Intrinsic anomalous Hall effect in ferromagnetic metals studied by the multi-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:math>-orbital tight-binding model

Kontani, Hiroshi; Tanaka, Tomoyasu; Yamada, Kōsaku

doi:10.1103/physrevb.75.184416

Cited by 80 publications

(193 citation statements)

References 54 publications

(175 reference statements)

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“…In the metallic state, the Fermi level µ is located in the upper (E + k ) or lower (E − k ) branch, and the relationship According to the linear-response theory, the intrinsic Hall conductivity is given by the summation of the Fermi surface term (I-term) and the Fermi sea term (II-term) [23]. In previous work, we have shown that the I-term is dominant in many metals [12,14,24]. Using the 3 × 3 Green functionĜ 0 k (ω) = (ω + µ −Ĥ 0 ) −1 , the I-term of the OHC at T = 0 is given by [8,12] …”

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confidence: 99%

Giant Orbital Hall Effect in Transition Metals: Origin of Large Spin and Anomalous Hall Effects

et al. 2009

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In transition metals and their compounds, the orbital degrees of freedom gives rise to an orbital current, in addition to the ordinary spin and charge currents. We reveal that considerably large spin and anomalous Hall effects (SHE and AHE) observed in transition metals originate from an orbital Hall effect (OHE). To elucidate the origin of these novel Hall effects, a simple periodic s-d hybridization model is proposed as a generic model. The giant positive OHE originates from the orbital Aharonov-Bohm phase factor, and induces spin Hall conductivity that is proportional to the spin-orbit polarization at the Fermi level, which is positive (negative) in metals with more than (less than) half-filling.PACS numbers: 72.25. Ba,72.10.Bg,72.80.Ga The Hall effect, first discovered at the end of 19th century, has revealed the profound nature of electron transport in metals and semiconductors via the anomalous Hall effect (AHE) and (fractional) quantum Hall effects. It has recently been recognized that conventional semiconductors and metals exhibit a spin Hall effect (SHE), which is the phenomenon where an electric field induces a spin current (a flow of spin angular momentum s z ) in a transverse direction [1][2][3][4][5]. Recently, a theory of the intrinsic Hall effect proposed by Karplus and Luttinger [6], which occurs in multiband systems and is independent of impurity scattering, has been intensively developed [7,8]. In particular, a quantum SHE has also been predicted and experimentally confirmed [9,10].The spin Hall conductivity (SHC) observed in transition metals has given rise to further issues regarding the origin of the SHE, since the SHC observed in Pt exceeds 200 e −1 · Ω −1 cm −1 , which is approximately 10 4 times larger than that of n-type semiconductors [5], and the SHCs in Nb and Mo are negative [11]. The large SHE and the sign change of the SHC in transition metals has attracted much interest, and many theoretical studies of the SHE have so far been conducted based on realistic multiband models for Ru-oxide [8] and various 4d and 5d metals [12], including Au, W [13], and Pt [14,15]. The calculated results for the SHC semi-quantitatively agree with the observed results. The mechanism for the SHE has been explained in such a way that spin-orbit interactions (SOI) and the phase of hopping integrals of electrons give rise to the Aharonov-Bohm (AB) effect, and therefore the conduction electrons are subject to an effective spin-dependent magnetic field.Since the transition metals have orbital degrees of freedom in addition to the spin and charge degrees of freedom, flow of the atomic orbital angular momentum (l z ), that is, an orbital current, may be realized in a nonequilibrium state. In fact, several authors have predicted the emergence of a large orbital Hall effect (OHE) [8,12,16], which is a phenomenon where an electric field induces a flow of p-and d-orbital angular momentum in a transverse direction. In particular, the predicted orbital Hall conductivity (OHC) in transition metals and oxides [8,12]...

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Giant Orbital Hall Effect in Transition Metals: Origin of Large Spin and Anomalous Hall Effects

et al. 2009

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“…′ sin k x sin k y , which breaks the mirror symmetry with respect to k x -and k y -axes, causes the large anomalous velocity [6]. This is the origin of huge SHE.…”

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confidence: 99%

“…′ sin k y cos k x is called the "anomalous velocity", which is the origin of the Hall effects [3,6]. Since v a x has the same symmetry as k y , v a x v y can remain finite after the k-summations.…”

Section: Introductionmentioning

confidence: 99%

Spin Hall effect in Sr2RuO4 and transition metals (Nb,Ta)

Tanaka

Kontani

Naito

et al. 2008

Journal of Physics and Chemistry of Solids

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We study the intrinsic spin Hall conductivity (SHC) and the d-orbital Hall conductivity (OHC) in metallic d-electron systems based on the multiorbital tight-binding model. The obtained Hall conductivities are much larger than that in p-type semiconductors. The origin of these huge Hall effects is the "effective Aharonov-Bohm phase" induced by the signs of inter-orbital hopping integrals as well as atomic spin-orbit interaction. Huge SHC and OHC due to this mecahnism is ubiquitous in multiorbital transition metals.

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“…The interorbital terms are ξ 1 = −2t cos k x , ξ 2 = −2t cos k y , and Fig. 2 (a)), which breaks the mirror symmetry with respect to k xand k y -axes, causes the large anomalous velocity [8]. This is the origin of intrinsic Hall effects.…”

Section: Introductionmentioning

confidence: 99%

“…These phenomena are fundamental issues in recent condensed matter physics. [7,8]. In this article, we explain that the atomic orbital degrees of freedom causes the huge SHE and OHE in d-and f -electron systems.…”

Section: Introductionmentioning

confidence: 99%

Intrinsic Spin and Orbital Hall Effects ind- andf-Electron Systems

et al. 2008

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We study the intrinsic spin Hall conductivity (SHC) and orbital Hall conductivity (OHC) in various d-and f -electron systems. The obtained SHC and OHC are much larger than that in semiconductors. The origin of these huge Hall effects is the "effective Aharonov-Bohm phase factor" induced by the atomic angular momentum with the aid of the atomic spin-orbit interaction. Huge SHC and OHC due to this mechanism is expected to be ubiquitous in multiorbital transition metal complexes, which will open the possibility of realizing spintronics as well as orbitronics devices.

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Intrinsic anomalous Hall effect in ferromagnetic metals studied by the multi-d-orbital tight-binding model

Cited by 80 publications

References 54 publications

Giant Orbital Hall Effect in Transition Metals: Origin of Large Spin and Anomalous Hall Effects

Giant Orbital Hall Effect in Transition Metals: Origin of Large Spin and Anomalous Hall Effects

Spin Hall effect in Sr2RuO4 and transition metals (Nb,Ta)

Intrinsic Spin and Orbital Hall Effects ind- andf-Electron Systems

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