Universal scaling of the anomalous Hall effect in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mi>Fe</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn>4</mml:mn></mml:msub></mml:mrow></mml:math>epitaxial thin films

Fernández-Pacheco, Amalio; Teresa, J. M. De; Orna, J.; Morellón, L.; Algarabel, P. A.; Pardo, J. A.; Ibarra, M. R.

doi:10.1103/physrevb.77.100403

Cited by 62 publications

(55 citation statements)

References 29 publications

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“…21 Furthermore, the xy AHE ϰ xx 1.6 scaling has been found for several lowconductivity materials independent of the details of the underlying transport mechanism ͑hopping or metallic conduction͒. [21][22][23][24][25] This is quite surprising and not understood in detail so far. Although theoretical models have been proposed for the AHE in low-conductivity ferromagnetic materials, 10,17 where transport is dominated by hopping, or in the Hall insulator phase, 26 no complete theoretical understanding has been developed.…”

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confidence: 85%

Anomalous Hall effect in magnetite: Universal scaling relation between Hall and longitudinal conductivity in low-conductivity ferromagnets

et al. 2008

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The anomalous Hall effect ͑AHE͒ 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 ͑001͒, ͑110͒, and ͑111͒ 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 xy AHE and the longitudinal conductivity xx over several orders of magnitude, a universal scaling relation xy AHE ϰ xx ␣ with ␣ = 1.69Ϯ 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.The physics of the Hall effect in ferromagnetic materials is discussed intensively and controversially since the 1950s. Early experimental work on ferromagnetic metals suggested that the Hall resistivity can be described by the empirical relation xy = R O 0 H + R A 0 M, where H is the applied magnetic field and M the spontaneous magnetization of the ferromagnet. The first term, proportional to H and characterized by the ordinary Hall coefficient R O , describes the ordinary Hall effect ͑OHE͒, whereas the second term, proportional to M and characterized by the anomalous Hall coefficient R A , represents the anomalous Hall effect ͑AHE͒. Although the AHE is generally observed in ferromagnetic metals and semiconductors, its origin has been one of the most intriguing and controversial issues in solid-state physics, and various theories based on intrinsic and extrinsic mechanisms have been proposed. 1-5 Whereas the extrinsic origins of the AHE are based on skew scattering 2,3 and side jump 4,5 mechanisms due to spin-orbit interaction connecting the spin polarization with the orbital motion of electrons, the intrinsic origin of the AHE is closely related to the Berry phase 6 of the Bloch electrons. 1,7-13 The dissipationless and topological nature of the intrinsic mechanism has attracted much attention recently, and various first-principles band-structure calculations have been performed to explain the AHE in transition metals, 14,15 ferromagnetic semiconductors, 9,10,16 and oxides. [17][18][19][20] A powerful experimental test for AHE models is the measurement of the scaling of the anomalous Hall resistivity ͑conductivity͒ xy AHE ͑ xy AHE ͒ with the longitudinal resistivity ͑conductivity͒ xx ͑ xx ͒. The skew scattering and side jump mechanisms are known to yield xy AHE ϰ xx ͑ xy AHE ϰ xx ͒ and xy AHE ϰ xx 2 ͑ xy AHE ϳ const͒, respectively. Recently, a unifie...

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Anomalous Hall effect in magnetite: Universal scaling relation between Hall and longitudinal conductivity in low-conductivity ferromagnets

et al. 2008

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“…We further analyze the scaling found in the dirty regime 1,20 in which the AHE seems to diminish in a manner that can be approximated as xy ϳ xx , with being close to 1.6. Some experimental results claim to confirm such scaling; [37][38][39][40][41] however, treatment of some of these experimental results has to be done with extra care as the region of interest is often restricted to less than a single decade, the materials have strong mangetoresistances and in-plane anisotropies associated with them, and most of the data associated with the zero-field calculation are in fact at very high magnetic fields.…”

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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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“…This scaling has been experimentally found in a large series of low-conductivity compounds irrespective of hopping or metallic conduction, 9 intriguingly suggesting a universal scaling behavior. [10][11][12][13] To our knowledge no single material has been found to span all three regimes proposed in Ref. 8.…”

Section: Introductionmentioning

confidence: 99%

Anomalous Hall effect in Fe (001) epitaxial thin films over a wide range in conductivity

et al. 2009

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We report Hall-effect measurements of epitaxial Fe ͑001͒ thin films grown on MgO ͑001͒. We have focused on the dependence of the anomalous Hall effect ͑AHE͒ in heteroepitaxial structures MgO ͑001͒ / /Fe͑t͒ / MgO with t = 10, 2.5, 2, 1.8, and 1.3 nm. Our results have been interpreted in terms of a recent unified theory of the AHE. We have demonstrated that the thickness and roughness of the Fe layer are control parameters to tune both the longitudinal conductivity xx and anomalous Hall conductivity xy . In this way, we report a crossover from the intrinsic moderately dirty region of conductivities where xy = const to the dirty region of poorly conducting materials ͑ xx Ͻ 10 4 S / cm͒ where we have found that the relation xy ϰ xx n with n = 1.66͑4͒ holds, in good agreement, with the expected universal scaling relationship reported in other ferromagnetic compounds.

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Universal scaling of the anomalous Hall effect inFe3O4epitaxial thin films

Cited by 62 publications

References 29 publications

Anomalous Hall effect in magnetite: Universal scaling relation between Hall and longitudinal conductivity in low-conductivity ferromagnets

Anomalous Hall effect in magnetite: Universal scaling relation between Hall and longitudinal conductivity in low-conductivity ferromagnets

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

Anomalous Hall effect in Fe (001) epitaxial thin films over a wide range in conductivity

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