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Topological kagome magnets RMn₆Sn₆(R = rare earth element) attract numerous interests due to their non-trivial band topology and room-temperature magnetism. Here, we report a high entropy version of kagome magnet, (Gd_0.38Tb_0.27Dy_0.20Ho_0.15)Mn₆Sn₆. Such a high entropy material exhibits multiple spin reorientation transitions, which is not seen in all the related parent compounds and can be understood in terms of competing magnetic interactions enabled by high entropy. Furthermore, we also observed an intrinsic anomalous Hall effect, indicating that the high entropy phase preserves the non-trivial band topology. These results suggest that high entropy may provide a route to engineer the magnetic structure and expand the horizon of topological materials.

Periodic space crystals are well established and widely used in physical sciences. Time crystals have been increasingly explored more recently, where time is disconnected from space. Periodic relativistic spacetime crystals on the other hand need to account for the mixing of space and time in special relativity through Lorentz transformation, and have been listed only in 2-dimensions. This work shows that there exists a transformation between the conventional Minkowski spacetime (MS) and what is referred to here as renormalized blended spacetime (RBS); they are shown to be equivalent descriptions of relativistic physics in flat spacetime. There are two elements to this reformulation of MS, namely, blending and renormalization. When observers in two inertial frames adopt each other’s clocks as their own, while retaining their original space coordinates; the observers become blended. This process reformulates the Lorentz boosts into Euclidean rotations while retaining the original spacetime hyperbola describing worldlines of constant spacetime length from the origin. By renormalizing the blended coordinates with an appropriate factor that is a function of the relative velocities between the various frames, the hyperbola is transformed into a Euclidean circle. With these two steps, one obtains the RBS coordinates complete with new light lines, but nowmore »with a Euclidean construction. One can now enumerate the RBS point and space groups in various dimensions with their mapping to the well-known space crystal groups. The RBS point group for flat isotropic RBS spacetime is identified to be that of cylinders in various dimensions: mm2 which is that of a rectangle in 2D, (∞⁄m)m which is that of a cylinder in 3D, and that of hypercylinder in 4D. An antisymmetry operation is introduced that can swap between space-like and time-like directions, leading to color spacetime groups. The formalism reveals RBS symmetries that are not readily apparent in the conventional MS formulation. Mathematica® script is provided for plotting the MS and RBS geometries discussed in the work.« less

It is shown that there are 41 types of multivectors representing physical quantities in non-relativistic physics in arbitrary dimensions within the formalism of Clifford algebra. The classification is based on the action of three symmetry operations on a general multivector: spatial inversion, 1 , time-reversal, 1′, and a third that is introduced here, namely wedge reversion, 1 † . It is shown that the traits of `axiality' and `chirality' are not good bases for extending the classification of multivectors into arbitrary dimensions, and that introducing 1 † would allow for such a classification. Since physical properties are typically expressed as tensors, and tensors can be expressed as multivectors, this classification also indirectly classifies tensors. Examples of these multivector types from non-relativistic physics are presented.