# Spin-Currents and Spin-Pumping Forces for Spintronics

## Abstract

**:**

## 1. Introduction

#### 1.1. Longitudinal Spin Relaxation

#### 1.2. Spin Precession

#### 1.3. Band Structure and s-d Relaxation

#### 1.4. Ferromagnetic Collective Variable

## 2. Introduction of the Ferromagnetic Degrees of Freedom

**Figure 1.**Illustration of the Σ configuration space of the ferromagnetic variable. The two potential minima and the ferromagnetic currents are sketched.

## 3. Two Spin-Channel Model

**Figure 2.**Spin-accumulation $\Delta \mu \left(x\right)$ trough a Non-Ferromagnetic/Ferromagnetic/Non-Ferromagntic junction with typical size of the order of the spin diffusion length. The spin-diffusion length has been taken as equal for both materials.

## 4. Spin Precession

## 5. The Role of the $d\downarrow $ Electronic Subband

## 6. Derivation of Spin Transfer due to Spin-Pumping Forces

## 7. Conclusions

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Wegrowe, J.-E.; Drouhin, H.-J. Spin-Currents and Spin-Pumping Forces for Spintronics. *Entropy* **2011**, *13*, 316-331.
https://doi.org/10.3390/e13020316

**AMA Style**

Wegrowe J-E, Drouhin H-J. Spin-Currents and Spin-Pumping Forces for Spintronics. *Entropy*. 2011; 13(2):316-331.
https://doi.org/10.3390/e13020316

**Chicago/Turabian Style**

Wegrowe, Jean-Eric, and Henri-Jean Drouhin. 2011. "Spin-Currents and Spin-Pumping Forces for Spintronics" *Entropy* 13, no. 2: 316-331.
https://doi.org/10.3390/e13020316