Publisher's Note: Spin-polarized electron transport in ferromagnet/semiconductor heterostructures: Unification of ballistic and diffusive transport [Phys. Rev. B<b>72</b>, 165322 (2005)]

Lipperheide, R.; Wille, U.

doi:10.1103/physrevb.72.169902

Cited by 4 publications

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“…(10) is different from that of Eq. (3.8) in [34]; in the spin-relaxed state, we have in the present case α ↑,↓ (x ) = 1, while in [34] we have α ↑,↓ (x ) = 1/2.] Using Eqs.…”

Section: Electron Densitiesmentioning

confidence: 49%

“…The thermoballistic description of spin-polarized electron transport in NMS [34] makes use, in a onedimensional geometry, of ballistic electron currents and densities in "ballistic intervals" between two points of local thermal equilibrium, x and x (x 1 ≤ x < x ≤ x 2 ); see Fig. 1.…”

Section: Points Of Thermal Equilibrium: Densities and Injected Currentsmentioning

confidence: 99%

“…in turn, are completely determined by the potential profiles ↑,↓ (x )], and, most importantly, by the spin-relaxed chemical potentialμ(x ), which is the only dynamical quantity appearing. The latter is to be calculated according to the thermoballistic procedure presented in [34] (see below).…”

Section: Spatial Behavior Of the Off-equilibrium Spin-polarized Currementioning

confidence: 99%

“…In the thermoballistic current, diffusive and ballistic transport are thus unified in a way that allows the effect of these two aspects of the transport mechanism to be studied. In [34], we have introduced spin relaxation into the thermoballistic description for the case of electron transport in NMS. There, we have disregarded any spin splitting of the conduction band.…”

Section: Introductionmentioning

confidence: 99%

“…There, we have disregarded any spin splitting of the conduction band. Applications [34,35] have dealt with spin-polarized transport in heterostructures formed of an NMS layer sandwiched between two ferromagnetic metal contacts. In the present paper, we put forward the systematic extension of the thermoballistic approach to spin-polarized electron transport across spin-split potential profiles.…”

Section: Introductionmentioning

confidence: 99%

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Thermoballistic spin-polarized electron transport in paramagnetic semiconductors

Lipperheide¹,

Wille²

2009

Ann. Phys.

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Spin-polarized electron transport in diluted magnetic semiconductors (DMS) in the paramagnetic phase is described within the thermoballistic transport model. In this (semiclassical) model, the ballistic and diffusive transport mechanisms are unified in terms of a thermoballistic current in which electrons move ballistically across intervals enclosed between arbitrarily distributed points of local thermal equilibrium. The contribution of each interval to the current is governed by the momentum relaxation length. Spin relaxation is assumed to take place during the ballistic electron motion. In paramagnetic DMS exposed to an external magnetic field, the conduction band is spin-split due to the giant Zeeman effect. In order to deal with this situation, we extend our previous formulation of thermoballistic spin-polarized transport so as to take into account an arbitrary (position-dependent) spin splitting of the conduction band. The current and density spin polarizations as well as the magnetoresistance are each obtained as the sum of an equilibrium term determined by the spin-relaxed chemical potential, and an off-equilibrium contribution expressed in terms of a spin transport function that is related to the splitting of the spin-resolved chemical potentials. The procedures for the calculation of the spin-relaxed chemical potential and of the spin transport function are outlined. As an illustrative example, we apply the thermoballistic description to spin-polarized transport in DMS/NMS/DMS heterostructures formed of a nonmagnetic semiconducting sample (NMS) sandwiched between two DMS layers. We evaluate the current spin polarization and the magnetoresistance for this case and, in the limit of small momentum relaxation length, find our results to agree with those of the standard drift-diffusion approach to electron transport.

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“…(10) is different from that of Eq. (3.8) in [34]; in the spin-relaxed state, we have in the present case α ↑,↓ (x ) = 1, while in [34] we have α ↑,↓ (x ) = 1/2.] Using Eqs.…”

Section: Electron Densitiesmentioning

confidence: 49%

Section: Points Of Thermal Equilibrium: Densities and Injected Currentsmentioning

confidence: 99%

Section: Spatial Behavior Of the Off-equilibrium Spin-polarized Currementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Thermoballistic spin-polarized electron transport in paramagnetic semiconductors

Lipperheide¹,

Wille²

2009

Ann. Phys.

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Thermoballistic spin‐polarized electron transport in paramagnetic semiconductors

Lipperheide

Wille²

2009

Annalen der Physik

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Spin‐polarized electron transport in diluted magnetic semiconductors (DMS) in the paramagnetic phase is described within the thermoballistic transport model. In this (semiclassical) model, the ballistic and diffusive transport mechanisms are unified in terms of a thermoballistic current in which electrons move ballistically across intervals enclosed between arbitrarily distributed points of local thermal equilibrium. The contribution of each interval to the current is governed by the momentum relaxation length. Spin relaxation is assumed to take place during the ballistic electron motion. In paramagnetic DMS exposed to an external magnetic field, the conduction band is spin‐split due to the giant Zeeman effect. In order to deal with this situation, we extend our previous formulation of thermoballistic spin‐polarized transport so as to take into account an arbitrary (position‐dependent) spin splitting of the conduction band. The current and density spin polarizations as well as the magnetoresistance are each obtained as the sum of an equilibrium term determined by the spin‐relaxed chemical potential, and an off‐equilibrium contribution expressed in terms of a spin transport function that is related to the splitting of the spin‐resolved chemical potentials. The procedures for the calculation of the spin‐relaxed chemical potential and of the spin transport function are outlined. As an illustrative example, we apply the thermoballistic description to spin‐polarized transport in DMS/NMS/DMS heterostructures formed of a nonmagnetic semiconducting sample (NMS) sandwiched between two DMS layers. We evaluate the current spin polarization and the magnetoresistance for this case and, in the limit of small momentum relaxation length, find our results to agree with those of the standard drift‐diffusion approach to electron transport.

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Spin injection from a ferromagnet into a semiconductor in the case of a rough interface

Roundy

Raǐkh

2015

Phys. Rev. B

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The effect of the interface roughness on the spin injection from a ferromagnet into a semiconductor is studied theoretically. Even a small interface irregularity can lead to a significant enhancement of the injection efficiency. When a typical size of the irregularity, a, is within a domain λF a λN , where λF and λN are the spin-diffusion lengths in the ferromagnet and semiconductor, respectively, the geometrical enhancement factor is ∼ λN /a. The origin of the enhancement is the modification of the local electric field on small scales ∼ a near the interface. We demonstrate the effect of enhancement by considering a number of analytically solvable examples of injection through curved ferromagnet-semiconductor interfaces. For a generic curved interface the enhancement factor is ∼ λN /R, where R is the local radius of curvature.

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Publisher's Note: Spin-polarized electron transport in ferromagnet/semiconductor heterostructures: Unification of ballistic and diffusive transport [Phys. Rev. B72, 165322 (2005)]

Cited by 4 publications

References 0 publications

Thermoballistic spin-polarized electron transport in paramagnetic semiconductors

Thermoballistic spin-polarized electron transport in paramagnetic semiconductors

Thermoballistic spin‐polarized electron transport in paramagnetic semiconductors

Spin injection from a ferromagnet into a semiconductor in the case of a rough interface

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