Overlooked contribution to the Hall effect in ferromagnetic metals

Hirsch, J. E.

doi:10.1103/physrevb.60.14787

Cited by 47 publications

(42 citation statements)

References 18 publications

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“…It is this effective Lorentz force that is responsible for the spin Hall effect. This our conclusion is similar to the conclusion of Hirsch [12] who studied the force exerted on a line of moving magnetic dipoles by the electrostatic field of charges arranged in a cubic lattice. For a cubic lattice (see below) our result for the effective Lorentz force coincides up to a factor of 2 with the result obtained by Hirsch.…”

supporting

confidence: 91%

Theory of Spin Hall Effect: Extension of the Drude Model

Chudnovsky

2007

Phys. Rev. Lett.

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An extension of Drude model is proposed that accounts for spin and spin-orbit interaction of charge carriers. Spin currents appear due to combined action of the external electric field, crystal field and scattering of charge carriers. The expression for spin Hall conductivity is derived for metals and semiconductors that is independent of the scattering mechanism. In cubic metals, spin Hall conductivity σs and charge conductivity σc are related through σs = [2π /(3mc 2 )]σ 2 c with m being the bare electron mass. Theoretically computed value is in agreement with experiment. 71.70.Ej It has been a common knowledge in atomic physics that due to spin-orbit interaction the spatial separation of electrons with different spin projections can be achieved through scattering of an unpolarized electron beam by an unpolarized target [1]. Dyakonov and Perel were the first to notice that in the presence of the electric current the scattering of charge carriers by impurities in a semiconductor must lead to a similar effect [2]. It was subsequently called the spin Hall effect [3] and observed in semiconductors [4,5] and metals [6]. A number of microscopic models have been developed that explain spatial separation of spin polarizations by various "extrinsic" (due to impurities) and "intrinsic" (impurity-free) mechanisms, see for review Ref. 7. While these models provide valuable insight into microscopic origin of the spin Hall effect, they are lacking universality of, e.g., Drude model of charge conductivity [8]. The Drude model, in spite of being classical in nature, has been very powerful in describing dc and ac conductivity and its temperature dependence. It also gives the accurate value of the Hall coefficient by catching correctly the orbital motion of charge carriers in the presence of the magnetic field. The power of the Drude model resides in the fact that it expresses conductivity, σ D = e 2 nτ /m, via charge e, concentration n, mass m, and relaxation time τ of charge carriers regardless of the scattering mechanism. Same parameters enter expressions describing experiments other than the Ohm's law, e.g., n and the sign of e can be extracted from measurements of the Hall coefficient R H = −(nec) −1 , τ can be extracted from measurements of the frequency dependence of the impedance, and m can be extracted from measurements of the cyclotron resonance. This allows one to test theoretical concepts of charge conductivity regardless of the degree of accuracy with which one can compute parameters entering σ D .In this Letter we will try to develop a similar approach to the spin Hall conductivity. We will take the Drude model a little further by incorporating spin and spin-orbit interaction into the dynamics of charge carriers. We will argue that such a straightforward extension of the Drude model allows one to obtain universal expression for spin Hall conductivity that is independent of the scattering mechanism. The spin Hall effect appears due to combined action of the external electric field, quadrupole crystal electric f...

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supporting

confidence: 91%

Theory of Spin Hall Effect: Extension of the Drude Model

Chudnovsky

2007

Phys. Rev. Lett.

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“…When calculating the spin torque, it was simpler to consider the case k m α. But the mechanical torque reaches its maximum at k m > α [see equation (122)] when the spin current is j y x = −α 3 2 /6πm ∼ 10 −8 erg/cm=10 −3 J/m. In order to estimate the displacement h of the cantilever end (see figure 13), we use the cantilever parameters from reference [134]: the length l = 120 µm and the spring constant k = F/h = 86 µN/m, where F is the force on the cantilever end.…”

Section: Experimental Detection Of Equilibrium Spin Currentsmentioning

confidence: 99%

Spin currents and spin superfluidity

Sonin

2010

Advances in Physics

241

300

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The present review analyzes and compares various types of dissipationless spin transport: (1) Superfluid transport, when the spin-current state is a metastable state (a local but not the absolute minimum in the parameter space). (2) Ballistic spin transport, when spin is transported without losses simply because sources of dissipation are very weak. (3) Equilibrium spin currents, i.e., genuine persistent currents. (4) Spin currents in the spin Hall effect. Since superfluidity is frequently connected with Bose condensation, recent debates about magnon Bose condensation are also reviewed. For any type of spin currents simplest models were chosen for discussion in order to concentrate on concepts rather than details of numerous models. The various hurdles on the way of using the concept of spin current (absence of the spin-conservation law, ambiguity of spin current definition, etc.) were analyzed. The final conclusion is that the spin-current concept can be developed in a fully consistent manner, and is a useful language for description of various phenomena in spin dynamics.

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“…If superfluid electrons are rotating in the absence of body rotation and magnetic fields, why is no current observed? The reason is that when electrons are expelled from the interior of the superconductor, interaction of the electron spin of the radially outgoing electron with the ionic lattice will deflect electrons of opposite spin tangentially in opposite directions [15,16]. As a consequence, macroscopic spin currents are predicted to exist in superconductors if this scenario is correct.…”

Section: The Quantized Fluxmentioning

confidence: 99%

The Lorentz force and superconductivity

Hirsch

2003

Physics Letters A

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To change the velocity of an electron requires that a Lorentz force acts on it, through an electric or a magnetic field. We point out that within the conventional understanding of superconductivity electrons appear to change their velocity in the absence of Lorentz forces. This indicates a fundamental problem with the conventional theory of superconductivity. A hypothesis is proposed to resolve this difficulty. This hypothesis is consistent with the theory of hole superconductivity.Comment: Spelling corrected: Lorenz --> Lorent

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Overlooked contribution to the Hall effect in ferromagnetic metals

Cited by 47 publications

References 18 publications

Theory of Spin Hall Effect: Extension of the Drude Model

Theory of Spin Hall Effect: Extension of the Drude Model

Spin currents and spin superfluidity

The Lorentz force and superconductivity

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