Topological Nature of Anomalous Hall Effect in Ferromagnets

Onoda, Masaru; Nagaosa, Naoto

doi:10.1143/jpsj.71.19

Cited by 378 publications

(388 citation statements)

References 38 publications

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“…the perturbation β or x −x, 2. it revelaed that there are different types of gauge field of different physical origin, 3. it was useful for developing symmetry analyses on various types of Berry phase transport.…”

Section: Discussionmentioning

confidence: 99%

“…(25,28) and the MM in momentum space has been of much theoretical interest. [3,4,10,31]. From a more general point of view, physics in noncommutative space-time coordinates has been of great theoretical interest, rather in high-energy physics community, in particular, in the context of string and M theories.…”

Section: Origin Of the Gauge Fieldmentioning

confidence: 99%

“…[22] Recently, the Berry phase in AHE has attracted a renewed attention, revealing its rich topological structures. [3,4,6,7,23,24,25,26] The Berry phase has also been generalized to a non-Abelian case. [27] The equations of motion (EOM) for a wave packet of Bloch functions 1 is instrumental in all the analyses done in the paper.…”

Section: Introductionmentioning

confidence: 99%

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Noncommutative geometry and non-Abelian Berry phase in the wave-packet dynamics of Bloch electrons

2005

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Motivated by a recent proposal on the possibility of observing a monopole in the band structure, and by an increasing interest on the role of Berry phase in spintronics, we studied the adiabatic motion of a wave packet of Bloch functions, under a perturbation varying slowly and incommensurately to the lattice structure. We show, using only the fundamental principles of quantum mechanics, that the effective wave-packet dynamics is conveniently described by a set of equations of motion (EOM) for a semiclassical particle coupled to a nonabelian gauge field associated with a geometric Berry phase.Our EOM can be viewed as a generalization of the standard Ehrenfest's theorem, and their derivation was asymptotically exact in the framework of linear response theory. Our analysis is entirely based on the concept of local Bloch bands, a good starting point for describing the adiabatic motion of a wave packet. One of the advantages of our approach is that the various types of gauge fields were classified into two categories by their different physical origin: (i) projection onto specific bands, (ii) timedependent local Bloch basis. Using those gauge fields, we write our EOM in a covariant form, whereas the gauge-invariant field strength stems from the noncommutativity of covariant derivatives along different axes of the reciprocal parameter space. On the other hand, the degeneracy of Bloch bands makes the gauge fields nonabelian.For the purpose of applying our wave-packet dynamics to the analyses on transport phenomena in the context of Berry phase engineering, we focused on the Hall-type and polarization currents. Our formulation turned out to be useful for investigating and classifying various types of topological current on the same footing. We highlighted their symmetries, in particular, their behavior under time reversal (T ) and space inversion (I).

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Section: Discussionmentioning

confidence: 99%

Section: Origin Of the Gauge Fieldmentioning

confidence: 99%

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Noncommutative geometry and non-Abelian Berry phase in the wave-packet dynamics of Bloch electrons

2005

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“…[10][11][12][13] Interest has also been increased by the ͑phenomenological͒ demonstration that a relatively simple intrinsic contribution that is a momentum-space Berry phase band-structure property dominates the AHE in many ferromagnets. [14][15][16][17][18][19][20][21][22] From one point of view, the main reason for the physical opaqueness of formal microscopic approaches to the AHE is that the Hall current is much weaker than the current parallel to the electric field. No Hall contribution appears in usual theories of the dc conductivity which use Gaussian disorder potential distribution models and evaluate conductivity to the leading order of the small parameter =1/͑k F l sc ͒, where l sc is the disorder scattering length.…”

Section: Introductionmentioning

confidence: 99%

Anomalous Hall effect in a two-dimensional Dirac band: The link between the Kubo-Streda formula and the semiclassical Boltzmann equation approach

et al. 2007

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The anomalous Hall effect ͑AHE͒ is a consequence of spin-orbit coupling in a ferromagnetic metal and related primarily to density-matrix response to an electric field that is off-diagonal in band index. For this reason disorder contributions to the AHE are difficult to treat systematically using a semiclassical Boltzmann equation approach, even when weak localization corrections are disregarded. In this article we explicitly demonstrate the equivalence of an appropriately modified semiclassical transport theory which includes anomalous velocity and side-jump contributions and microscopic Kubo-Streda perturbation theory, with particular unconventional contributions in the semiclassical theory identified with particular Feynman diagrams when calculations are carried out in a band-eigenstate representation. The equivalence we establish is verified by explicit calculations for the case of the two-dimensional Dirac model Hamiltonian relevant to graphene.

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“…Theoretical studies of the AHE have a long history beginning with the work of Karplus and Luttinger. 5 A number of papers on the AHE also appeared not so long ago [6][7][8][9][10][11][12] after the interpretation of the AHE based on the Berry phase 13 was proposed. Nevertheless, theoretical description of the AHE is far from being complete and it often involves cumbersome calculations without transparent interpretations.…”

Section: Introductionmentioning

confidence: 99%

Transport theory for disordered multiple-band systems: Anomalous Hall effect and anisotropic magnetoresistance

et al. 2009

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We present a study of transport in multiple-band noninteracting Fermi metallic systems based on the Keldysh formalism and the self-consistent T-matrix approximation ͑TMA͒ taking into account the effects of Berry curvature due to spin-orbit coupling. We apply this formalism to a Rashba two-dimensional electron-gas ferromagnet and calculate the anomalous Hall effect ͑AHE͒ and anisotropic magnetoresistance ͑AMR͒. The numerical calculations of the AHE reproduce analytical results in the metallic regime revealing the crossover between the skew-scattering mechanism dominating in the clean systems and intrinsic mechanism dominating in the moderately dirty systems. As we increase the disorder further, the AHE starts to diminish due to the spectral broadening of the quasiparticles. Although for certain parameters this reduction of the AHE can be approximated as xy ϳ xx , with varying around 1.6, this is found not to be true in general as xy can go through a change in sign as a function of disorder strength in some cases. Furthermore, the disordered region consistent with the TMA is relatively narrow and a theory with a wider range of applicability in strong disorder limit is called for. By considering the higher order skew-scattering processes, we resolve some discrepancies between the AHE results obtained by using the Keldysh, Kubo, and Boltzmann approaches. We also show that similar higher order processes are important for the AMR when the nonvertex and vertex parts cancel each other. We calculate the AMR in anisotropic systems properly taking into account the anisotropy of the nonequilibrium distribution function. These calculations confirm recent findings on the unreliability of common approximations to the Boltzmann equation.

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Topological Nature of Anomalous Hall Effect in Ferromagnets

Cited by 378 publications

References 38 publications

Noncommutative geometry and non-Abelian Berry phase in the wave-packet dynamics of Bloch electrons

Noncommutative geometry and non-Abelian Berry phase in the wave-packet dynamics of Bloch electrons

Anomalous Hall effect in a two-dimensional Dirac band: The link between the Kubo-Streda formula and the semiclassical Boltzmann equation approach

Transport theory for disordered multiple-band systems: Anomalous Hall effect and anisotropic magnetoresistance

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