Abstract
A spin-torque switchable magnetic tunnel junction contains two ferromagnetic electrodes across a barrier that supports spin-polarized tunnel current. The spin-torque induced magnetic switching of its more agile, or “free” layer provides the “write” mechanism. Often the dynamics of the non-switching “reference” layer is also important. Here, we illustrate such dynamics involving both the free and the reference layers by using an exchange-coupled two-macrospin-moment numerical model, described by a set of Landau–Lifshitz–Gilbert (LLG) equations, together with a stochastic Langevin-field for finite temperature. Damping-like spin-transfer torque is included for both moments. In steady-state, the coupled precession is shown to reduce effective spin-current delivered to the free layer due to a precessional resonant spin-current back flow. This back-flow of spin current preferentially affects the parallel state dynamics. It is not directly related to the reference layer’s thermal stability, nor its spin-torque switching threshold, as determined by the total anisotropy energy and magnetic volume. Rather, the spin-current reduction relates primarily to the matching of precession frequency between the free- and the reference-layer. Therefore, a desirable materials choice is to avoid anisotropy fields giving the free and the reference layer similar dynamic frequencies, so as to prevent such resonance-related spin-current loss.
Highlights
We model an magnetic tunnel junction (MTJ) numerically by two macrospin m1,2 in a coupled Landau–Lifshitz–Gilbert Equation set, including all relevant spin-current and exchange coupling terms
The dynamics of a single macrospin m in a rotational field in unit-vector form with the definition of nm = m/∣m∣ can be written as 1 γ dnm dt
With Ha the applied field including time-dependent terms such as a precessional field, Hk the total anisotropy field, and HL the Langevin field reflecting finite temperature thermal agitation
Summary
We model an MTJ numerically by two macrospin m1,2 in a coupled Landau–Lifshitz–Gilbert Equation set, including all relevant spin-current and exchange coupling terms. We consider two moments that are mutually coupled via an exchange interaction of energy Eex. The over-all energy of the two-moment system is Expressed in torque-dynamics form, and adding to the coupled system a (tunnel) spin-current term from m2 to m1 with a polarization direction of nm2, and vise versa from m1 to m2,20 the coupled LLG equation becomes
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