Altermagnetism: spin-momentum locked phase protected by non-relativistic symmetries

The search for novel magnetic quantum phases, phenomena and functional materials has been guided by relativistic magnetic-symmetry groups in coupled spin and real space from the dawn of the field in 1950s to the modern era of topological matter. However, the magnetic groups cannot disentangle non-relativistic phases and effects, such as the recently reported unconventional spin physics in collinear antiferromagnets, from the typically weak relativistic spin-orbit coupling phenomena. Here we discover that more general spin symmetries in decoupled spin and crystal space categorize non-relativistic collinear magnetism in three phases: conventional ferromagnets and antiferromangets, and a third distinct phase combining zero net magnetization with an alternating spin-momentum locking in energy bands, which we dub "altermagnetic". For this third basic magnetic phase, which is omitted by the relativistic magnetic groups, we develop a spin-group theory describing six characteristic types of the altermagnetic spin-momentum locking. We demonstrate an extraordinary spin-splitting mechanism in altermagnetic bands originating from a local electric crystal field, which contrasts with the conventional magnetic or relativistic splitting by global magnetization or inversion asymmetry. Based on first-principles calculations, we identify altermagnetic candidates ranging from insulators and metals to a parent crystal of cuprate superconductor. Our results underpin emerging research of quantum phases and spintronics in high-temperature magnets with light elements, vanishing net magnetization, and strong spin-coherence.

Intrinsic ferroelectricity in Y-doped HfO2 thin films

Ferroelectric HfO2-based materials hold great potential for widespread integration of ferroelectricity into modern electronics due to their robust ferroelectric properties at the nanoscale and compatibility with the existing Si technology. Earlier work indicated that the nanometer crystal grain size was crucial for stabilization of the ferroelectric phase of hafnia. This constraint caused high density of unavoidable structural defects of the HfO2-based ferroelectrics, obscuring the intrinsic ferroelectricity inherited from the crystal space group of bulk HfO2. Here, we demonstrate the intrinsic ferroelectricity in Y-doped HfO2 films of high crystallinity. Contrary to the common expectation, we show that in the 5% Y-doped HfO2 epitaxial thin films, high crystallinity enhances the spontaneous polarization up to a record-high 50 µC/cm2 value at room temperature. The high spontaneous polarization persists at reduced temperature, with polarization values consistent with our theoretical predictions, indicating the dominant contribution from the intrinsic ferroelectricity. The crystal structure of these films reveals the Pca21 orthorhombic phase with a small rhombohedral distortion, underlining the role of the anisotropic stress and strain. These results open a pathway to controlling the intrinsic ferroelectricity in the HfO2-based materials and optimizing their performance in applications.

A novel sodium-fluorescent crystal

In this work, a novel sodium-fluorescent crystal (Na-FS) was synthesized from 4-dimethylaminobenzoic acid and sodium hydroxide by one-pot hydrothermal method. The structure and conformation of Na-FS were confirmed by single-crystal X-ray diffraction and scanning electron microscope, and the optical properties were studied by fluorescence spectrometer. The results showed that: Na-FS was a triclinic crystal, space group was P-1, cell parameters a , b and c were 10.5113(3), 15.9198(5) and 15.9560(5) Å, respectively, and the number of independent atoms Z in a structure cell was two. Additionally, Na-FS has a blue fluorescence emission (around 360 nm under excited at the range of 230–300 nm) with great photostability and photobleaching resistance, and the quantum yield of Na-FS is 30.58%.

Orbital-Free Quantum Crystallographic View on Noncovalent Bonding: Insights into Hydrogen Bonds, π∙∙∙π and Reverse Electron Lone Pairs∙∙∙π Interactions

A detailed analysis of a complete set of the local potentials that appear in the Euler equation for electron density is carried out for noncovalent interactions in the uracil derivative using experimental X-ray charge density. The interplay between the quantum theory of atoms in molecules and crystals and the local potentials and corresponding inner-crystal electronic forces of electrostatic and kinetic origin is explored. Novel physically grounded bonding descriptors derived within the orbital-free quantum crystallography provided the detailed examination of pi-stacking and intricate C=O...pi interactions and nonclassical hydrogen bonds. The donor-acceptor character of these interactions is revealed by analysis of Pauli and von Weizsäcker potentials together with more well-known functions. Partitioning of crystal space into atomic-like potential basins led us to the definite description of the charge transfer. In this way, our analysis throws light on aspects of these closed-shell interactions hitherto hidden from the description.

Orbital-Free Quantum Crystallographic View on Noncovalent Bonding: Insights into Hydrogen Bonds, π∙∙∙π and Reverse Electron Lone Pairs∙∙∙π Interactions

A detailed analysis of a complete set of the local potentials that appear in the Euler equation for electron density is carried out for noncovalent interactions in the uracil derivative using experimental X-ray charge density. The interplay between the quantum theory of atoms in molecules and crystals and the local potentials and corresponding inner-crystal electronic forces of electrostatic and kinetic origin is explored. Novel physically grounded bonding descriptors derived within the orbital-free quantum crystallography provided the detailed examination of pi-stacking and intricate C=O...pi interactions and nonclassical hydrogen bonds. The donor-acceptor character of these interactions is revealed by analysis of Pauli and von Weizsäcker potentials together with more well-known functions. Partitioning of crystal space into atomic-like potential basins led us to the definite description of the charge transfer. In this way, our analysis throws light on aspects of these closed-shell interactions hitherto hidden from the description.

From atoms to bonds, angles and torsions: molecular metrics from crystal space, and two Excel implementations

Values of molecular bond lengths, bond angles and (less frequently) bond torsion angles are readily available from databases, from crystallographic software, and/or from interactive molecular and crystal visualization programs such as Jmol. However, the methods used to calculate these values are less well known. In this paper, the computational methods are described in detail, and live Excel implementations, which permit readers to readily perform the calculations for their own molecular systems, are provided. The methods described apply to both fractional coordinates in crystal space and Cartesian coordinates in Euclidean space (space in which the geometric postulates of Euclid are valid) and are vector/matrix based. In their simplest computational form, they are applied as algebraic expansions which are summed. They are also available in matrix formulations, which are readily manipulated and calculated using the matrix functions of Excel. In particular, their general formulation as metric matrices is introduced. The methods in use are illustrated by a detailed example of the calculations. This contribution provides a significant practical application which can also act as motivation for the study of matrix mathematics with respect to its many uses in chemistry.

Groupoid description of modular structures

Modular structures are crystal structures built by subperiodic (zero-, mono- or diperiodic) substructures, called modules. The whole set of partial operations relating substructures in a modular structure build up a groupoid; modular structures composed of identical substructures are described by connected groupoids, or groupoids in the sense of Brandt. A general approach is presented to describe modular structures by Brandt's groupoids and how to obtain the corresponding space groups, in which only the partial operations that have an extension to the whole crystal space appear.