Linking emergent phenomena and broken symmetries through one-dimensional objects and their dot/cross products

The symmetry of the whole experimental setups, including specific sample environments and measurables, can be compared with that of specimens for observable physical phenomena. We, first, focus on one-dimensional (1D) experimental setups, independent from any spatial rotation around one direction, and show that eight kinds of 1D objects (four; vectorlike, the other four; director-like), defined in terms of symmetry, and their dot and cross products are an effective way for the symmetry consideration. The dot products form a Z2xZ2xZ2 group with Abelian additive operation, and the cross products form a Z2xZ2 group with Abelian additive operation or Q8, a non-abelian group of order eight, depending on their signs. Those 1D objects are associated with characteristic physical phenomena. When a 3D specimen has Symmetry Operational Similarity (SOS) with (identical or lower, but not higher, symmetries than) an 1D object with a particular phenomenon, the 3D specimen can exhibit the phenomenon. This SOS approach can be a transformative and unconventional avenue for symmetry-guided materials designs and discoveries

Nonequivalent Spin Exchanges of the Hexagonal Spin Lattice Affecting the Low-Temperature Magnetic Properties of RInO₃ (R = Gd, Tb, Dy): Importance of Spin–Orbit Coupling for Spin Exchanges between Rare-Earth Cations with Nonzero Orbital Moments

Rare-earth indium oxides RInO₃ (R = Gd, Tb, Dy) consist of spin-frustrated hexagonal spin lattices made up of rare-earth ions R³⁺, where R³⁺ = Gd³⁺ (f⁷, <i>L</i> = 0), Tb³⁺ (f⁸, <i>L</i> = 3), and Dy³⁺ (f⁹, <i>L</i> = 5). We carried out DFT calculations for RInO₃, including on-site repulsion U with/without spin–orbit coupling (SOC), to explore if their low-temperature magnetic properties are related to the two nonequivalent nearest-neighbor (NN) spin exchanges of their hexagonal spin lattices. Our DFT + U + SOC calculations predict that the orbital moments of the Tb³⁺ and Dy³⁺ ions are smaller than their free-ion values by ∼2μ_B while the Tb³⁺ spins have an in-plane magnetic anisotropy, in agreement with the experiments. This suggests that the f orbitals of each R³⁺ (R = Tb, Dy) ion are engaged, though weakly, in bonding with the surrounding ligand atoms. The magnetic properties of GdInO₃ with the zero orbital moment are adequately described by the spin exchanges extracted by DFT + U calculations. In describing the magnetic properties of TbInO₃ and DyInO₃ with nonzero orbital moments, however, the spin exchanges extracted by DFT + U + SOC calculations are necessary. The spin exchanges of RInO₃ (R = Gd, Tb, Dy) are dominated by the two NN spin exchanges <i>J</i>₁ and <i>J</i>₂ of their hexagonal spin lattice, in which the honeycomb lattice of <i>J</i>₂ forms spin-frustrated (<i>J</i>₁, <i>J</i>₁, <i>J</i>₂) triangles. The <i>J</i>₂/<i>J</i>₁ ratios are calculated to be ∼3, ∼1.7, and ∼1 for GdInO₃, TbInO₃, and DyInO₃, respectively. This suggests that the antiferromagnetic (AFM) ordering of GdInO₃ below 1.8 K is most likely an AFM ordering of its honeycomb spin lattice and that TbInO₃ would exhibit low-temperature magnetic properties similar to those of GdInO₃ while DyInO₃ would not

Topological Phase Transition with Nanoscale Inhomogeneity in (Bi_1–<i>x</i>In_<i>x</i>)₂Se₃

Topological insulators are a class of band insulators with nontrivial topology, a result of band inversion due to the strong spin–orbit coupling. The transition between topological and normal insulator can be realized by tuning the spin–orbit coupling strength and has been observed experimentally. However, the impact of chemical disorders on the topological phase transition was not addressed in previous studies. Herein, we report a systematic scanning tunneling microscopy/spectroscopy and first-principles study of the topological phase transition in single crystals of In-doped Bi₂Se₃. Surprisingly, no band gap closure was observed across the transition. Furthermore, our spectroscopic-imaging results reveal that In defects are extremely effective “suppressors” of the band inversion, which leads to microscopic phase separation of topological-insulator-like and normal-insulator-like nano regions across the “transition”. The observed topological electronic inhomogeneity demonstrates the significant impact of chemical disorders in topological materials, shedding new light on the fundamental understanding of topological phase transition

