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Abstract It is well recognized that interpreting transport experiment results can be challenging when the samples being measured are spatially nonuniform. However, quantitative understanding on the differences between measured and actual transport coefficients, especially the Hall effects, in inhomogeneous systems is lacking. In this work we use homogenization theory to find exact bounds of the measured or homogenized anomalous Hall conductivity (AHC) in inhomogeneous conductors under minimal assumptions. In particular, we prove that the homogenized AHC cannot exceed the bounds of the local AHC. However, in common experimental setups, anomalies that appear to violate the above bounds can occur, with a popular example being the “humps” or “dips” of the Hall hysteresis curves usually ascribed to the topological Hall effect (THE). We give two examples showing how such apparent anomalies could be caused by different types of inhomogeneities and discuss their relevance in experiments. 

Abstract Recent demonstrations of moiré magnetism, featuring exotic phases with noncollinear spin order in the twisted van der Waals (vdW) magnet chromium triiodide CrI₃, have highlighted the potential of twist engineering of magnetic (vdW) materials. However, the local magnetic interactions, spin dynamics, and magnetic phase transitions within and across individual moiré supercells remain elusive. Taking advantage of a scanning single-spin magnetometry platform, here we report observation of two distinct magnetic phase transitions with separate critical temperatures within a moiré supercell of small-angle twisted double trilayer CrI₃. By measuring temperature-dependent spin fluctuations at the coexisting ferromagnetic and antiferromagnetic regions in twisted CrI₃, we explicitly show that the Curie temperature of the ferromagnetic state is higher than the Néel temperature of the antiferromagnetic one by ~10 K. Our mean-field calculations attribute such a spatial and thermodynamic phase separation to the stacking order modulated interlayer exchange coupling at the twisted interface of moiré superlattices. 

Abstract Effective control of magnetic phases in two-dimensional magnets would constitute crucial progress in spintronics, holding great potential for future computing technologies. Here, we report a new approach of leveraging tunneling current as a tool for controlling spin states in CrI₃. We reveal that a tunneling current can deterministically switch between spin-parallel and spin-antiparallel states in few-layer CrI₃, depending on the polarity and amplitude of the current. We propose a mechanism involving nonequilibrium spin accumulation in the graphene electrodes in contact with the CrI₃layers. We further demonstrate tunneling current-tunable stochastic switching between multiple spin states of the CrI₃tunnel devices, which goes beyond conventional bi-stable stochastic magnetic tunnel junctions and has not been documented in two-dimensional magnets. Our findings not only address the existing knowledge gap concerning the influence of tunneling currents in controlling the magnetism in two-dimensional magnets, but also unlock possibilities for energy-efficient probabilistic and neuromorphic computing. 

Abstract Spin-orbit torques (SOT) enable efficient electrical control of the magnetic state of ferromagnets, ferrimagnets and antiferromagnets. However, the conventional SOT has severe limitation that only in-plane spins accumulate near the surface, whether interpreted as a spin Hall effect (SHE) or as an Edelstein effect. Such a SOT is not suitable for controlling perpendicular magnetization, which would be more beneficial for realizing low-power-consumption memory devices. Here we report the observation of a giant magnetic-field-like SOT in a topological antiferromagnet Mn₃Sn, whose direction and size can be tuned by changing the order parameter direction of the antiferromagnet. To understand the magnetic SHE (MSHE)- and the conventional SHE-induced SOTs on an equal footing, we formulate them as interface spin-electric-field responses and analyzed using a macroscopic symmetry analysis and a complementary microscopic quantum kinetic theory. In this framework, the large out-of-plane spin accumulation due to the MSHE has an inter-band origin and is likely to be caused by the large momentum-dependent spin splitting in Mn₃Sn. Our work demonstrates the unique potential of antiferromagnetic Weyl semimetals in overcoming the limitations of conventional SOTs and in realizing low-power spintronics devices with new functionalities. 

Charge transport in solids at low temperature reveals a material’s mesoscopic properties and structure. Under a magnetic field, Shubnikov–de Haas (SdH) oscillations inform complex quantum transport phenomena that are not limited by the ground state characteristics and have facilitated extensive explorations of quantum and topological interest in two- and three-dimensional materials. Here, in elemental metal Cr with two incommensurately superposed lattices of ions and a spin-density-wave ground state, we reveal that the phases of several low-frequency SdH oscillations in ${\sigma }_{\mathit{xx}} \left({\rho }_{\mathit{xx}}\right)$and ${\sigma }_{\mathit{yy}} \left({\rho }_{\mathit{yy}}\right)$are no longer identical but opposite. These relationships contrast with the SdH oscillations from normal cyclotron orbits that maintain identical phases between ${\sigma }_{\mathit{xx}} \left({\rho }_{\mathit{xx}}\right)$and ${\sigma }_{\mathit{yy}} \left({\rho }_{\mathit{yy}}\right)$ . We trace the origin of the low-frequency SdH oscillations to quantum interference effects arising from the incommensurate orbits of Cr’s superposed reciprocal lattices and explain the observed $\pi$-phase shift by the reconnection of anisotropic joint open and closed orbits.