1. On what factors Slonczewski Spin-transfer torque parameters (Lambda and epsilon prime) depend for a multi-layer system? and how to evaluate them?
2. Is there any way to evaluate these parameters theoretically using material parameters and current density?
I am studying spin transfer torque nano oscillator of a system with ferromagnetic reference layer, spacer layer and a fixed layer(ferromagnetic layer) through micro-magnetic simulations using mumax3 software. In the literature, I didn't find any link or the meaning of why these parameters have specific values. (I mean like, Lambda = 1, epsilon prime = 0)
Sateesh Kandukuri We often do simulations using parameters that we do not understand well, but that play a fundamental role in the final solution of the problem. In this case, the EpsilonPrime and Lambda parameters, to be honest, I haven't figured out how to evaluate them experimentally, but I believe I understood why their values are often used. Looking carefully at the equations behind OOMMF and MUMAX, we have the definition of the spin torque equation derived by Slonczewski:
STT = |gamma|beta * (ε(mp x m) - ε'*mp)
gamma -> Gilbert gyromagnetic ratio
beta = |C| * J/t*Msat
m -> reduced magnetization
mp -> electron polarization direction
ε -> in-plane spin-torque term
ε'-> out-of-plane spin-torque term (equivalent to EpsilonPrime in Mumax)
EpsilonPrime definition in http://mumax.github.io/api.html
EpsilonPrime = Slonczewski "secondairy" STT term
ε' = 0 (out-of-plane spin-torque term)
ε = P*Λ²/(Λ² + 1)+(Λ² - 1)(m.mp) // (in-plane spin-torque term)
Lambda -> Slonczewski Λ parameter Λ = 1
P -> polarization
Lambda must be larger than or equal to 1; set Lambda=1 to remove the dependence of ε on (m.mp). If you want non-zero ε', it is set directly as EpsilonPrime.
I performed the simulation of the EpsilonPrime parameter with values: 0 and 0.5, note that the magnetization changes significantly. If you find something that complements this subject, please post here, good research.
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