Novel Geometric Ferroelectric EuInO₃ Single Crystals with Topological Vortex Domains

RInO3 (R: rare-earth element) has drawn unprecedented research attention due to its geometric ferroelectricity and spin liquid state. However, the structure–property relationship needs further investigation based on well-developed single crystals. A EuInO3 crystal was obtained for the first time by the laser floating zone method. The presence of ferroelectricity was revealed by polarization–electric field hysteresis loops of the bulk EuInO3 single crystal. Moreover, interesting topological vortex domains were revealed by vertical piezoresponse force microscopy. The lattice dynamics of EuInO3 was probed by correlating various Raman modes with the structural distortion of the unit cell. The improper ferroelectricity and topological ferroelectric vortices of the EuInO3 crystal provide great potential for vortex memory devices

Simultaneous Imaging of Dopants and Free Charge Carriers by Monochromated EELS

Doping inhomogeneities in solids are not uncommon, but their microscopic observation and understanding are limited due to the lack of bulk-sensitive experimental techniques with high enough spatial and spectral resolution. Here, we demonstrate nanoscale imaging of both dopants and free charge carriers in La-doped BaSnO3 (BLSO) using high-resolution electron energy-loss spectroscopy (EELS). By analyzing high- and low-energy excitations in EELS, we reveal chemical and electronic inhomogeneities within a single BLSO nanocrystal. The inhomogeneous doping leads to distinctive localized infrared surface plasmons, including a previously unobserved plasmon mode that is highly confined between high- and low-doping regions. We further quantify the carrier density, effective mass, and dopant activation percentage by EELS and transport measurements on the bulk single crystals of BLSO. These results not only represent a practical approach for studying heterogeneities in solids and understanding structure–property relationships at the nanoscale, but also demonstrate the possibility of infrared plasmon tuning by leveraging nanoscale doping texture

Ferrorotational Selectivity in Ilmenites

Unlike what happens in conventional ferroics, the ferrorotational (FR) domain manipulation and visualization in FR materials are nontrivial as they are invariant under both space-inversion and time-reversal operations. FR domains have recently been observed by using the linear electrogyration (EG) effect and X-ray diffraction (XRD) diffraction mapping. However, ferrorotational selectivity, such as the selective processing of the FR domains and direct visualization of the FR domains, e.g., under an optical microscope, would be the next step to study the FR domains and their possible applications in technology. Unexpectedly, we discovered that the microscopic FR structural distortions in ilmenite crystals can be directly coupled with macroscopic mechanical rotations in such a way that FR domains can be visualized under an optical microscope after innovative rotational polishing, a combined ion milling with a specific rotational polishing, or a twisting-induced fracturing process. Thus, the FR domains could be a unique medium to register the memory of a rotational mechanical process due to a novel selective coupling between its microscopic structural rotations and an external macroscopic rotation. Analogous to the important enantioselectivity in modern chemistry and the pharmaceutical industry, this newly discovered ferrorotational selectivity opens up opportunities for FR manipulation and new FR functionality-based applications

Record High-Proximity-Induced Anomalous Hall Effect in (Bi_<i>x</i>Sb_1–<i>x</i>)₂Te₃ Thin Film Grown on CrGeTe₃ Substrate

Quantum anomalous Hall effect (QAHE) can only be realized at extremely low temperatures in magnetically doped topological insulators (TIs) due to limitations inherent with the doping process. In an effort to boost the quantization temperature of QAHE, the magnetic proximity effect in magnetic insulator/TI heterostructures has been extensively investigated. However, the observed anomalous Hall resistance has never been more than several ohms, presumably owing to the interfacial disorders caused by the structural and chemical mismatch. Here, we show that, by growing (BixSb1–x)2Te3 (BST) thin films on structurally and chemically well-matched, ferromagnetic-insulating CrGeTe3 (CGT) substrates, the proximity-induced anomalous Hall resistance can be enhanced by more than an order of magnitude. This sheds light on the importance of structural and chemical matches for magnetic insulator/TI proximity systems

