3.016 Final Project:
Spintronics

What is spin? What is spintronics?

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Introduction to the spin valve

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TMR and Julliere’s formula; Drift diffusion model and spin diffusion length

Understanding the spin valve-- Spin injection

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nextStep:=Module[{τCollision,velocity,λCollision},
pythagorasCondition=y^2+x^2== λ^2;
fieldBias=driftVelocity== currentDensity/(electronsDensity chargeElectron);
distanceConditionX=Solve[fieldBias/.{driftVelocity-> (distanceX/τ)},distanceX];
τCollision=3;
λCollision=velocity*τCollision;
velocity=(currentDensity/(electronsDensity chargeElectron))/.{chargeElectron->-1,currentDensity->-0.05,electronsDensity->3};
λCollision=velocity*τCollision;
maxX=λCollision;
travelX= RandomReal[{-.5 maxX,maxX}];
solutionsY=Solve[pythagorasCondition/.{x-> travelX,λ-> λCollision},y];
travelY=y/.RandomChoice[solutionsY];
{travelX,travelY}
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nextPoint={0,0};
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ListPlot[ranWalk,PlotStyle->{PointSize[.015],Magenta},Frame->True,FrameLabel->{"Distance into paramagnetic layer","","Biased random walk model, for small current density"},LabelStyle->{14,Black},ImageSize->400]

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ImageSize->300,PlotLabel->"Random Walk simulation, small current density"],
{n,1,Length[ranWalk]-1,1},AnimationRunning->False,SaveDefinitions->True
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τCollision=3;
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Understanding the spin valve-- Spin extraction

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densityDownSpinElectrons=((totalElectronDensity/2)+deviation E^(-αP x))/.{αP-> (currentDensity/(chargeElectron*totalElectronDensity)+Sqrt[currentDensity/(chargeElectron*totalElectronDensity)^2 +4 (diffusionCoefficient/τRelaxation)])/(2 diffusionCoefficient),deviation-> totalElectronDensity/(Sqrt[1+4 diffusionCoefficient/(τRelaxation currentDensity/(chargeElectron*totalElectronDensity)^2 )]-1)};
densityUpSpinElectrons=((totalElectronDensity/2)-deviation E^(-αP x))/.{αP-> (currentDensity/(chargeElectron*totalElectronDensity)+Sqrt[currentDensity/(chargeElectron*totalElectronDensity)^2 +4 (diffusionCoefficient/τRelaxation)])/(2 diffusionCoefficient),deviation-> totalElectronDensity/(Sqrt[1+4 diffusionCoefficient/(τRelaxation currentDensity/(chargeElectron*totalElectronDensity)^2 )]-1)};

Manipulate[
Plot[{densityDownSpinElectrons/.{totalElectronDensity->1,currentDensity->CurrentDensity,chargeElectron->1,diffusionCoefficient->2,τRelaxation->1},densityUpSpinElectrons/.{totalElectronDensity->1,currentDensity->CurrentDensity,chargeElectron->1,diffusionCoefficient->2,τRelaxation->1}},{x,0,5},PlotRange->{{0,5},{0,1}},PlotStyle->{Thickness[.007],Magenta},Frame->True,FrameLabel->{"Distance away from boundary, into the paramagnetic layer","Spin Polarization","Up and down spin polarization in paramagnetic layer"},PlotLegends->{"(Subscript[P, down])","(Subscript[P, up])"},LabelStyle->{14,Black},ImageSize->400],{CurrentDensity,.00001,Evaluate[(chargeElectron totalElectronDensity Sqrt[diffusionCoefficient/(2 τRelaxation)])/.{totalElectronDensity->1,currentDensity->i,chargeElectron->1,diffusionCoefficient->2,τRelaxation->1}]},SaveDefinitions->True
];

