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Noncollinear antiferromagnets can generate a transverse electrical response known as the anomalous Hall effect, even though they possess almost no net magnetization. The microscopic origin of this behaviour, however, has remained unclear…
Broken symmetries in solids involving higher order multipolar degrees of freedom are historically referred to as "hidden orders" due to the formidable task of detecting them with conventional probes. Examples of such hidden orders include…
Order parameters not only characterize symmetry-broken equilibrium phases but also govern transport phenomena in the nonequilibrium regime. Altermagnets, a class of magnetic systems integrating ferromagnetic and antiferromagnetic features,…
This review presents recent breakthroughs in the realm of nonlinear Hall effects, emphasizing central theoretical foundations and recent experimental progress. We elucidate the quantum origin of the second-order Hall response, focusing on…
In the presence of time reversal symmetry, a non-linear Hall effect can occur in systems without an inversion symmetry. One of the prominent candidates for detection of such Hall signals are Weyl semimetals. In this article, we investigate…
Multipole moments serve as order parameters for characterizing higher-order magnetic effects in momentum space, providing a framework to describe diverse magnetic responses by extending the concept of magnetism. In this letter, we introduce…
We propose novel triple-${\bm q}$ multipole orders as possible candidates for the two distinct low-temperature symmetry broken phases in quadrupolar system PrV$_2$Al$_{20}$. An analysis of the experiment under [111] magnetic fields…
The nonlinear Hall effect, which is the second-order harmonic charge Hall effect from the Berry curvature dipole in momentum space, has received much attention recently. As the responses to higher harmonics of the driving ac electric field…
The third-order nonlinear Hall effect induced by Berry-connection polarizability tensor has been observed in Weyl semimetals T$_d$-MoTe$_2$ as well as T$_d$-TaIrTe$_4$. The experiments were performed on bulk samples, and the results were…
The anomalous Hall effect has been front and center in solid state research and material science for over a century now, and the complex transport phenomena in nontrivial magnetic textures have gained an increasing amount of attention, both…
Exotic high-rank multipolar order parameters have been found to be unexpectedly active in more and more correlated materials in recent years. Such multipoles are usually dubbed as "Hidden Orders" since they are insensitive to common…
It has recently been demonstrated that various topological states, including Dirac, Weyl, nodal-line, and triple-point semimetal phases, can emerge in antiferromagnetic (AFM) half-Heusler compounds. However, how to determine the AFM…
The anomalous Hall effect (AHE) has been extended into the nonlinear regime, where the Hall voltage shows higher-order response to the applied current. Nevertheless, the microscopic mechanism of the nonlinear AHE remains unclear. Here we…
Crystalline symmetries determine the linear and nonlinear response of materials to external stimuli such as mechanical pressure and electromagnetic fields, governing phenomena such as piezoelectricity, optical activity, and multiple wave…
When a conduction electron couples with a non-coplanar localized magnetic moment, the realspace Berry curvature is exerted to cause the geometrical Hall effect, which is not simply proportional to the magnetization. So far, it has been…
The nonlinear Hall effect is a new member of the Hall effect family, which attracts intense research interests, and it is closely related to the quantum geometry of quantum materials. The previous studies primarily concentrate on the…
In recent years, it has been shown that Berry curvature monopoles and dipoles play essential roles in the anomalous Hall effect and the nonlinear Hall effect respectively. In this work, we demonstrate that Berry curvature multipoles (the…
We investigate the second-order anomalous Hall response in two-dimensional higher-wave symmetric magnets, including the recently discovered class of collinear magnets known as altermagnets, when subjected to a symmetry-breaking external…
Hidden multipolar orders in spin-orbit-coupled Mott insulators provide a promising setting for correlated quantum matter, yet their control and detection remain major challenges. Here, we demonstrate that circularly polarized light enables…
The second-order nonlinear Hall effect illuminates a frequency-doubling transverse current emerging in quantum materials with broken inversion symmetry even when time-reversal symmetry is preserved. This nonlinear response originates from…