Bilayer Square Lattice Tb₂SrAl₂O₇ with Structural Z₈ Vortices and Magnetic Frustration

The bilayer perovskites’ family A3B2O7 holds rich structural complexity. When magnetism freedom is added in, great opportunities appear for new physics. Magnetic Tb ions in Tb2SrAl2O7 are known to crystallize in a bilayer square lattice. The results of our comprehensive neutron, X-ray diffraction, and transmission electron microscopy (TEM) experiments reveal a crystallographic P42/mnm symmetry accompanied with room-temperature topological type-II Z8 vortex domains, whose density is controllable by cooling rates, as described by the Kibble–Zurek mechanism. The DC magnetic susceptibility without long-range order down to 1.8 K suggests frustrated magnetism, while a spin freezing <2.5 K is observed in the AC susceptibility, which is likely due to the antisite disorder and another possible cause of no long-range ordering. Strong temperature evolution of magnetic anisotropy indicates an interplay of low-lying crystal electric field levels and anisotropic exchange interactions. Our results suggest that Tb2SrAl2O7 is a promising candidate of magnetic frustration in a bilayer square lattice, and this system can be a new playground for exploring exotic magnetic states in bilayer square lattices, topological magnetic edge states at coherent crystallographic domain walls, and multifunctional applications

Observation of a ferro-rotational order coupled with second-order nonlinear optical fields

The ferro-rotational order, whose order parameter (OP) is an axial vector invariant under both time reversal (TR) and spatial inversion (SI) operations, is the last remaining category of ferroics to be observed after the ferroelectric, ferromagnetic, and ferro-toroidal orders. This order has become increasingly popular in many new quantum materials, especially in complex oxides, and is considered responsible for a number of novel phenomena such as polar vortices, giant magnetoelectric coupling, and type-II multiferroics. However, physical properties of the ferro-rotational order have been rarely studied either theoretically or experimentally. Here, using high sensitivity rotational anisotropy second harmonic generation (RA SHG), we have, for the first time, exploited the electric quadrupole (EQ) contribution to the SHG to directly couple to this centrosymmetric ferro-rotational order in an archetype of type-II multiferroics, RbFe(MoO4)2. Surprisingly, we have found that two types of domains with opposite ferro-rotational vectors emerge with distinct populations at the critical temperature Tc ~195 K and gradually evolve to reach an even ratio at lower temperatures. Moreover, we have identified the ferro-rotational order phase transition as weak first order, and have revealed its conjugate coupling field as a unique combination of the induced EQ SHG and the incident fundamental electric fields. Our results on physical properties of a ferro-rotational order provide crucial knowledge for understanding and searching for novel phases of matter built upon the ferro-rotational order. Further, these results open the possibility of revealing unconventional centrosymmetric orders and identifying their conjugate coupling fields with second order nonlinear optics

Bilayer Square Lattice Tb₂SrAl₂O₇ with Structural Z₈ Vortices and Magnetic Frustration

The bilayer perovskites’ family A3B2O7 holds rich structural complexity. When magnetism freedom is added in, great opportunities appear for new physics. Magnetic Tb ions in Tb2SrAl2O7 are known to crystallize in a bilayer square lattice. The results of our comprehensive neutron, X-ray diffraction, and transmission electron microscopy (TEM) experiments reveal a crystallographic P42/mnm symmetry accompanied with room-temperature topological type-II Z8 vortex domains, whose density is controllable by cooling rates, as described by the Kibble–Zurek mechanism. The DC magnetic susceptibility without long-range order down to 1.8 K suggests frustrated magnetism, while a spin freezing <2.5 K is observed in the AC susceptibility, which is likely due to the antisite disorder and another possible cause of no long-range ordering. Strong temperature evolution of magnetic anisotropy indicates an interplay of low-lying crystal electric field levels and anisotropic exchange interactions. Our results suggest that Tb2SrAl2O7 is a promising candidate of magnetic frustration in a bilayer square lattice, and this system can be a new playground for exploring exotic magnetic states in bilayer square lattices, topological magnetic edge states at coherent crystallographic domain walls, and multifunctional applications