Manipulate[
Show[up[t],down[t]],{{t,3,"start electron motion"},3,∞,Trigger},ControlPlacement->Top,TrackedSymbols->True,
Initialization:>(
Do[ϕx[n]=RandomReal[{0,2π}],{n,1,1000}];Do[ϕy[n]=RandomReal[{0,2 π}],{n,1,1000}];Do[ωx[n]=RandomReal[{-.5,2}],{n,1,1000}];Do[ωy[n]=RandomReal[{-.5,.5}],{n,1,1000}];
Do[ϕxDown[n]=RandomReal[{0,2π}],{n,1,1000}];Do[ϕyDown[n]=RandomReal[{0,2π}],{n,1,1000}];Do[ωxDown[n]=RandomReal[{-.5,2}],{n,1,1000}];Do[ωyDown[n]=RandomReal[{-.5,.5}],{n,1,1000}];
biased[n_,t_]:=4.5+2*4.5*Piecewise[{{-Sin[(3/2)Mod[ϕx[n]+.1ωx[n]t,2Pi/3]],Mod[ϕx[n]+.1ωx[n]t,2*Pi]>(4Pi/3)},
{Sin[(3/4)Mod[ϕx[n]+.1ωx[n]t,4Pi/3]],(Mod[ϕx[n]+.1ωx[n]t,2*Pi]≤(4Pi/3))&&Mod[(ϕx[n]+.1ωx[n]t-Mod[ϕx[n]+.1ωx[n]t,4*Pi/3])/(Pi),2]==0},{Sin[(3/4)(ϕx[n]+.1ωx[n]t+2Pi/3)],(Mod[ϕx[n]+.1ωx[n]t,2*Pi]≤(4Pi/3))&&Mod[(ϕx[n]+.1ωx[n]t-Mod[ϕx[n]+.1ωx[n]t,4*Pi/3])/(Pi),2]≠ 0}}];
y[n_,t_]:=4.5Sin[ϕy[n]+.1ωy[n]t];
biasedDown[n_,t_]:=(4.5*Piecewise[{{-Sin[(3/2)Mod[ϕx[n]+.1ωx[n]t,2Pi/3]],Mod[ϕx[n]+.1ωx[n]t,2*Pi]>(4Pi/3)},
{Sin[(3/4)Mod[ϕx[n]+.1ωx[n]t,4Pi/3]],(Mod[ϕx[n]+.1ωx[n]t,2*Pi]≤(4Pi/3))&&Mod[(ϕx[n]+.1ωx[n]t-Mod[ϕx[n]+.1ωx[n]t,4*Pi/3])/(Pi),2]==0},{Sin[(3/4)(ϕx[n]+.1ωx[n]t+2Pi/3)],(Mod[ϕx[n]+.1ωx[n]t,2*Pi]≤(4Pi/3))&&Mod[(ϕx[n]+.1ωx[n]t-Mod[ϕx[n]+.1ωx[n]t,4*Pi/3])/(Pi),2]≠ 0}}])/.{x-> ϕxDown[m]+.1ωxDown};
yDown[m_,t_]:=4.5Sin[ϕyDown[m]+.1ωyDown[m]t];up[t_]:=Graphics[{Table[{Disk[{biased[n,t],y[n,t]},.4],Green,Thickness[.005],Arrowheads[.02],Arrow[{{biased[n,t],y[n,t]-.3},{biased[n,t],y[n,t]+.3}}]},{n,1,140}]},PlotRange->{{-5,14.5},{-5,5}},ImageSize->600];

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),SaveDefinitions->True];

Summary

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dialogFuncDoWork[cell_Cell]:=Module[{position=RandomInteger[{1,10}]},CreateDialog[Notebook[{cell,RowBox[ReplacePart[ConstantArray["\t\t",{10}],position->buttonCell[cell]]]},WindowFloating->True,WindowSize->{Scaled[0.25],All},PageWidth->$dialogW,WindowMargins->{{Automatic,10},{Automatic,20}},StyleDefinitions->styleNotebook,Saveable->False,TaggingRules->{"count"->$userWaitTime}]]]

nextScript[]:=Module[{first},If[$scriptList=!={},{first,$scriptList}={First[$scriptList],Rest[$scriptList]};
dialogFuncDoWork[first];]];

getSolution[file_]:=Module[
{thekey,templateDirectory},
thekey=Input["Enter the supplied key"];
If[!StringQ[thekey],thekey=ToString[thekey]];
If[($Failed==Quiet[Get[FileNameJoin[{NotebookDirectory[],"solutions",file<>"_encrypted.m"}],thekey]]),Print["Failed to open solution with provided key"];Return[]];
$scriptList=Get[FileNameJoin[{NotebookDirectory[],"solutions",file<>"_encrypted.m"}],thekey];
(*templateDirectory=FileNameJoin[{"/","Users","ccarter","Dropbox","MSC_2.0","TUTORIAL_PACKAGES","Packages_In_Development","New_Template_Development","New_Template","solutions"}];
styleNotebook=Import[FileNameJoin[{templateDirectory,"style_notebook.nb"}]];*)
$destinationNotebook=CreateDocument[Cell["Prototype Solution from "<>file<>"  "<>DateString[],"WorkedTitle"],WindowTitle->"Prototype Solution from "<>file<>"  "<>DateString[],Saveable->False,WindowMargins->{{20,Automatic},{20,Automatic}},Background->GrayLevel[0.98],StyleDefinitions->styleNotebook];
SelectionMove[$destinationNotebook,After,Notebook];
nextScript[];]

(*snb = Import["/Users/ccarter/Dropbox/MSC_2.0/TUTORIAL_PACKAGES/Packages_In_Development/Brick_Wall_Package/front_end_source_materials/style_notebook.nb"]*)