Uncovering Hidden Orders within Deformable Materials: The Case of Dysprosium

The intrinsic orders within deformable materials can be masked by lattice defects, an issue that has been largely overlooked. Uncovering these hidden orders is likely to offer new insights into material properties. Here, we address this issue by introducing a zero-gravity synthesis method to fabricate highly crystalline and nearly stress-free microspheres from deformable materials, as demonstrated with dysprosium metal. Interestingly, we find that the intrinsic atomic order of dysprosium is an unusual low-symmetry orthorhombic Cmcm phase, which contrasts with the widely accepted hexagonal P6₃/mmc structure. Through first-principles crystal field theory calculations, we determine the intrinsic orbital order, showing that the Cmcm phase arises from a nonzero quadrupole operator for the Dy's 4f-electron shell in its ferromagnetic state. This operator possesses an opposite sign compared to that of terbium, driving contrary significant magnetoelastic distortions within the basal plane. These findings aid in understanding the functions of rare-earth-related functional materials like giant magnetostriction. We expect to uncover more hidden orders in deformable materials, thereby deepening our knowledge of their performances.