Bulletin of the American Physical Society
2007 APS March Meeting
Volume 52, Number 1
Monday–Friday, March 5–9, 2007; Denver, Colorado
Session H3: Anomalous Hall Effect: Theory and Experiments |
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Sponsoring Units: DCMP Chair: Qian Niu, University of Texas at Dallas Room: Colorado Convention Center Korbel 2A-3A |
Tuesday, March 6, 2007 8:00AM - 8:36AM |
H3.00001: Intrinsic vs. extrinsic mechanisms of anomalous Hall effect Invited Speaker: Anomalous Hall effect (AHE) in ferromagnets has been a fundamental and intriguing issue in condensed-matter physics. Various mechanisms have been proposed, including the Karplus-Luttinger's band intrinsic mechanism, and extrinsic skew-scattering and side-jump mechanisms. However, the controversy on the mechanism has not been resolved yet. In this talk, a unified theory of the anomalous Hall effect (AHE) is presented for multi-band ferromagnetic metallic systems with dilute impurities [1], using the gauge-covariant formalism for the Keldysh Green's function [2]. In the clean limit, the AHE is mostly due to the extrinsic skew- scattering, and is sensitive to details of impurity potential. When the Fermi level is located around anti-crossing of band dispersions split by spin-orbit interaction, the intrinsic AHE to be calculated ab initio is resonantly enhanced by its non- perturbative nature. Then, an extrinsic-to-intrinsic crossover occurs when the relaxation rate is comparable to the spin-orbit interaction energy. Futher increasing the relaxation rate, a new scaling relation $\sigma_{xy}\propto\sigma_{xx}^{1.6}$ appears in the hopping-conduction regime. Various experimental data on transition-metals and oxcides are understood in terms of this theory [3]. \newline \newline [1] S. Onoda, N. Sugimoto, and N. Nagaosa, Phys. Rev. Lett. {\bf 97}, 126602 (2006). \newline [2] S. Onoda, N. Sugimoto, and N. Nagaosa, Prog. Theor. Phys. {\bf 116}, 61 (2006). \newline [3] T. Miyasato {\it et al.}, cond-mat/0610324. [Preview Abstract] |
Tuesday, March 6, 2007 8:36AM - 9:12AM |
H3.00002: The Anomalous Hall effect in MnSi and Fe$_x$TaS$_2$ Invited Speaker: In a high-purity ferromagnet with long carrier lifetime $\tau$, e.g. MnSi, the ordinary Hall conductivity $\sigma_H^N$ can dominate the intrinsic Anomalous Hall effect (AHE) conductivity $\sigma_H^A$. We show that the large magnetoresistance provides a way to separate accurately the two Hall currents. Below $T_C$, we find that the AHE conductivity is strictly proportional to the magnetization $M$, viz. $\sigma_H^A = S_HM$ with a parameter $S_H$ that is independent of both temperature $T$ and field $H$. This implies that $\sigma_H^A$ is strictly independent of $\tau$. In the layered, hard ferromagnet Fe$_x$TaS$_2$, the large coercivity leads to abrupt reversals of $M$ when it switches. We show that this provides an accurate way to separate $\sigma_H^A$ from $\sigma_H^N$. Again, $\sigma_H^A$ is independent of $T$ from 5 to 50 K. We compare the observed constancy at low $T$ with theories for the AHE. We also describe a Hall anomaly recently observed in MnSi under pressure. This anomaly appears to arise from strong sensitivity of the Hall current to the spin texture, possibly reflecting its finite chirality. The dependence of the anomaly to $T$ and $H$ will be reported. \newline \newline **This work is done in collaboration with Y. Onose, J. G. Checkelsky, E. Morosan, R. J. Cava, Y. Tokura and N. P. Ong. [Preview Abstract] |
Tuesday, March 6, 2007 9:12AM - 9:48AM |
H3.00003: Investigation of the Anomalous Hall Effect in Three Unusual Ferromagnets Invited Speaker: The Hall resistivity ($\rho _{xy})$, resistivity ($\rho _{xx})$, and magnetization of three metallic ferromagnets are investigated as a function of magnetic field and temperature [1]. The three ferromagnets, EuFe$_{4}$Sb$_{12}$ (T$_{c} \approx $ 84 K), Yb$_{14}$MnSb$_{11}$ (T$_{c}$ $\approx $ 53 K), and Eu$_{8}$Ga$_{16}$Ge$_{30}$ (T$_{c} \approx $ 36 K) are Zintl compounds with carrier concentrations between 1 x 10$^{21}$cm$^{-3}$ and 3.5 x 10$^{21}$ cm$^{-3}$. The relative decrease in $\rho_{xx}$ below T$_{c}$ [$\rho_{xx}$(T$_{c})$/$\rho_{xx}$(2 K)] is 28, 6.5, and 1.3 for EuFe$_{4}$Sb$_{12}$, Yb$_{14}$MnSb$_{11}$, and Eu$_{8}$Ga$_{16}$Ge$_{30}$ respectively. The low carrier concentrations coupled with low magnetic anisotropies allow a relatively clean separation between the anomalous ($\rho^{'}_{xy})$, and normal contributions to the measured Hall resistivity. For each compound the anomalous contribution in the zero field limit is fit to $a\rho _{xx}+\sigma _{xy} \rho_{xx}^{2}$ for temperatures T $<$T$_{c}$. The anomalous Hall conductivity, $\sigma _{xy}$, is -220 $\pm $ 5 ($\Omega ^{-1}$ cm$^{-1})$, -14.7 $\pm $ 1 ($\Omega ^{-1}$ cm$^{-1})$, and 28 $\pm $ 3 ($\Omega ^{-1}$ cm$^{-1})$ for EuFe$_{4}$Sb$_{12}$, Yb$_{14}$MnSb$_{11}$, and