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Register a new userIntrinsic Second-Order Anomalous Hall Effect and Its Application in Compensated Antiferromagnets
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Response properties that are purely intrinsic to physical systems are of paramount importance in physics research, as they probe fundamental properties of band structures and allow quantitative calculation and comparison with experiment. For anomalous Hall transport in magnets, an intrinsic effect can appear at the second order to the applied electric field. We show that this intrinsic second-order anomalous Hall effect is associated with an intrinsic band geometric property -- the dipole moment of Berry-connection polarizability (BCP) in momentum space. The effect has scaling relation and symmetry constraints that are distinct from the previously studied extrinsic contributions. Particularly, in antiferromagnets with $mathcal{PT}$ symmetry, the intrinsic effect dominates. Combined with first-principles calculations, we demonstrate the first quantitative evaluation of the effect in the antiferromagnet Mn$_{2}$Au. We show that the BCP dipole and the resulting intrinsic second-order conductivity are pronounced around band near degeneracies. Importantly, the intrinsic response exhibits sensitive dependence on the N{e}el vector orientation with a $2pi$ periodicity, which offers a new route for electric detection of the magnetic order in $mathcal{PT}$-invariant antiferromagnets.
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The amorphous iron-germanium system ($a$-Fe$_x$Ge$_{1-x}$) lacks long-range structural order and hence lacks a meaningful Brillouin zone. The magnetization of aFeGe is well explained by the Stoner model for Fe concentrations $x$ above the onset of magnetic order around $x=0.4$, indicating that the local order of the amorphous structure preserves the spin-split density of states of the Fe-$3d$ states sufficiently to polarize the electronic structure despite $mathbf{k}$ being a bad quantum number. Measurements reveal an enhanced anomalous Hall resistivity $rho_{xy}^{mathrm{AH}}$ relative to crystalline FeGe; this $rho_{xy}^{mathrm{AH}}$ is compared to density functional theory calculations of the anomalous Hall conductivity to resolve its underlying mechanisms. The intrinsic mechanism, typically understood as the Berry curvature integrated over occupied $mathbf{k}$-states but shown here to be equivalent to the density of curvature integrated over occupied energies in aperiodic materials, dominates the anomalous Hall conductivity of $a$-Fe$_x$Ge$_{1-x}$ ($0.38 leq x leq 0.61$). The density of curvature is the sum of spin-orbit correlations of local orbital states and can hence be calculated with no reference to $mathbf{k}$-space. This result and the accompanying Stoner-like model for the intrinsic anomalous Hall conductivity establish a unified understanding of the underlying physics of the anomalous Hall effect in both crystalline and disordered systems.
The anomalous Hall effect has been indispensable in our understanding of numerous magnetic phenomena. This concerns both ferromagnetic materials, as well as diverse classes of antiferromagnets, where in addition to the anomalous and crystal Hall effects, the topological Hall effect in non-coplanar antiferromagnets has been a subject of intensive research in the past decades. Here, we uncover a new flavour of the anomalous Hall effect in canted spin systems. Using advanced theoretical tools we demonstrate that upon canting, the anomalous Hall effect acquires a contribution which is sensitive to the sense of imprinted vector chirality among spins. We explore the origins and basic properties of corresponding chiral Hall effect, and closely tie it to the symmetry properties of the system. Our findings suggest that the chiral Hall effect and corresponding chiral magneto-optical effects emerge as novel versatile tools in characterizing an interplay of structure and chirality in complex magnets, as well as in tracking their chiral dynamics and fluctuations.
We predict an anomalous thermal Hall effect (ATHE) mediated by photons in networks of Weyl semi-metals. Contrary to the photon thermal Hall effect in magneto-optical systems which requires the application of an external magnetic field the ATHE in a Weyl semi-metals network is an intrinsic property of these systems. Since the Weyl semi-metals can exhibit a strong nonreciprocal response in the infrared over a broad spectral range the magnitude of thermal Hall flux in these systems can be relatively large compared to the primary flux. This ATHE paves the way for a directional control of heat flux by localy tuning the magnitude of temperature field without changing the direction of temperature gradient.
We study the mechanisms of the spin Hall effect (SHE) and anomalous Hall effect (AHE) in 3$d$ ferromagnetic metals (Fe, Co, permalloy (Ni$_{81}$Fe$_{19}$; Py), and Ni) by varying their resistivities and temperature. At low temperatures where the phonon scattering is negligible, the skew scattering coefficients of the SHE and AHE in Py are related to its spin polarization. However, this simple relation breaks down for Py at higher temperatures as well as for the other ferromagnetic metals at any temperature. We find that, in general, the relation between the SHE and AHE is more complex, with the temperature dependence of the SHE being much stronger than that of AHE.
The nonlinear Hall effect is mostly studied as a Berry curvature dipole effect in nonmagnetic materials, which depends linearly on the relaxation time. On the other hand, in magnetic materials, an intrinsic nonlinear Hall effect can exist, which does not depend on the relaxation time. Here we show that the intrinsic nonlinear Hall effect can be observed in an antiferromagnetic metal: tetragonal CuMnAs, and the corresponding conductivity can reach the order of mA/V$^2$ based on density functional theory calculations. The dependence on the chemical potential of such nonlinear Hall conductivity can be qualitatively explained by a tilted massive Dirac model. Moreover, we demonstrate its strong temperature-dependence and briefly discuss its competition with the second order Drude conductivity. Finally, a complete survey of magnetic point groups are presented, providing guidelines for finding candidate materials with the intrinsic nonlinear Hall effect.
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