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Register a new userUniversal Scaling Behavior of Anomalous Hall Effect and Anomalous Nernst Effect in Itinerant Ferromagnets
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Anomalous Hall effect (AHE) and anomalous Nernst effect (ANE) in a variety of ferromagnetic metals including pure metals, oxides, and chalcogenides, are studied to obtain unified understandings of their origins. We show a universal scaling behavior of anomalous Hall conductivity $sigma_{xy}$ as a function of longitudinal conductivity $sigma_{xx}$ over five orders of magnitude, which is well explained by a recent theory of the AHE taking into account both the intrinsic and extrinsic contributions. ANE is closely related with AHE and provides us with further information about the low-temperature electronic state of itinerant ferromagnets. Temperature dependence of transverse Peltier coefficient $alpha_{xy}$ shows an almost similar behavior among various ferromagnets, and this behavior is in good agreement quantitatively with that expected from the Mott rule.
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The anomalous Hall effect (AHE) has been studied systematically in the low-conductivity ferromagnetic oxide Fe$_{3-x}$Zn$_x$O$_4$ with $x = 0$, 0.1, and 0.5. We used (001), (110), and (111) oriented epitaxial Fe$_{3-x}$Zn$_x$O$_4$ films grown on MgO and sapphire substrates in different oxygen partial pressure to analyze the dependence of the AHE on crystallographic orientation, Zn content, strain state, and oxygen deficiency. Despite substantial differences in the magnetic properties and magnitudes of the anomalous Hall conductivity $sigma_{xy}^{rm AHE}$ and the longitudinal conductivity $sigma_{xx}$ over several orders of magnitude, a universal scaling relation $sigma_{xy}^{rm AHE} propto sigma_{xx}^{alpha}$ with $alpha = 1.69 pm 0.08$ was found for all investigated samples. Our results are in agreement with recent theoretical and experimental findings for ferromagnetic metals in the dirty limit, where transport is by metallic conduction. We find the same scaling relation for magnetite, where hopping transport prevails. The fact that this relation is independent of crystallographic orientation, Zn content, strain state, and oxygen deficiency suggests that it is universal and particularly does not depend on the nature of the transport mechanism.
Utilizing the first-principles density functional theory calculations together with group theory analyses, we systematically investigate the spin order-dependent magneto-optical effect (MOE), anomalous Hall effect (AHE), and anomalous Nernst effect (ANE) in a recently discovered two-dimensional room-temperature ferromagnet $1T$-CrTe$_2$. We find that the spin prefers an in-plane direction by the magnetocrystalline anisotropy energy calculations. The MOE, AHE, and ANE display a period of $2pi/3$ when the spin rotates within the atomic plane, and they are forbidden if there exists a mirror plane perpendicular to the spin direction. By reorienting the spin from in-plane to out-of-plane direction, the MOE, AHE, and ANE are enhanced by around one order of magnitude. Moreover, we establish the layer-dependent magnetic properties for multilayer $1T$-CrTe$_2$ and predict antiferromagnetism and ferromagnetism for bilayer and trilayer $1T$-CrTe$_2$, respectively. The MOE, AHE, and ANE are prohibited in antiferromagnetic bilayer $1T$-CrTe$_2$ due to the existence of the spacetime inversion symmetry, whereas all of them are activated in ferromagnetic trilayer $1T$-CrTe$_2$ and the MOE is significantly enhanced compared to monolayer $1T$-CrTe$_2$. Our results show that the magneto-optical and anomalous transports proprieties of $1T$-CrTe$_2$ can be effectively modulated by altering spin direction and layer number.
A short review paper for the quantum anomalous Hall effect. A substantially extended one is published as Adv. Phys. 64, 227 (2015).
In metallic ferromagnets, the Berry curvature of underlying quasiparticles can cause an electric voltage perpendicular to both magnetization and an applied temperature gradient, a phenomenon called the anomalous Nernst effect (ANE). Here, we report the observation of a giant ANE in the full-Heusler ferromagnet Co$_2$MnGa, reaching $S_{yx}sim -6$ $mu$V/K at room $T$, one order of magnitude larger than the maximum value reported for a magnetic conductor. With increasing temperature, the transverse thermoelectric conductivity or Peltier coefficient $alpha_{yx}$ shows a crossover between $T$-linear and $-T log(T)$ behaviors, indicating the violation of Mott formula at high temperatures. Our numerical and analytical calculations indicate that the proximity to a quantum Lifshitz transition between type-I and type-II magnetic Weyl fermions is responsible for the observed crossover properties and an enhanced $alpha_{yx}$. The $T$ dependence of $alpha_{yx}$ in experiments and numerical calculations can be understood in terms of a quantum critical scaling function predicted by the low energy effective theory over more than a decade of temperatures. Moreover, the observation of chiral anomaly or an unsaturated positive longitudinal magnetoconductance also provide evidence for the existence of Weyl fermions in Co$_2$MnGa.
Thermoelectric properties of a model Skyrmion crystal were theoretically investigated, and it was found that its large anomalous Hall conductivity, corresponding to large Chern numbers induced by its peculiar spin structure leads to a large transverse thermoelectric voltage through the anomalous Nernst effect. This implies the possibility of finding good thermoelectric materials among Skyrmion systems, and thus motivates our quests for them by means of the first-principles calculations as were employed here.
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