2009.04.06-ECE659-L32-notes

2009.04.06-ECE659-L32-notes - ECE 659 Quantum Transport:...

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ECE 659 Quantum Transport: Atom to Transistor Lecture 32: Spin Torque/Pseudo spin Supriyo Datta Spring 2009 Notes prepared by Samiran Ganguly
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m 1 μ 2 m ( 29 2 B S B - × a a ( 29 ( 29 ( 29 n n n n in in op i I HG G H G G G G + + = - + Σ - Σ + Σ - Σ ( 29 n op G i H s t I i t ψψ ψ + + = + Σ + ( 29 , 1 1. , . , 1 1. n n n op m m m m m m m m m m m m m I H G H G H G - - + + = + + , m m Spin torque: ( 29 ( 29 , . 2 1 n B m m m m Trace H G S B i σ - × a a a With a usual magnet we get B=1T 1 A 1 Ang 1 Ang 23 10 0.1 B B J meV - = We can increase the field by including the magnet in the channel
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This can give rise to 1 eV splitting : 10 4 T due to exchange interaction 26 2 2 6 2 6 2 6 18 1 2 2 3 3 4 3 Fe s s p s p s d = dhhhDhhh± d: 4 unpaired electrons 4 B μ A thin magnet (a few monolayers) can be flipped by this force If: B km = a a 4 10 B T unit cell ( 29 ( 29 B B dm g S km dt g m kS = × = - × a a a a a 5 10 B unit cell - ( 29 ( 29 B B dS g S B dt dm g S B dt = - × = + × a a a a a a Moving electrons Magnet 0.1 kS T a enough to flip a magnet This torque, however is applicable only on the surface monolayers because electrons start to align themselves in the direction of magnetic field inside the magnet, thereby decreasing the torque.
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This note was uploaded on 01/30/2011 for the course ECE 659 taught by Professor Staff during the Spring '08 term at Purdue.

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2009.04.06-ECE659-L32-notes - ECE 659 Quantum Transport:...

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