Heusler, Weyl, and Berry (1802.03771v1)

Abstract: Heusler materials, initially discovered by Fritz Heusler more than a century ago, have grown into a family of more than 1000 compounds, synthesized from combinations of more than 40 elements. These materials show a wide range of properties, but new properties are constantly being found. Most recently, by incorporating heavy elements that can give rise to strong spin-orbit coupling (SOC), non-trivial topological phases of matter, such as topological insulators (TIs), have been discovered in Heusler materials. Moreover, the interplay of symmetry, SOC and magnetic structure allows for the realization of a wide variety of topological phases through Berry curvature design. Weyl points and nodal lines can be manipulated by various external perturbations, which results in exotic properties such as the chiral anomaly, and large anomalous spin and topological Hall effects. The combination of a non-collinear magnetic structure and Berry curvature gives rise a non-zero anomalous Hall effect, which was first observed in the antiferromagnets Mn3Sn and Mn3Ge. Besides this k-space Berry curvature, Heusler compounds with non-collinear magnetic structures also possess real-space topological states in the form of magnetic antiskyrmions, which have not yet been observed in other materials. The possibility of directly manipulating the Berry curvature shows the importance of understanding both the electronic and magnetic structures of Heusler compounds. Together, with the new topological viewpoint and the high tunability, novel physical properties and phenomena await discovery in Heusler compounds.

• The paper reveals Heusler compounds' tunability in achieving non-trivial topological states such as Weyl semimetals via enhanced spin-orbit coupling.
• It demonstrates how Berry curvature engineering modulates the anomalous Hall effect, achieving conductivities up to 2020 Ω cm⁻¹ in materials like Co₂TiSn.
• The study paves the way for spintronic applications by leveraging magnetic skyrmions and quantum anomalous Hall phenomena for next-generation devices.

Insights into Heusler Compounds and Their Topological Characteristics

The paper "Heusler, Weyl, and Berry" presented by Manna et al. provides an in-depth perspective into the multifaceted properties of Heusler compounds, a class comprising more than 1000 compounds synthesized from over 40 elements. These compounds feature a range of physical phenomena due to their unique ability to support diverse electronic and magnetic configurations, often augmented by significant spin-orbit coupling (SOC). The review meticulously elaborates on the intersection of Heusler compounds with topological physics, accentuating their role in the realization of exotic quantum states such as Weyl semimetals and topological insulators.

Core Findings and Numerical Insights

One of the seminal attributes of Heusler compounds highlighted in this work is their structural and topological versatility. Manna et al. delineate how non-trivial topological phases, including Weyl semimetals and topological insulators, can be achieved by incorporating heavier elements to enhance SOC. The paper emphasizes the tunability of Weyl points, which are pivotal in generating phenomena like the anomalous Hall effect (AHE) and topological Hall effect (THE), both driven by Berry curvature dynamics. Noteworthy is the intrinsic nature of AHE in Weyl semimetals, which scales with the separation and number of Weyl points in the Brillouin zone, offering a significant advantage for observing quantum phenomena like the chiral anomaly.

In Heusler compounds, results have shown that Berry curvature engineering can modulate the AHE, leading to a Hall conductivity as high as 2020 Ω cm^-1, especially in compounds such as Co2TiSn. In contrast, the anomalous Hall angle in systems like GdPtBi can reach up to 10%, attributable to a low carrier density and a favorable band topology near the Weyl points. The authors also discuss real-space topological excitations such as magnetic skyrmions and antiskyrmions, which introduce non-trivial modifications to transport phenomena and open avenues for spintronic applications.

Theoretical and Practical Implications

The theoretical framework established for Heusler compounds supports the exploration of other tunable material classes, potentially broadening the scope of new discoveries in topological states. The ability to control electronic and magnetic properties via elemental substitution enhances the attractiveness of Heusler compounds for technological applications in spintronics, quantum computing, and information storage.

From a practical perspective, the insights presented pave the way for developing next-generation devices exploiting quantum anomalous Hall effects and spin-polarized currents. The paper also hints at the possibility of achieving high-temperatures quantum AHE, which could revolutionize room-temperature applications in magnetic tunnel junctions and MRAM technology.

Future Prospects in AI and Material Science

Given the inherent tunability of Heusler compounds and their amenability to topological manipulations, future research could harness machine learning algorithms to optimize material properties and predict new phenomena. The intersection of AI with material science could expedite the discovery of Heusler alloys with desired topological characteristics, thereby accelerating the innovation cycle.

In summary, the paper by Manna et al. underscores the rich landscape of Heusler compounds as platforms for exploring and harnessing novel topological states. The multifarious properties and tunability of these materials portend substantial advancements in both fundamental research and pragmatic applications in condensed matter physics and allied fields. The work positions Heusler compounds at the forefront of topological materials research, providing a solid foundation for both theoretical exploration and technological innovation.