Hall effect in dilute magnetic alloys

Fert, A.; Friederich, A.; Hamzić, Amir

doi:10.1016/0304-8853(81)90079-2

Cited by 101 publications

(104 citation statements)

References 37 publications

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“…Accordingly, their theoretical description is quite similar [4][5][6][7][8][9][10][11][12][13][14][15]. For ideal systems an intrinsic mechanism was identified which allows the expression of the corresponding response function in terms of the Berry curvature [5,7].…”

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confidence: 98%

Extrinsic and Intrinsic Contributions to the Spin Hall Effect of Alloys

Lowitzer¹,

et al. 2011

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A fully relativistic description of the spin-orbit induced spin Hall effect is presented that is based on Kubo's linear response formalism. Using an appropriate operator for the spin-current density a KuboStředa-like equation for the spin Hall conductivity (SHC) is obtained. An implementation using the Korringa-Kohn-Rostoker band structure method in combination with the coherent potential approximation allow detailed investigations on various alloy systems. A decomposition of the SHC into intrinsic and extrinsic contributions is suggested. Accompanying calculations for the skew-scattering contribution of the SHC using the Boltzmann equation demonstrate the equivalence to the Kubo formalism in the dilute alloy regime and support the suggested decomposition scheme. DOI: 10.1103/PhysRevLett.106.056601 PACS numbers: 72.25.Ba, 71.15.Rf, 75.76.+j, 85.75.Àd The emerging research field of spintronics has developed very rapidly during recent years. The reason for the broad interest in this field is based on the close connection to fundamental scientific questions as well as its impact on technology [1,2]. In this context, the spin Hall effect (SHE) is one of the most promising phenomena. It denotes the observation that a charge current flowing through a solid is accompanied by a transversal spin current. This occurs even for nonmagnetic solids as was demonstrated by experiments on pure Pt [3].Both the anomalous Hall effect (AHE) in ferromagnets and the SHE are caused by the influence of spin-orbit coupling (SOC). Accordingly, their theoretical description is quite similar [4][5][6][7][8][9][10][11][12][13][14][15]. For ideal systems an intrinsic mechanism was identified which allows the expression of the corresponding response function in terms of the Berry curvature [5,7]. On this basis, ab initio calculations for the intrinsic spin Hall conductivity (SHC) were performed [8][9][10][11]. As for the AHE, the additional extrinsic SHC in dilute and concentrated alloys is ascribed to skew and sidejump scattering caused by SOC. The role of these mechanisms for the SHE has been studied so far primarily by model calculations [12,13]. First principle calculations for the extrinsic SHC of dilute alloys on the basis of the Boltzmann formalism that account for the skew-scattering mechanism have been performed only very recently [14,15]. However, a complete description of intrinsic and extrinsic mechanisms giving rise to the SHE applicable to ideal as well as alloy systems, as it is presented below, was missing so far. As pointed out by several authors [16,17], a central issue for such an approach is an adequate definition for the spin-current density operator that accounts for SOC. This was supplied recently by Vernes et al. [18] by starting from the Bargmann-Wigner four-vector spin polarization operator T [19]. Demanding that the spin polarization is connected with the spin-current density via a corresponding continuity equation an explicit expression for the spin-current operator was given.An adequate formal basis for the di...

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confidence: 98%

Extrinsic and Intrinsic Contributions to the Spin Hall Effect of Alloys

Lowitzer¹,

et al. 2011

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“…In magnetic materials with relatively low Curie temperature, the temperature (T) induced variation of the magnetization must be taken into account [13]. For the simplest case that ρAH scales proportionally with magnetization (M) which is not the fact in some magnetic systems [14,15], the AHE scaling can be modified into a more general expression explicitly as ρAH/f = a0 ρxx0+bρxx…”

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Anomalous Hall effect inL10−MnAlfilms with controllable orbital two-channel Kondo effect

