Quantum geometry in condensed-matter physics has two components: the real part quantum metric and the imaginary part Berry curvature. Whereas the effects of Berry curvature have been observed through phenomena such as the quantum Hall effect in two-dimensional electron gases and the anomalous Hall effect (AHE) in ferromagnets, the quantum metric has rarely been explored. Here, we report a nonlinear Hall effect induced by the quantum metric dipole by interfacing even-layered MnBi ₂ Te ₄ with black phosphorus. The quantum metric nonlinear Hall effect switches direction upon reversing the antiferromagnetic (AFM) spins and exhibits distinct scaling that is independent of the scattering time. Our results open the door to discovering quantum metric responses predicted theoretically and pave the way for applications that bridge nonlinear electronics with AFM spintronics.

The discovery of an intrinsic ferromagnetic axion insulator MnB _i8 Te ₁₃ paves the way for quantized magnetoelectric effect.

A first-principles density-functional description of the electronic structures of the high-T_c cuprates has remained a long-standing problem since their discovery in 1986, with calculations failing to capture either the insulating (magnetic) state of the pristine compound or the transition from the insulating to metallic state with doping. Here, by taking lanthanum cuprate as an exemplar high-T_c cuprate, we show that the recently developed non-empirical, strongly constrained and appropriately normed density functional accurately describes both the antiferromagnetic insulating ground state of the pristine compound and the metallic state of the doped system. Our study yields new insight into the low-energy spectra of cuprates and opens up a pathway toward wide-ranging first-principles investigations of electronic structures of cuprates and other correlated materials.

We show how an accurate first-principles treatment of the antiferromagnetic ground state of ${\mathrm{La}}_2{\mathrm{CuO}}_4$ can be obtained without invoking any free parameters such as the Hubbard $U$. The magnitude and orientation of our theoretically predicted magnetic moment of $0.495{\mu }_B$ on Cu sites along the (100) direction are in excellent accord with experimental results. The computed values of the band gap (1.00 eV) and the exchange coupling ($-138$ meV) match the corresponding experimental values. We identify interesting band splittings below the Fermi energy, including an appreciable Hund's splitting of 1.25 eV. The magnetic form factor obtained from neutron scattering experiments is also well described by our calculations. Our study thus opens up a pathway for first-principles investigations of electronic and atomic structures and phase diagrams of cuprates and other complex materials.

Significance: High-temperature superconductivity, first discovered in materials with copper-oxide planes, is still not well understood. Cuprates exhibit complex phase diagrams under temperature and doping and have not been amenable to first-principles description using previous density functionals, but the recent SCAN functional correctly predicts many properties of the undoped and doped YBCO compounds. In the oxygen-doped YBa ₂ Cu ₃ O ₇ , SCAN finds many competing states with charge and spin stripes. Thermal energies will mix these states, creating fluctuations of the spin moments on the copper atoms in the pseudogap phase from which superconductivity emerges. Our study suggests a paradigm in which the physics of the mysterious pseudogap phase in the cuprates is encoded through a landscape of underlying competing phases in the material.

An emerging frontier in condensed matter physics involves novel electromagnetic responses, such as the anomalous Hall effect (AHE), in ferromagnetic Weyl semimetals (FM-WSMs). Candidate FM-WSMs have been limited to materials that preserve inversion symmetry and generate Weyl crossings by breaking the time-reversal symmetry. These materials share three common features: a centrosymmetric lattice, a collinear FM ordering, and a large AHE observed when the field is parallel to the magnetic easy axis. Here we present CeAlSi as a FM-WSM in which the Weyl nodes are stabilized by breaking the inversion symmetry, but their positions are tuned by breaking the time-reversal symmetry. Unlike the other FM-WSMs, CeAlSi has a noncentrosymmetric lattice, a noncollinear FM ordering, and a novel AHE that is anisotropic between the easy and hard magnetic axes. It also exhibits large FM domains that are promising for exploring both device applications and the interplay between the Weyl nodes and FM domain walls.