy-efficient and area-efficient in-memory computing. In this Review, we survey the four physical mechanisms that lead to such resistive switching: redox reactions, phase transitions, spin-polarized tunnelling and ferroelectric polarization. We discuss how these mechanisms equip RSMs with desirable properties for representation capability, switching speed and energy, reliability and device density. These properties are the key enablers of processing-in-memory platforms, with applications ranging from neuromorphic computing and general-purpose memcomputing to cybersecurity. Finally, we examine the device requirements for such systems based on RSMs and provide suggestions to address challenges in materials engineering, device optimization, system integration and algorithm design. Resistive switching materials enable novel, in-memory information processing, which may resolve the von Neumann bottleneck. This Review focuses on how the switching mechanisms and the resultant electrical properties lead to various computing applications.

Resistive switching materials for information processing

Since the early 1980s, most electronics have relied on the use of complementary metal–oxide–semiconductor (CMOS) transistors. However, the principles of CMOS operation, involving a switchable semiconductor conductance controlled by an insulating gate, have remained largely unchanged, even as transistors are miniaturized to sizes of 10 nanometres. We investigated what dimensionally scalable logic technology beyond CMOS could provide improvements in efficiency and performance for von Neumann architectures and enable growth in emerging computing such as artifical intelligence. Such a computing technology needs to allow progressive miniaturization, reduce switching energy, improve device interconnection and provide a complete logic and memory family. Here we propose a scalable spintronic logic device that operates via spin–orbit transduction (the coupling of an electron’s angular momentum with its linear momentum) combined with magnetoelectric switching. The device uses advanced quantum materials, especially correlated oxides and topological states of matter, for collective switching and detection. We describe progress in magnetoelectric switching and spin–orbit detection of state, and show that in comparison with CMOS technology our device has superior switching energy (by a factor of 10 to 30), lower switching voltage (by a factor of 5) and enhanced logic density (by a factor of 5). In addition, its non-volatility enables ultralow standby power, which is critical to modern computing. The properties of our device indicate that the proposed technology could enable the development of multi-generational computing. A scalable spintronic device operating via spin–orbit transduction and magnetoelectric switching and using advanced quantum materials shows non-volatility and improved performance and energy efficiency compared with CMOS devices.

Scalable energy-efficient magnetoelectric spin-orbit logic.

Spin–orbit torque switching using the spin Hall effect in heavy metals and topological insulators has a great potential for ultralow power magnetoresistive random-access memory. To be competitive with conventional spin-transfer torque switching, a pure spin current source with a large spin Hall angle (θSH > 1) and high electrical conductivity (σ > 105 Ω−1 m−1) is required. Here we demonstrate such a pure spin current source: conductive topological insulator BiSb thin films with σ ≈ 2.5 × 105 Ω−1 m−1, θSH ≈ 52 and spin Hall conductivity σSH ≈ 1.3 × 107 
 $$\frac{\hbar }{{2e}}$$
 Ω−1 m−1 at room temperature. We show that BiSb thin films can generate a very large spin–orbit field of 2.3 kOe MA–1 cm2 and a critical switching current density as low as 1.5 MA cm–2 in Bi0.9Sb0.1/MnGa bilayers, which underlines the potential of BiSb for industrial applications. A large spin–orbit torque, generated in a conductive topological insulator (TI) Bi0.9Sb0.1 is further employed to effectively switch the magnetization of MnGa in a BiSb/MnGa bilayer Hall-bar device at room temperature.

A conductive topological insulator with large spin Hall effect for ultralow power spin-orbit torque switching.