2016

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Abstract：The anomalous Hall effect (AHE) in strongly disordered magnetic systems has been buried in persistent confusion despite its long history. We report the AHE in perpendicularly magnetized L10-MnAl epitaxial films with variable orbital two-channel Kondo (2CK) effect arising from the strong coupling of conduction electrons and the structural disorders of two-level systems. The AHE is observed to excellently scale with ρAH/f=a0ρxx0+bρxx 2 at high temperatures where phonon scattering prevails. In contrast, significant deviation occurs at low temperatures where the orbital 2CK effect becomes important, suggesting a negative AHE contribution. The deviation of the scaling agrees with the orbital 2CK effect in the breakdown temperatures and deviation magnitudes. The scaling between longitudinal resistivity (ρxx) and anomalous Hall resistivity (ρAH) can provide access to the detailed mechanisms of the AHE. Present theories predict a scaling of ρAH~ρxx n , with n = 2 for side jump and intrinsic contribution [4,5], and n = 1 for skew scattering [6]. The intrinsic contribution is related to the topological Berry curvature of band structure [4], while the extrinsic side jump and skew scattering result from spin-orbit interaction-induced asymmetric impurity scattering of conduction electrons [5,6]. Notably, in contrast to the conventional picture that ρAH scales with the total resistivity irrespective of its sources [3], recent experimental studies have revealed that both ρAH and the scaling relation are qualitatively different for various types of electron scattering. Phonon scattering was found to have no distinguishable contribution to extrinsic part of ρAH in ferromagnetic Fe, Co, Ni, L10-Mn1.5Ga films, Co/Pt multilayers, and paramagnetic Ni34Cu66 films [7][8][9][10][11][12]. When ρxx is dominated by phonon and static defect scattering, the AHE has a scaling of ρAH = a0 ρxx0+bρxx 2 , where ρxx0 is the residual resistivity, a0ρxx0 is the extrinsic contribution from both side jump and skew scattering, and b is the intrinsic anomalous Hall conductivity (AHC). In magnetic materials with relatively low Curie temperature, the temperature (T) induced variation of the magnetization must be taken into account [13]. For the simplest case that ρAH scales proportionally with magnetization (M) which is not the fact in some magnetic systems [14,15], the AHE scaling can be modified into a more general expression explicitly as ρAH/f = a0 ρxx0+bρxx 2 . Here, f = M / M0, where M0 is magnetization at 0 K; the Tindependence of a0 and b is not considered. In the presence of strong disorder effects (dirty metal [1]), the AHE scaling is more complex. In the hopping conduction regime, the AHE was reported to scale as ρAH~ρxx 0.4 [19][20][21]. Therefore, further experimental and theoretical attempts are crucial for better understanding of the AHE, especially in disordered magnetic systems. Key words：AnomalousThe Kondo effect is a striking consequence of conduction electrons coupling with localized spin or "pseudospin" impurities. The on...

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“…The exchange coupling constant for Fe impurities in Cu has been previously calculated as J CuFe = 0.91 ± 0.2e V [ 38]. From studies on CuMn dilute alloys a value of J/V = 0.133 [39] is used with J CuMn = 0.4 ± 0.1eV [38], and maintaining an equal impurity perturbation potential V , provides a ratio J/V = 0.30 for Fe impurities in Cu. Finally, assuming for Fe 3+ impurities S = 5/2, we obtain a value for ǫ m of 0.29 in reasonable agreement with our result.…”

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Spin relaxation through Kondo scattering in Cu/Py lateral spin valves

et al. 2015

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The temperature dependence of the spin diffusion length typically reflects the scattering mechanism responsible for spin relaxation. Within nonmagnetic metals it is reasonable to expect the Elliot-Yafet mechanism to play a role and thus the temperature dependence of the spin diffusion length might be inversely proportional to resistivity. In lateral spin valves, measurements have found that at low temperatures the spin diffusion length unexpectedly decreases. By measuring the transport properties of lateral Py/Cu/Py spin valves, fabricated from Cu with magnetic impurities of <1 ppm and ∼ 4 ppm, we extract a spin diffusion length which shows this suppression below 30 K only in the presence of the Kondo effect. We have calculated the spin-relaxation rate and isolated the contribution from magnetic impurities. We find the spin-flip probability of a magnetic impurity to be 34%. Our analysis demonstrates the dominant role of Kondo scattering in spin relaxation, even in low concentrations of order 1 ppm, and hence illustrates its importance to the reduction in spin diffusion length observed by ourselves and others.

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Hall effect in dilute magnetic alloys

Cited by 101 publications

References 37 publications

Extrinsic and Intrinsic Contributions to the Spin Hall Effect of Alloys

Extrinsic and Intrinsic Contributions to the Spin Hall Effect of Alloys

Anomalous Hall effect inL10−MnAlfilms with controllable orbital two-channel Kondo effect

Spin relaxation through Kondo scattering in Cu/Py lateral spin valves

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