^{1,a)}, R. I. Shekhter

^{2}and M. Jonson

^{3}

### Abstract

We show theoretically that a significant spin accumulation can occur in electric point contacts between two ferromagnetic electrodes with different magnetizations. Under appropriate conditions an inverse population of spin-split electronic levels results in stimulated emission of photons in the presence of a resonant electromagnetic field. The intensity of the emitted radiation can be several orders of magnitude higher than in typical semiconductor laser materials for two reasons. (1) The density of conduction electrons in a metalpoint contact is much larger than in semiconductors. (2) The strength of the coupling between the electron spins and the electromagnetic field that is responsible for the radiative spin-flip transitions is set by the magnetic exchange energy and can therefore be very large, as suggested by Kadigrobov *et al.* [Europhys. Lett. **67**, 948 (2004)].

Financial support from the European Commission (FP7-ICT-FET-225955 STELE), the Swedish VR, and the Korean WCU program funded by MEST/NFR (R31-2008-000-10057-0) is gratefully acknowledged.

I. Introduction

II. “Exchange–orbital” interaction between free electron spin and electromagnetic field

III. Formulation of the problem

IV. Spin accumulation in the point contact

V. Photocurrent

VI. Conclusions

### Key Topics

- Point contacts
- 33.0
- Photons
- 19.0
- Electromagnetic interactions
- 17.0
- Metal to metal contacts
- 9.0
- Conduction electrons
- 8.0

##### H01F13/00

## Figures

Diffusive point contact under irradiation. A voltage bias *V* injects a spin-polarized current from ferromagnetic metal 1 with magnetic moment **M** _{1} into ferromagnetic metal 2 with magnetic moment **M** _{2}. A spin-up electron is shown to move along a diffusive trajectory from metal 1 to metal 2 (red line *a*) where it resonantly interacts with the electromagnetic field, which results in a spin-flip and the emission of a photon. Continuing along its diffusive path with spin down (blue line *b*), the spin-dependent contact resistance implies that the radiation-induced spin-flip contributes to a change of the magnetoresistance of the point contact.

Diffusive point contact under irradiation. A voltage bias *V* injects a spin-polarized current from ferromagnetic metal 1 with magnetic moment **M** _{1} into ferromagnetic metal 2 with magnetic moment **M** _{2}. A spin-up electron is shown to move along a diffusive trajectory from metal 1 to metal 2 (red line *a*) where it resonantly interacts with the electromagnetic field, which results in a spin-flip and the emission of a photon. Continuing along its diffusive path with spin down (blue line *b*), the spin-dependent contact resistance implies that the radiation-induced spin-flip contributes to a change of the magnetoresistance of the point contact.

Zero-temperature energy distributions for (a) magnetic moment-up (spin-down), *f* ** _{p} **

_{↑}, and (b) magnetic moment-down (spin-up) electrons,

*f*

_{p}_{↓}, at point

**r**in ferromagnetic metal 2 of the point contact. The inset (c) shows the Zeeman energy splitting and the magnetization direction

**M**

_{2}. All states are occupied up to ε

_{↑}= ε

_{ f }−

*eV*/2 −

*I*and ε

_{↓}= ε

_{ f }−

*eV*/2 +

*I*, respectively (blue rectangles,

*1*), but in the intervals (ε

_{↑}, ε

_{↑}+

*eV*) and (ε

_{↓}, ε

_{↓}+

*eV*) the states are only partly occupied (red rectangles,

*2*) and to an extent that is determined by the probabilities α

_{↑}

**(**

_{p}**r**) and α

_{↓}

**(**

_{p}**r**) for “hot” electrons in the ferromagnetic metal to reach

**r**. Clearly, the difference between the densities of spin-down and spin-up electrons,

*n*

_{↑}(

**r**) −

*n*

_{↓}(

**r**) ∝ [(α

_{↑}

^{(2)}− α

_{↓}

^{(2)})

*eV*− 2

*I*], depends on the bias voltage

*V*. It follows that the spin population can be inverted, so that

*n*

_{↑}(

**r**) >

*n*

_{↓}(

**r**), for large enough

*V*if α

_{↑}

^{(2)}> α

_{↓}

^{(2)}.

Zero-temperature energy distributions for (a) magnetic moment-up (spin-down), *f* ** _{p} **

_{↑}, and (b) magnetic moment-down (spin-up) electrons,

*f*

_{p}_{↓}, at point

**r**in ferromagnetic metal 2 of the point contact. The inset (c) shows the Zeeman energy splitting and the magnetization direction

**M**

_{2}. All states are occupied up to ε

_{↑}= ε

_{ f }−

*eV*/2 −

*I*and ε

_{↓}= ε

_{ f }−

*eV*/2 +

*I*, respectively (blue rectangles,

*1*), but in the intervals (ε

_{↑}, ε

_{↑}+

*eV*) and (ε

_{↓}, ε

_{↓}+

*eV*) the states are only partly occupied (red rectangles,

*2*) and to an extent that is determined by the probabilities α

_{↑}

**(**

_{p}**r**) and α

_{↓}

**(**

_{p}**r**) for “hot” electrons in the ferromagnetic metal to reach

**r**. Clearly, the difference between the densities of spin-down and spin-up electrons,

*n*

_{↑}(

**r**) −

*n*

_{↓}(

**r**) ∝ [(α

_{↑}

^{(2)}− α

_{↓}

^{(2)})

*eV*− 2

*I*], depends on the bias voltage

*V*. It follows that the spin population can be inverted, so that

*n*

_{↑}(

**r**) >

*n*

_{↓}(

**r**), for large enough

*V*if α

_{↑}

^{(2)}> α

_{↓}

^{(2)}.

Dependence of the relative resistance change under irradiation on the irradiation frequency ω normalized by the electron spin-flip relaxation frequency *ν _{sf} * for

*ν*/

_{sf}*I*= 10

^{−1}(here

*I*is the exchange energy).

Dependence of the relative resistance change under irradiation on the irradiation frequency ω normalized by the electron spin-flip relaxation frequency *ν _{sf} * for

*ν*/

_{sf}*I*= 10

^{−1}(here

*I*is the exchange energy).

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