# Presentation: 014218

## Transport Simulation of Precessing Spin 

**Distribution across Semiconductor **
**Heterojunctions**
- Paul von Allmen
- Motorola Labs, Solid State Research Center, Tempe, AZ
- Gerhard Klimeck
- Jet Propulsion Lab, California Institute of Technology, Pasadena, CA

## Nanoelectronics & Spintronics Why? What? How? 

**Objective**
- Low power and high speed electronics
- High sensitivity detectors
**Approach**
- Small(er) devices
- Utilize quantum effects
**Problems**
- Small coherence times / lengths
- Low temperature operation
- Size control / quality control

**Quantum quantities**
- Electron charge
- Electron state (in a small system / artificial atom)
- Electron Spin
**Related length scales**
- Few nanometerse2/2C >> kBT
- Few nanometersE = En+1-En >> kBT
- Many micrometers (expect radiation hardness)
**Spin-injection / creation**
- Magnetic materials
- Optical injection

## Experimental Setup

** ****Pump beam:**
**    **** **
**   **
** ****Probe beam:**
**  **** **
**   **
** ****Pump-probe time delay ***********t*****:  **
**    **

**I. Malajovich, J.M. Kikkawa, D. Awschalom, J.J. Berry and N. Samarth, PRL 84, 1015 (2000)**

**Notes:**
TRKR in the two-color configuration measures the magnetization in the epilayer
 The Kerr effect is that the polarization plane of linearly polarized light rotates by an angle proportional to the magnetic field (or magnetization)
 The circularly polarized pump beam produces a spin polarized distribution with spin oriented parallel to the propagation of the pump beam
Faraday effect rotation of linearly light - angle of rotation propotional to B
Works also on reflection
X is growth direction 
Faraday effect is a resonance effect -  need to be resonant with the band-edge - off resonant in the GaAs

## TIME RESOLVED KERR ROTATION

** ****Pump beam:**
**  ****energy E****g****(GaAs) < E****p**** < E****g****(ZnSe) **
**  ****circular polarization generates spin polarized electrons in CB**
** ****Probe beam:**
**  ****energy E****probe**** ******** E****g****(ZnSe) **
**  ****linear polarization - resonant Faraday effect measures ZnSe magnetization**
** ****Pump-probe time delay ***********t*****:  ****   ****spin dynamics**

**I. Malajovich, J.M. Kikkawa, D. Awschalom, J.J. Berry and N. Samarth, PRL 84, 1015 (2000)**

**Notes:**
TRKR in the two-color configuration measures the magnetization in the epilayer
 The Kerr effect is that the polarization plane of linearly polarized light rotates by an angle proportional to the magnetic field (or magnetization)
 The circularly polarized pump beam produces a spin polarized distribution with spin oriented parallel to the propagation of the pump beam
Faraday effect rotation of linearly light - angle of rotation propotional to B
Works also on reflection
X is growth direction 
Faraday effect is a resonance effect -  need to be resonant with the band-edge - off resonant in the GaAs

## SPIN Transport Across an Interface

**Problem Statement**

- x (m)

- 0

- 0.1

- GaAs

- ZnSe

**Inject** spin polarized
- Electrons **in GaAs** andmeasure spin populationand precession in ZnSe
- Zero Bias:
- Transmitted spins precess **ZnSe-like**

**I. Malajovich, J.M. Kikkawa, D. Awschalom, J.J. Berry and N. Samarth, PRL 84, 1015 (2000)**

**Notes:**
Transmission coefficient at interface decreases exponentially with time which allows for the accumulation process.
 Origin of transmission coefficient decay is attributed to energy relaxation of non-equilibrium energy distribution generated by pump above GaAs CB
 This slide is the qualitative explanation

## ELECTRIC FIELD DEPENDENT

**I. Malajovich, J.J. Berry, N. Samarth and D.D. Awschalom, Nature 411, 770 (2001)**

**Larmor frequency:**

**Land****é** **factors:**

**ELECTRIC FIELD DEPENDENT**
**SPIN DYNAMICS**

**Spin dynamics:**
**   ****zero bias: ZnSe-like**
**   ****non-zero bias: GaAs-like**

**Notes:**
The band offset at the GaAs/ZnSe critically depend on growth conditions and is poorly understood
 As electric field increases the spin dynamics evolves from ZnSe-like to GaAs-like

## Why is Landé factor GaAs-like at E>0?

**   ****The Land****é**** factor describes how the band energies vary with B**
**   ****in the material where the electron is located**

**Expect precession at ZnSe Larmor frequency as soon as the electron enters ZnSe.**
**However, at non-zero bias experiments show that the GaAs spin parameters determine the spin dynamics in the ZnSe epilayer.**

**Why is Land****é**** factor GaAs-like at E>0?**

**The apparent contradiction is lifted by examining the interplay of the transport and precession dynamics.**

**Notes:**
Experimental data seems to suggest that spin precession is not entirely a local property. Is there an unexpected “proximity effect”
 The goal of this paper is to understand this data without violating locality properties of material properties within effective mass approximation
 We will show that data can be explained by interplay of transport and spin dynamics

## SPIN DIFFUSION MODEL

**SPIN DIFFUSION MODEL**

**Space dependent material parameters:**
**  ****spin relaxation time **********, Land****é factor *****g***** and diffusion coefficient *****D***
**Numerical method:**
**  ****finite difference in space, Crank-Nicholson in time**
**Reflection at interface: **
**  ****diffusion coefficient at one grid point reduced by a time dependent**
**  ****transmission factor**