Spin-orbit-torque (SOT) switching using the spin Hall effect (SHE) in heavy metals and topological insulators (TIs) has great potential for ultra-low power magnetoresistive random-access memory (MRAM) To be competitive with conventional spin-transfer-torque (STT) switching, a pure spin current source with large spin Hall angle (${\theta}_{SH}$ > 1) and high electrical conductivity (${\sigma} > 10^5 {\Omega}^{-1}m^{-1}$) is required Here, we demonstrate such a pure spin current source: BiSb thin films with ${\sigma}{\sim}25*10^5 {\Omega}^{-1}m^{-1}$, ${\theta}_{SH}{\sim}52$, and spin Hall conductivity ${\sigma}_{SH}{\sim}13*10^7 {\hbar}/2e{\Omega}^{-1}m^{-1}$ at room temperature We show that BiSb thin films can generate a colossal spin-orbit field of 2770 Oe/(MA/cm$^2$) and a critical switching current density as low as 15 MA/cm$^2$ in Bi$_{09}$Sb$_{01}$ / MnGa bi-layers BiSb is the best candidate for the first industrial application of topological insulators

A conductive topological insulator with colossal spin Hall effect for ultra-low power spin-orbit-torque switching

We grew and characterized Bi1-xSbx thin films on GaAs(111)A substrates by molecular beam epitaxy. By optimizing the growth condition, we were able to grow Bi1-xSbx thin films epitaxially with the Sb concentration ranging from 0% to 100% and the epitaxial orientation of Bi1-xSbx(001)//GaAs(111). The conductivity of Bi1-xSbx exceeds 105 Ω−1 m−1 and approaches those of bulk values for thick enough thin films, which are higher than those of other Bi-based topological insulators by at least an order of magnitude. From the temperature dependence of their electrical conductivity, we confirmed the existence of metallic surface states of Bi1-xSbx inside and outside of the topological insulating region. Our results demonstrate the potential of Bi1-xSbx as a spin Hall material with high conductivity and possibly large spin Hall angle for spintronic applications.

Epitaxial growth and characterization of Bi1-xSbx spin Hall thin films on GaAs(111)A substrates

We report on the crystal growth as well as the structural and magnetic properties of Bi0.8Sb0.2 topological insulator (TI)/MnxGa1-x bi-layers grown on GaAs(111)A substrates by molecular beam epitaxy. By optimizing the growth conditions and Mn composition, we were able to grow MnxGa1-x thin films on Bi0.8Sb0.2 with the crystallographic orientation of Bi0.8Sb0.2(001)[1 1 ¯ 0]//MnGa (001)[100]. Using magnetic circular dichroism (MCD) spectroscopy, we detected both the L10 phase ( x 0.6) of MnxGa1-x. For 0.50 ≤ x ≤ 0.55, we obtained ferromagnetic L10-MnGa thin films with clear perpendicular magnetic anisotropy, which were confirmed by MCD hysteresis, anomalous Hall effect as well as superconducting quantum interference device measurements. Our results show that the BiSb/MnxGa1-x bi-layer system is promising for perpendicular magnetization switching using the giant spin Hall effect in TIs.

Growth and characterization of MnGa thin films with perpendicular magnetic anisotropy on BiSb topological insulator

We report on epitaxial crystal growth and spin Hall effect in BiSb topological insulator thin films. We show that BiSb thin films with conductivity as high as σ ~ 2.5∗105 Ω-1m-1 can be epitaxially grown on GaAs(111)A substrate. Meanwhile, evaluation of spin-orbit-torque in Bi0.9Sb0.1/MnGa bi-layers reveals a colossal spin Hall angle of θSH ~ 52 and a spin Hall conductivity σSH ~ 1.3∗107 ℏ/2e Ω-1m-1 at room temperature. We demonstrate that BiSb thin films can generate a colossal spin-orbit field of 2.3 kOe/(MA/cm2) and a critical switching current density as low as 1.5 MA/cm2 in Bi0.9Sb0.1/MnGa bi-layers. BiSb is the best candidate for the first industrial application of topological insulators.

Yugo Ueda

Papers

A conductive topological insulator with large spin Hall effect for ultralow power spin-orbit torque switching.

A conductive topological insulator with colossal spin Hall effect for ultra-low power spin-orbit-torque switching

Epitaxial growth and characterization of Bi1-xSbx spin Hall thin films on GaAs(111)A substrates

Growth and characterization of MnGa thin films with perpendicular magnetic anisotropy on BiSb topological insulator

Conductive BiSb topological insulator with colossal spin Hall effect for ultra-low power spin-orbit-torque switching