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MTJ Magnetization Dynamics Model

MTJ Magnetization Dynamics Model. Introducing Temperature and Bias Voltage Dependencies. LLGE with Spin-Torque Transfer (1). LLGE with Spin-Torque Transfer (2). “Efficiency” Factor: b( θ ). Dependant upon θ, the angle between the magnetizations of the free and fixed layers. [m·p = cos(θ)]

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MTJ Magnetization Dynamics Model

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  1. MTJ Magnetization Dynamics Model Introducing Temperature and Bias Voltage Dependencies

  2. LLGE with Spin-Torque Transfer (1)

  3. LLGE with Spin-Torque Transfer (2)

  4. “Efficiency” Factor: b(θ) • Dependant upon θ, the angle between the magnetizations of the free and fixed layers. [m·p = cos(θ)] • Higher spin-polarization “efficiency” in the anti-parallel state. • P→AP requires approximately 20-50% more current than AP→P

  5. Magnetization Saturation • Modeled using Weiss theory of ferromagnetism • TC is the Currie Temperature • β is material dependant

  6. Spin-Polarization (1) • TMR can be written in terms of conductance: • Conductance dependant on spin-polarization: • Spin-polarization exhibits the following temperature dependency*: • Conductance: • TMR:

  7. Spin-Polarization (2) • Spin-polarization changing with temperature affects RP, RAP, TMR, and b(θ). • P0 for ferromagnetic CoFeB can as high as 65%. • α for a MgO barrier is on the order of 4x10-5 [K-3/2]

  8. Bias Voltage

  9. Future Work • Working on Matlab and VerilogA implementation • Should verify model with device people • Fit model to fabricated MTJs • Paper

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