Chiral Hall Effect in Noncollinear Magnets from a Cyclic Cohomology Approach

Universal scaling law for chiral antiferromagnetism

The chiral antiferromagnetic (AFM) materials, which have been widely investigated due to their rich physics, such as non-zero Berry phase and topology, provide a platform for the development of antiferromagnetic spintronics. Here, we find two distinctive anomalous Hall effect (AHE) contributions in the chiral AFM Mn3Pt, originating from a time-reversal symmetry breaking induced intrinsic mechanism and a skew scattering induced topological AHE due to an out-of-plane spin canting with respect to the Kagome plane. We propose a universal AHE scaling law to explain the AHE resistivity (ρ A H ) in this chiral magnet, with both a scalar spin chirality (SSC)-induced skew scattering topological AHE term,a s k and non-collinear spin-texture induced intrinsic anomalous Hall term,b i n . We found thata s k andb i n can be effectively modulated by the interfacial electron scattering, exhibiting a linear relation with the inverse film thickness. Moreover, the scaling law can explain the anomalous Hall effect in various chiral magnets and has far-reaching implications for chiral-based spintronics devices.

Unified theory of the anomalous and topological Hall effects with phase-space Berry curvatures

Spontaneously broken time-reversal symmetry in magnetic materials leads to a Hall response, with a nonzero voltage transverse to an applied current, even in the absence of external magnetic fields. It is common to analyze the Hall resistivity of chiral magnets as the sum of two terms: an anomalous Hall effect arising from spin-orbit coupling and a topological Hall signal coming from skyrmions, which are topologically nontrivial spin textures. The theoretical justification for such a decomposition has long remained an open problem. Using a controlled semiclassical approach that includes all phase-space Berry curvatures, we show that the solution of the Boltzmann equation leads to a Hall resistivity that is just the sum of an anomalous term arising from momentum-space curvature and a topological term related to the real-space curvature. We also present numerically exact results from a Kubo formalism that complement the semiclassical approach.

Spin-orbit enabled all-electrical readout of chiral spin-textures

Chirality and topology are intimately related fundamental concepts, which are heavily explored to establish spin-textures as potential magnetic bits in information technology. However, this ambition is inhibited since the electrical reading of chiral attributes is highly non-trivial with conventional current perpendicular-to-plane (CPP) sensing devices. Here we demonstrate from extensive first-principles simulations and multiple scattering expansion the emergence of the chiral spin-mixing magnetoresistance (C-XMR) enabling highly efficient all-electrical readout of the chirality and helicity of respectively one- and two-dimensional magnetic states of matter. It is linear with spin-orbit coupling in contrast to the quadratic dependence associated with the unveiled non-local spin-mixing anisotropic MR (X-AMR). Such transport effects are systematized on various non-collinear magnetic states – spin-spirals and skyrmions – and compared to the uncovered spin-orbit-independent multi-site magnetoresistances. Owing to their simple implementation in readily available reading devices, the proposed magnetoresistances offer exciting and decisive ingredients to explore with all-electrical means the rich physics of topological and chiral magnetic objects.

One challenge for encoding information in chiral spin textures is how to read the information electrically. Here, Lima Fernandes et al. show that chiral spin textures exhibit a magnetoresistance signature which could allow for efficient electric readout of the chirality and helicity.

Transverse Transport in Two-Dimensional Relativistic Systems with Nontrivial Spin Textures

Using multiple scattering theory, we show that the generally accepted expression of transverse resistivity in magnetic systems that host skyrmions, given by the linear superposition of the ordinary, the anomalous, and the topological Hall effect, is incomplete and must be amended by an additional term, the "noncollinear" Hall effect (NHE). Its angular form is determined by the magnetic texture, the spin-orbit field of the electrons, and the underlying crystal structure, allowing us to disentangle the NHE from the various other Hall contributions. Its magnitude is proportional to the spin-orbit interaction strength. The NHE is an essential term required for decoding two- and three-dimensional spin textures from transport experiments.

Real-space observation of ferroelectrically induced magnetic spin crystal in SrRuO3

Unusual features in the Hall Resistivity of thin film systems are frequently associated with whirling spin textures such as Skyrmions. A host of recent investigations of Hall Hysteresis loops in SrRuO₃ heterostructures have provided conflicting evidence for different causes for such features. We have constructed an SrRuO₃-PbTiO₃ (Ferromagnetic – Ferroelectric) bilayer that exhibits features in the Hall Hysteresis previously attributed to a Topological Hall Effect, and Skyrmions. Here we show field dependent Magnetic Force Microscopy measurements throughout the key fields where the ‘THE’ presents, revealing the emergence to two periodic, chiral spin textures. The zero-field cycloidal phase, which then transforms into a ‘double-q’ incommensurate spin crystal appears over the appearance of the ‘Topological-like’ Hall effect region, and develop into a ferromagnetic switching regime as the sample reaches saturation, and the ‘Topological-like’ response diminishes. Scanning Tunnelling Electron Microscopy and Density Functional Theory is used to observe and analyse surface inversion symmetry breaking and confirm the role of an interfacial Dzyaloshinskii–Moriya interaction at the heart of the system.

There is an ongoing debate in the origin of unusual bumps in the resistive Hall measurements in SrRuO3 systems. Here, the authors analyze surface inversion symmetry breaking and confirm the role of an interfacial Dzyaloshinskii–Moriya interaction at the heart of the system, revealing a magnetic spin crystal emergent across the unusual bumps.

Giant anomalous Hall effect from spin-chirality scattering in a chiral magnet

The electrical Hall effect can be significantly enhanced through the interplay of the conduction electrons with magnetism, which is known as the anomalous Hall effect (AHE). Whereas the mechanism related to band topology has been intensively studied towards energy efficient electronics, those related to electron scattering have received limited attention. Here we report the observation of giant AHE of electron-scattering origin in a chiral magnet MnGe thin film. The Hall conductivity and Hall angle, respectively, reach [Formula: see text] Ω-1 cm-1 and [Formula: see text]% in the ferromagnetic region, exceeding the conventional limits of AHE of intrinsic and extrinsic origins, respectively. A possible origin of the large AHE is attributed to a new type of skew-scattering via thermally excited spin-clusters with scalar spin chirality, which is corroborated by the temperature-magnetic-field profile of the AHE being sensitive to the film-thickness or magneto-crystalline anisotropy. Our results may open up a new platform to explore giant AHE responses in various systems, including frustrated magnets and thin-film heterostructures.