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Electric-field control of strain-mediated magnetoelectric random access memory
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18.The hard layer is usually pinned as a part of a trilayer known as synthetic antiferromagnet (SAF) that is free of stray magnetic field in conventional MTJ-based MRAMs (Ref. 4), however in the present SME-RAM device, the SAF trilayer is not necessary since there is no external magnetic field applied during the reading process. Instead, an individual magnetic layer in which the magnetization vector is more difficult to rotate upon the electric field is used, as compared to that in the free layer.
20.Suppose the transverse electric field is not high enough to induce an out-of-plane switching of the spontaneous magnetization. Hence, the direction cosine is considered to be zero herein (Ref. 15).
21.The exchange coupling in a MTJ unit is usually weaker than that in a spin-valve structure based on the GMR effect due to the utilization of an insulating oxide barrier rather than a nonmagnetic metal layer. Accordingly, a relative small anisotropy energy value is assumed for the present calculations.
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30.Note the spontaneous orientation in the free layer may orient along the  direction, i.e., , if not pinned by the upper hard layer (Ref. 15).
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A strain-mediated magnetoelectric random access memory with electric-field-writing is presented, which consists of a magnetic tunnel junction (MTJ) in intimate contact with a ferroelectric (FE) layer. The calculations show that the magnetization vector in the free layer of the MTJ unit can switch in-plane by 90° upon applying an appropriate electric field to the FE layer, as compared to the common 180° reversal induced by magnetic field or spin-current. A perfect interface between the FE layer and the MTJ is assumed. The free layers used for illustration include either (001)-oriented or polycrystalline magnetic films of Fe–Co alloy, (CFO), Ni, and . Among them, the (001)-oriented FeCo and CFO films with positive magnetocrystalline anisotropy constant (i.e., ) show an abrupt magnetization switching, while a gradual magnetization switching takes place in the (001)-oriented Ni and films with as well as the polycrystalline films. Such electric-field-induced in-plane magnetization switching can result in a remarkable change in the MTJ’s electric resistance. In particular, hysteretic dependence of the device resistance on the applied electric field is obtained for the cases of the (001)-oriented FeCo and CFO free layers that exhibit the abrupt magnetization switching, whereby a nonvolatile information storage process can be achieved. The influence of the shape of the free layer on both magnetization and resistance switching features is discussed.
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