Masaki Uchida

Recent observation of anomalous Hall effect (AHE) induced by magnetic field or spin magnetization lying in the Hall deflection plane has sparked interest in diverse mechanisms for inducing the Hall vector component perpendicular to the applied magnetic field. Such off‐diagonal coupling, which is strictly constrained by symmetry of the system, provides new degrees of freedom for engineering Hall responses. However, spontaneous response as extensively studied for out‐of‐plane AHE remains unexplored. Here, in‐plane AHE in a typical ferromagnetic oxide SrRuO ₃ is elucidated. The (111)‐orientated ultrathin films with in‐plane easy axes of spin magnetization exhibit spontaneous AHE at zero field, which is intrinsically coupled to the in‐plane spin magnetization and controllable via its direction. Systematic measurements by varying azimuthal and polar field angles further reveal complex Hall responses shaped by higher‐order terms allowed by trigonal distortion of the films. These findings highlight versatile and controllable in‐plane Hall responses with out‐of‐plane orbital ferromagnetism.

Intrinsic anomalous Hall effect (AHE) formulated by geometric properties of Bloch wave functions is a ubiquitous transport phenomenon not limited to magnetic systems but also allowed in nonmagnetic ones under an external field breaking time-reversal symmetry. On the other hand, detection of field-induced AHE is practically challenging because the band modulation through the Zeeman and spin-orbit couplings is typically small compared to other contributions as induced by the Lorentz force. Here, we demonstrate on Dirac semimetal Cd_{3}As_{2} films that the field-induced AHE in nonmagnetic systems can be quantitatively probed by applying and rotating the magnetic field within the Hall deflection plane. Measurements on the Cd_{3}As_{2} (112) plane reveal that AHE emerges as a clear threefold symmetric component for the in-plane field rotation. This intrinsic response becomes more pronounced in ultralow-electron-density films where significant variations in the geometric properties are expected under the magnetic field. Our findings open new opportunities in the research of Hall responses manifested as orbital magnetization in nonmagnetic systems.

The Hall effect, particularly that arising from in-plane magnetic field, has recently emerged as a sensitive probe of quantum geometric properties in solids. Especially in trigonal systems, in-plane anomalous Hall effect (AHE) can be explicitly induced by nontrivial off-diagonal coupling between the magnetic field and the Hall vector on the principal plane. Here we elucidate multipolar dependence of the off-diagonal coupling in the in-plane AHE, by systematically measuring on the (001) principal plane of trigonal antiferromagnet EuCd2Sb2 thin films for each magnetic phase. Around zero field, magneto-cubic dependence of anomalous Hall resistivity is clearly observed not only in the paramagnetic phase but also even in the antiferromagnetic phase. An off-diagonal component of the octupolar tensor also exhibits unconventional decay above the magnetic ordering temperature, roughly depending on the inverse temperature to the third power. In the forced ferromagnetic phase, on the other hand, magneto-linear dependence dominantly appears and notably persists up to very high fields. Our findings clarify key aspects of the off-diagonal coupling in the in-plane AHE, paving the way for its future investigations and potential applications beyond conventional expectations about the Hall effect.

Recent observation of the in-plane anomalous Hall effect in magnetic Weyl semimetal EuCd2Sb2 has drawn attention to out-of-plane orbital magnetization induced by an in-plane field component. Here we study EuZn2Sb2, a sister compound of EuCd2Sb2, to demonstrate sensitive changes of the in-plane anomalous Hall effect on the band modulation. The Hall resistivity measured with rotating the magnetic field within the (001) principal plane of EuZn2Sb2 films exhibits a clear three-fold component corresponding to the in-plane anomalous Hall effect, which is distinct from the two-fold component of the planar Hall effect. The in-plane anomalous Hall effect of EuZn2Sb2 is highly contrasting to EuCd2Sb2, especially in terms of its opposite sign and field dependence, which can be explained by model calculations with different band inversion parameters. Our results pave the way for systematically controlling the in-plane anomalous Hall effect and orbital magnetization through elaborate band engineering.

Intrinsic anomalous Hall effect (AHE) formulated by geometric properties of Bloch wavefunctions is a ubiquitous transport phenomenon not limited to magnetic systems but also allowed in non-magnetic ones under an external field breaking time-reversal symmetry. On the other hand, detection of field-induced AHE is practically challenging because the band modulation through the Zeeman and spin-orbit couplings is typically small compared to other contributions as induced by the Lorentz force. Here, we demonstrate on Dirac semimetal Cd$_3$As$_2$ films that the field-induced AHE in non-magnetic systems can be quantitatively probed by applying and rotating the magnetic field within the Hall deflection plane. Measurements on the Cd$_3$As$_2$ (112) plane reveal that AHE emerges as a clear three-fold symmetric component for the in-plane field rotation. This intrinsic response becomes more pronounced in ultralow-electron-density films where significant variations in the geometric properties are expected under the magnetic field. Our findings open new opportunities in the research of Hall responses manifested as orbital magnetization in non-magnetic systems.