ИСТИНА

Measured switching voltage-field diagrams of perpendicular MTJ exhibit unexpected behavior at high voltages. The boundaries deviate from the critical lines corresponding to the coercive field, which contrasts with the theoretically predicted behavior of a standard macrospin model. Here we are proposing to modify the model by taking into account the Joule heating during a writing pulse, which reduces the anisotropy, thereby reducing the coercive field during the switching. Our model is based on the experimental studies of temperature dependence of PMA that give an expression for uniaxial anisotropy constant K=K0(Ms(T)/Ms0)2 [1]. Supposing that Ms(T)=Ms0(1-T/Tc)1/3 for anisotropic ferromagnet with Curie temperature Tc [2] and assuming that the temperature varies with voltage as T∼V2 due to Joule heating, the resulting voltage dependence of the PMA writes K=K0(1-kvV2/Tc)2/3. Here kv is a function of writing pulse duration, thermal capacity of the storage layer and its resistance. It depends on the polarity of the current as suggested by earlier experimental study [3]. Numerical macrospin simulations based on this model reproduce very well experimental data. They are consistent also with the results of linearization of LLG equation in frames of Slavin-Tiberkevich theory [4]. [1] J.Alzate et al APL 104, 112410 (2014) [2] R.Skomski et al J.App.Phys. 99, 08E916 (2006) [3] E.Gapihan et al APL 100, 202410 (2012) [4] A.Slavin, V.Tiberkevich IEEE Trans. Magn. 45 1875 (2009)