Topological insulators (TIs), Weyl and Dirac semimetals are new quantum states of matter, which have attracted considerable interest from the condensed matter community. Heusler compounds are a remarkable class of materials which exhibit a wide range of extraordinary multi-functionalities including tunable topological insulators, half metallic ferromagnets and non collinear topological spin structures . Weyl and Dirac semimetals open up new research directions and applications that result from the large Berry phases that they exhibit: these lead to giant anomalous Hall effect (AHE), spin Hall effects (SHE) and topological spin structures. In the C1b Heusler compounds, the inclusion of rare earth atoms allows the use of magnetic exchange fields to induce Weyl points in magnetic fields, which break time-reversal symmetry.
Recently Co2TiSn and other Co2-Heusler compounds were found to be Weyl semimetals [2-4]: these materials have an energy-gap for one spin orientation and crossing points in the other spin direction. The Berry phase induces a giant AHE in these ferromagnets . However, even antiferromagnetic Manganese-rich Heusler compounds can be designed with frustrated spins, large Berry curvature as a consequence of Weyl points close to the Fermi energy : this has recently been proven via a giant AHE for single crystals of Mn3Sn and Mn3Ge [6,7]. In general Mn-rich Heusler compounds with heavy transition metals such as Mn2RnSn show a large Dzyaloshinskii-Moriya interaction and therefore non-collinear spin structures. Skyrmions, topologically stable spin textures, are of great interest for new generations of spintronic devices. Depending on the crystal symmetries, two distinct types of swirling of the skyrmions, named Bloch and Neel types. In a family of acentric tetragonal Heusler compounds with D2d crystal symmetry Skyrmions with a special type of spin-swirling, called antiskyrmions, can even realized. The interplay between the anisotropic exchange and DMI modifies a helical magnetic phase that propagates in the tetragonal basal plane into antiskyrmions arranged on a hexagonal lattice. The flexibility of their manipulation in the present system is demonstrated by the achievement of antiskyrmions up to 400 K and their zero field metastable state at low temperatures . The family of tetragonal Heusler materials including non-collinear spin structures and Skyrmions opens a new spintronics direction including the realization of skyrmionics.
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