<i>Ab Initio</i>Theory of the Scattering-Independent Anomalous Hall Effect

Weischenberg, Jürgen; Freimuth, Frank; Sinova, Jairo; Blügel, Stefan; Mokrousov, Yuriy

doi:10.1103/physrevlett.107.106601

Cited by 74 publications

(90 citation statements)

References 29 publications

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“…The latter is suppressed for ferromagnets away from the clean regime, as expected in doped systems like Mn 1−x Fe x Si. We have further estimated the extrinsic side-jump contribution to the AHE and find not more than 10% of the intrinsic values [34]. Hence, the calculated AHC is in excellent agreement with experiment as concerns (i) the magnitude, (ii) the change of sign, and (iii) the reduction of the AHC under Fe doping.…”

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confidence: 66%

Real-Space and Reciprocal-Space Berry Phases in the Hall Effect ofMn1−xFexSi

et al. 2014

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We report an experimental and computational study of the Hall effect in Mn1−xFexSi, as complemented by measurements in Mn1−xCoxSi, when helimagnetic order is suppressed under substitutional doping. For small x the anomalous Hall effect (AHE) and the topological Hall effect (THE) change sign. Under larger doping the AHE remains small and consistent with the magnetization, while the THE grows by over a factor of ten. Both the sign and the magnitude of the AHE and the THE are in excellent agreement with calculations based on density functional theory. Our study provides the long-sought material-specific microscopic justification, that while the AHE is due to the reciprocal-space Berry curvature, the THE originates in real-space Berry phases.PACS numbers: 71.15.Mb, 71.20.Be Measurements of the Hall effect in chiral magnets with B20 crystal structure have recently attracted great interest [1][2][3][4][5][6][7]. Due to a hierarchy of energy scales [8], comprising in decreasing strength ferromagnetic exchange, Dzyaloshinsky-Moriya (DM) spin-orbit interactions, and higher order spin-orbit coupling terms, magnetic order in these systems displays generically long-wavelength helical modulations. Under a small applied magnetic field this hierarchy of energy scales stabilizes a skyrmion lattice phase (SLP) in the vicinity of the magnetic transition temperature, i.e., a lattice composed of topologically non-trivial whirls of the magnetization [9-16]. The Hall effect, which has been studied most extensively in MnSi [1][2][3][17][18][19], displays thereby three contributions, notably an ordinary Hall effect (OHE), an anomalous Hall effect (AHE) related to the uniform magnetization, and an additional topological Hall effect (THE) in the SLP due to the non-trivial topology of the spin order.It was only recently noticed that the THE and AHE represent the real-and reciprocal-space limits of generalised phase-space Berry phases of the conduction electrons, respectively. First principles calculations in MnSi suggest that these phase-space Berry phases account quantitatively for the DM interaction and may even give rise to an electric charge of the skyrmions [20,21]. However, so far perhaps most spectacular because of the experimental evidence is the notion that the non-trivial topological winding of skyrmions gives rise to Berry phases in real space that may be viewed as an emergent magnetic field B eff = Φ 0 Φ of one flux quantum (Φ 0 = h/e) times the winding number Φ = −1 per skyrmion [1]. The same mechanism also leads to large spin transfer torques in MnSi [22,23] and FeGe at ultralow current densities. In turn, a very large THE in MnGe [4] and SrFeO 3 [5] has fuelled speculations that the emergent fields may even approach the quantum limit.Despite this wide range of interest, the account of Berry phases in the Hall effect has been essentially phenomenological, in particular for the THE, while a material-specific microscopic justification has been missing. This situation is aggravated by the microscopic sensitivity of the TH...

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confidence: 66%

Real-Space and Reciprocal-Space Berry Phases in the Hall Effect ofMn1−xFexSi

et al. 2014

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“…The formation energies and thermodynamics of these defects have been thoroughly studied [19], but their influence on transport and optical properties remains largely unexplored. Modeling the effects of disorder from first principles is a challenging task in general, but there are noteworthy examples where the AHC in ferromagnetic materials has been calculated using the coherent potential approximation [20][21][22][23][24][25]; also, an ab initio implementation of the side-jump contribution to the AHC has been carried out assuming scattering centers with δ-function potentials [26].…”

Section: Monolayers Of Mosmentioning

confidence: 99%

Valley Hall effect in disordered monolayerMoS2from first principles

Olsen

Souza

2015

Phys. Rev. B

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Electrons in certain two-dimensional crystals possess a pseudospin degree of freedom associated with the existence of two inequivalent valleys in the Brillouin zone. If, as in monolayer MoS 2 , inversion symmetry is broken and time-reversal symmetry is present, equal and opposite amounts of k-space Berry curvature accumulate in each of the two valleys. This is conveniently quantified by the integral of the Berry curvature over a single valley-the valley Hall conductivity. We generalize this definition to include contributions from disorder described with the supercell approach, by mapping ("unfolding") the Berry curvature from the folded Brillouin zone of the disordered supercell onto the normal Brillouin zone of the pristine crystal, and then averaging over several realizations of disorder. We use this scheme to study from first principles the effect of sulfur vacancies on the valley Hall conductivity of monolayer MoS 2 . In dirty samples the intrinsic valley Hall conductivity receives gating-dependent corrections that are only weakly dependent on the impurity concentration, consistent with side-jump scattering and the unfolded Berry curvature can be interpreted as a k-space resolved side jump. At low impurity concentrations skew scattering dominates, leading to a divergent valley Hall conductivity in the clean limit. The implications for the recently observed photoinduced anomalous Hall effect are discussed.

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“…Although it is caused by the presence of impurities in a host, the corresponding contribution to the spin Hall conductivity does not depend on their concentration [5]. Furthermore, for uncorrelated short-range disorder it is even independent of the type of impurities [17]. In contrast to the skew scattering, the side-jump mechanism is not only caused by the vertex corrections but has a contribution independent of them [5].…”

Section: Introductionmentioning

confidence: 98%

Separation of the individual contributions to the spin Hall effect in dilute alloys within the first-principles Kubo-Středa approach

et al. 2015

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We present a procedure for the separation of the intrinsic, side-jump, and skew-scattering contributions to the spin Hall conductivity within the ab initio Kubo-Středa approach. Furthermore, two distinct contributions to the side-jump mechanism, either independent of the vertex corrections or solely caused by them, are quantified as well. This allows for a detailed analysis of individual microscopic contributions to the spin Hall effect. The efficiency of the proposed method is demonstrated by a first-principles study of dilute metallic alloys based on Cu, Au, and Pt hosts.

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Ab InitioTheory of the Scattering-Independent Anomalous Hall Effect

Cited by 74 publications

References 29 publications

Real-Space and Reciprocal-Space Berry Phases in the Hall Effect ofMn1−xFexSi

Real-Space and Reciprocal-Space Berry Phases in the Hall Effect ofMn1−xFexSi

Valley Hall effect in disordered monolayerMoS2from first principles

Separation of the individual contributions to the spin Hall effect in dilute alloys within the first-principles Kubo-Středa approach

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