Eu$_{8}$Ga$_{16}$Ge$_{30}$ respectively and is independent of temperature for T $<$ T$_{c}$ if the change in spontaneous magnetization (order parameter) with temperature is taken into account. These data appear to be consistent with recent theories of the anomalous Hall effect that suggest that even for stochiometric ferromagnetic crystals, such as those studied in this work, the intrinsic Hall conductivity is finite at T = 0, and is a ground state property that can be calculated from the electronic structure. New measurements on single crystals of the tetragonal compound Yb$_{14}$MnSb$_{11}$, however, indicate that the intrinsic Hall conductivity can change sign, depending on the direction of the current and magnetic field with respect to the crystallographic axes. These new results will also be discussed within the context of recent theories. Research was done in collaboration with Rongying Jin, David Mandrus and Peter Khalifah. \newline \newline [1] B. C. Sales et al. Phys. Rev. B 73 (2006) 224435. [Preview Abstract] |
Tuesday, March 6, 2007 9:48AM - 10:24AM |
H3.00004: Ordinary and anomalous Hall effects of ferromagnetic Mn5Ge3 Invited Speaker: It is well know that in ferromagnetic materials, the Hall effect includes two contributions: the ordinary Hall effect (OHE), which is proportional to the applied magnetic field, and the anomalous Hall effect (AHE), which originates from the magnetization of the material. Although both phenomena have been throughly studied, there are still questions about the origins of both OHE and AHE in ferromagnetic materials with complicated band structures. Using ferromagnetic Mn5Ge3 thin films as an example, we investigate the Hall effect experimentally and theoretically. We have separated the intrinsic and extrinsic contributions to the experimental AHE and calculated the intrinsic anomalous Hall conductivity from the Berry curvature of the Bloch states using first-principles methods. The intrinsic anomalous Hall conductivity depends linearly on the magnetization, which can be understood from the long-wavelength fluctuations of the spin orientation at finite temperatures. The \textit{quantitative }agreement between theory and experiment is remarkably good, not only near 0 K but also at finite temperatures, up to about 240 K (0.8\textit{Tc}) [1]. The measured ordinary Hall coefficient is found to change its sign as a function of temperature. From a detailed analysis, which includes magneto-resistance measurements, magnetic characterization, and first-principles calculations, we establish that the sign change of the OHE is mainly caused by the mixing of the AHE with the magneto-resistance and differential susceptibility. This work was done in collaboration with Y. Yao, Di Xiao, Q. Niu, and H.H. Weitering. \newline \newline [1] Changgan Zeng, Yugui Yao, Qian Niu, and Hanno, H. Weitering, Phys. Rev. Lett. 96, 037204 (2006). [Preview Abstract] |
Tuesday, March 6, 2007 10:24AM - 11:00AM |
H3.00005: Berry phase, Orbital Magnetization, and Anomalous Hall/Nernst Effect Invited Speaker: It is now well recognized that the Berry phase of the electronic wave function plays an important role in the dynamics of Bloch electrons. For instance, the electron will acquire an anomalous velocity term transverse to the applied electric field, giving rise to an intrinsic contribution to the anomalous Hall effect. We have recently discovered that the Berry phase also modifies the phase-space density of states in the presence of a magnetic field. This surprising result has a number of implications, such as a field-dependent Fermi sea volume, Berry phase correction to the orbital magnetization, and linear (in field) magnetoresistance. Based on a general, finite-temperature, formula for orbital magnetization, we are able to develop a satisfactory theory for anomalous transport in ferromagnets driven by statistical forces (the gradient of temperature or chemical potential). Here a charge Hall current arises from the Berry-phase correction to the orbital magnetization rather than from the anomalous velocity, which does not exist in the absence of a mechanical force. We provide an explicit expression for the off-diagonal thermoelectric conductivity, establish the Mott relation between the anomalous Nernst and Hall effects, and reaffirm the Onsager relation between reciprocal thermoelectric conductivities. A first-principles evaluation of our expression is carried out for the material CuCr$_2$Se$_{4-x}$Br$_x$ , obtaining quantitative agreement with a recent experiment. This work is done in collaboration with Q. Niu, J.-R. Shi, Y.-G Yao, Z. Fang. \\ \\ 1. D. Xiao, J. Shi, and Q. Niu, Phys. Rev. Lett. {\bf 95}, 137204 (2005). \\ 2. D. Xiao, Y. Yao, Z. Fang, and Q. Niu, Phys. Rev. Lett. {\bf 97}, 026603 (2006). \\ 3. Y. Yao, \textit{et. al.}, cond-mat/0609714. [Preview Abstract] |
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