We present a review of experimental and theoretical studies of the anomalous Hall effect (AHE), focusing on recent developments that have provided a more complete framework for understanding this subtle phenomenon and have, in many instances, replaced controversy by clarity. Synergy between experimental and theoretical work, both playing a crucial role, has been at the heart of these advances. On the theoretical front, the adoption of Berry-phase concepts has established a link between the AHE and the topological nature of the Hall currents which originate from spin-orbit coupling. On the experimental front, new experimental studies of the AHE in transition metals, transition-metal oxides, spinels, pyrochlores, and metallic dilute magnetic semiconductors, have more clearly established systematic trends. These two developments in concert with first-principles electronic structure calculations, strongly favor the dominance of an intrinsic Berry-phase-related AHE mechanism in metallic ferromagnets with moderate conductivity. The intrinsic AHE can be expressed in terms of Berry-phase curvatures and it is therefore an intrinsic quantum mechanical property of a perfect cyrstal. An extrinsic mechanism, skew scattering from disorder, tends to dominate the AHE in highly conductive ferromagnets. We review the full modern semiclassical treatment of the AHE together with the more rigorous quantum-mechanical treatments based on the Kubo and Keldysh formalisms, taking into account multiband effects, and demonstrate the equivalence of all three linear response theories in the metallic regime. Finally we discuss outstanding issues and avenues for future investigation.

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Anomalous hall effect

Strong electronic correlations are often associated with the proximity of a Mott-insulating state. In recent years however, it has become increasingly clear that the Hund’s rule coupling (intra-atomic exchange) is responsible for strong correlations in multiorbital metallic materials that are not close to a Mott insulator. Hund’s coupling has two effects: It influences the energetics of the Mott gap and strongly suppresses the coherence scale for the formation of a Fermi liquid. A global picture has emerged recently, which emphasizes the importance of the average occupancy of the shell as a control parameter. The most dramatic effects occur away from half-filling or single occupancy. We review the theoretical understanding and physical properties of these Hund’s metals, together with the relevance of this concept to transition-metal oxides (TMOs) of the 3d, and especially 4d, series (such as ruthenates), as well as to the iron-based superconductors (iron pnictides and chalcogenides).

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Strong Correlations from Hund’s Coupling

Correlated electron fluids can exhibit a startling array of complex phases, among which one of the more surprising is the electron nematic, a translationally invariant metallic phase with a spontaneously generated spatial anisotropy. Classicalnematicsgenerally occur in liquids of rod-like molecules; given that electrons are point like, the initial theoretical motivation for contemplating electron nematics came from thinking of the electron fluid as a quantum melted electron crystal, rather than a strongly interacting descendent of a Fermi gas. Dramatic transport experiments in ultra-clean quantum Hall systems in 1999 and in Sr3Ru2O7 in a strong magnetic field in 2007 established that such phases exist in nature. In this article, we briefly review the theoretical considerations governing nematic order, summarize the quantum Hall and Sr3Ru2O7 experiments that unambiguously establish the existence of this phase, and survey some of the current evidence for such a phase in the cuprate and Fe-based high temperature superconductors.

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Nematic Fermi Fluids in Condensed Matter Physics

Magnetic oxides show a variety of extrinsic magnetotransport phenomena: grain-boundary, tunnelling and domain-wall magnetoresistance. In view of these phenomena the role of some magnetic oxides is outstanding: these are believed to be half-metallic having only one spin-subband at the Fermi level. These fully spin-polarized oxides have great potential for applications in spin-electronic devices and have, accordingly, attracted intense research activity in recent years. This review is focused on extrinsic magnetotransport effects in ferromagnetic oxides. It consists of two parts; the second part is devoted to an overview of experimental data and theoretical models for extrinsic magnetotransport phenomena. Here a critical discussion of domain-wall scattering is given. Results on surface and interfacial magnetism in oxides are presented. Spin-polarized tunnelling in ferromagnetic junctions is reviewed and grain-boundary magnetoresistance is interpreted within a model of spin-polarized tunnelling through natural oxide barriers. The situation in ferromagnetic oxides is compared with data and models for conventional ferromagnets. The first part of the review summarizes basic material properties, especially data on the spin polarization and evidence for half-metallicity. Furthermore, intrinsic conduction mechanisms are discussed. An outlook on the further development of oxide spin-electronics concludes this review.

Extrinsic magnetotransport phenomena in ferromagnetic oxides

The concept of quantum criticality is proving to be central to attempts to understand the physics of strongly correlated electrons. Here, we argue that observations on the itinerant metamagnet Sr3Ru2O7 represent good evidence for a new class of quantum critical point, arising when the critical end point terminating a line of first-order transitions is depressed toward zero temperature. This is of interest both in its own right and because of the convenience of having a quantum critical point for which the tuning parameter is the magnetic field. The relationship between the resultant critical fluctuations and novel behavior very near the critical field is discussed.

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Magnetic field-tuned quantum criticality in the metallic ruthenate Sr3Ru2O7.

${\mathrm{SrRuO}}_{3}$ is a metallic ferromagnet. Its electrical resistivity is reported for temperatures up to 1000 K, its Hall coefficient for temperatures up to 300 K, and its specific heat for temperatures up to 230 K. The energy bands have been calculated by self-consistent spin-density functional theory, which finds a ferromagnetic ordered moment of 1.45${\mathrm{\ensuremath{\mu}}}_{\mathit{B}}$ per Ru atom. The measured linear specific heat coefficient \ensuremath{\gamma} is 30 mJ/mol, which exceeds the theoretical value by a factor of 3.7. A transport mean free path at room temperature of \ensuremath{\approxeq}10 \AA{} is found. The resistivity increases nearly linearly with temperature to 1000 K in spite of such a short mean free path that resistivity saturation would be expected. The Hall coefficient is small and positive above the Curie temperature, and exhibits both a low-field and a high-field anomalous behavior below the Curie temperature. \textcopyright{} 1996 The American Physical Society.

https://arxiv.org/pdf/cond-mat/9601106.pdf

P. B. Allen

Papers

Transport properties, thermodynamic properties, and electronic structure of SrRuO3.