General switching voltages for magnetic tunnel junctions with in-plane and/or perpendicular-to-plane anisotropy free layers

We analytically calculate the switching voltages for MgO-based magnetic tunnel junctions for the generalized case where the free layer has two generic “intrinsic” fields oriented along orthogonal directions. The magnetization of the reference layer and the applied field are assumed to be parallel to one of the two intrinsic field axis. Both the in-plane and the field-like spin-torque terms are taken into account, with the field-like torque assumed to have a quadratic dependence on the applied voltage and to favour the antiparallel state [1]. The switching voltages thus determined can be particularized for different geometries by replacing the two generic intrinsic field terms with the appropriate expressions for the anisotropy and demagnetizing fields, according to the specific free and reference layer configuration considered. The results are consistent with numerical integration of the Landau-Lifshitz-Gilbert equation with the relevant spin-torque terms.
For in-plane MgO-based magnetic tunnel junctions, one of the two intrinsic fields of the free layer corresponds to the (negative) demagnetizing field, which pulls the magnetization of the free layer towards the film plane. The orthogonal intrinsic field component is the easy-axis anisotropy, parallel to the current polarization and the external field direction. We demonstrate that in this configuration the quadratic dependence of the field-like torque on the applied voltage can cause back-hopping (a somewhat obscure behaviour characteristic to tunnel junctions, whereby reliable switching to the desired state is achieved for applied voltages of the order of the critical voltage, but a larger applied bias induces a telegraph-noise behaviour [2, 3]). For perpendicular anisotropy tunnel junctions without in-plane shape anisotropy, the only intrinsic field present in the free layer is parallel the effective anisotropy, parallel to the reference layer direction. In this case, we find that neither back-hopping, nor spin-transfer driven steady stare precession are expected, as evidenced by experimental results [4]. Finally, if an in-plane shape anisotropy is considered in addition to the effective perpendicular anisotropy, a variety of canted states are predicted [5].
REFERENCES
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