**M.D. Stiles and A. Zangwill, preprint (2002)**

**Continuity equation for spin accumulation**

*********d***** is the accumulation lifetime**

**Notes:**
Simplest model is to describe spin polarized cloud with spin accumulation, which obeys a conservation equation plus loss term plus precession term
 1-D solution ... standard
 reflection at interface cannot be described explicitly because we have no explicit propagation of electrons
 one approach would be to use Monte Carlo to solve diffusion, where reflection at interface can be introduced explicitly
 we choose an ad hoc numerical device which is to set the diffusion coefficient to a smaller value at one grid point. This results in a discontinuity in the spin density, which is the same result as reflection would cause
m is spin density / accumulation (spin density - spin at equilibrium)

## SPIN DIFFUSION MODEL

**SPIN DIFFUSION MODEL**

**Look at 3 cases:**
**no external magnetic field - no spin precession**
**1) ****	****no electric field -> spin diffusion / presence **
**With external magnetic fields - > spin precession**
**2) ****	****No electric field: ZnSe like precession**
**3) ****	****With electric field: GaAs-like precession**

**Continuity equation for spin accumulation**

**Notes:**
Simplest model is to describe spin polarized cloud with spin accumulation, which obeys a conservation equation plus loss term plus precession term
 1-D solution ... standard
 reflection at interface cannot be described explicitly because we have no explicit propagation of electrons
 one approach would be to use Monte Carlo to solve diffusion, where reflection at interface can be introduced explicitly
 we choose an ad hoc numerical device which is to set the diffusion coefficient to a smaller value at one grid point. This results in a discontinuity in the spin density, which is the same result as reflection would cause
m is spin density / accumulation (spin density - spin at equilibrium)

## SPIN TRANSFER AT ZERO BIAS

**SPIN TRANSFER AT ZERO BIAS**
**AND ZERO MAGNETIC FIELD**

**Simulations: **
**  ****- Accumulation lifetime ***********d***** is finite**
**  ****- Fraction transferred is within experimental range 5-10%**
**  ****- Large times: exponential decay with lifetime ***********ZS***
**  ****- Larger ********(GaAs) induces larger transfer**

**Experiment**

**Simulation**

**Notes:**
Transmission coefficient at interface decreases exponentially with lifetime Tau(d)
 Blue exponential on simulation plot is fit at large t. Gives spin relaxation time for ZnSe
 Difference between the two blue curves gives time behavior of residual spin. It describes dynamics of spin accumulation,
 The epilayer magnetization is the integral of m over the epilayer
 The initial spin polarization distribution (m) is given by optical intensity profile of pump beam. Dynamics during pumping is neglected (100fs long pulse)

## ZERO-BIAS SPIN DYNAMICS

- x (m)

- 0

- 0.1

- GaAs

- ZnSe

**Barrier at heterojunction establishes two separate spin-precessing**
**populations in GaAs and ZnSe.**
**Therefore, TRKR measures the precession frequency in ZnSe**

**Notes:**
Transmission coefficient at interface decreases exponentially with time which allows for the accumulation process.
 Origin of transmission coefficient decay is attributed to energy relaxation of non-equilibrium energy distribution generated by pump above GaAs CB
 This slide is the qualitative explanation

## SPIN PRECESSION – NO BIAS

***d*=2e-10 s
- D(GaAs)=0.1 cm2/s
- D(ZnSe)=2 cm2/s

**SPIN PRECESSION – NO BIAS**

**Experiment**

**Simulation**

**Simulations:**
**  ****- Accumulation lifetime ***********d***** is finite**
**  ****- Spin dynamics according ZnSe parameters**
**  ****- Spin coherence decreases as magnetic field increases**
**  ****- Phase shift increases as magnetic field increases**

**Notes:**
Simulations reproduce all of the major features of experimental data.
 Difficult to be quantitative because we don’t have access to experimental data first hand.

## NON-ZERO BIAS SPIN DYNAMICS

- x (m)

- 0

- 0.1

- GaAs

- ZnSe

**Transit time through epilayer (diffusion):**

**Dephasing in ZnSe epilayer:**

**Therefore, TRKR measures the precession frequency in GaAs**

**Notes:**
The main condition for this to work is that at non-zero bias the barrier disappears and the transmission coefficient is always equal to one
 The phase shift due to a different Lande factor in the ZnSe is very small
 This slide is the qualitative explanation

## SPIN PRECESSION – BIASED

**SPIN PRECESSION – BIASED**

**Experiment**

**Simulation**

**Simulations:**
**  ****- Accumulation lifetime ***********d***** is infinite, transmission coefficient T=1**
**  ****- Spin dynamics according GaAs parameters**

**Notes:**
- At non-zero bias the spin dynamics is GaAs-like ... it works!!!

## SPIN Transport Across an Interface

**Conclusion**

**Spin density diffusion model reproduces experimental data for biased and unbiased samples.**
**2. ****	****Switch from ZnSe-like to GaAs-like spin dynamics is explained by fast transit times through ZnSe epilayer and barrier at interface.**

- Inject spins
- in GaAs

- Measure spins
- in ZnSe

**Notes:**
Transmission coefficient at interface decreases exponentially with time which allows for the accumulation process.
 Origin of transmission coefficient decay is attributed to energy relaxation of non-equilibrium energy distribution generated by pump above GaAs CB
 This slide is the qualitative explanation