We develop an efficient and general method for optimizing the microwave field that achieves magnetization switching with a smaller static field. This method is based on optimal control and renders an exact solution for the 3D microwave field that tri
ggers the switching of a nanomagnet with a given anisotropy and in an oblique static field. Applying this technique to the particular case of uniaxial anisotropy, we show that the optimal microwave field, that achieves switching with minimal absorbed energy, is modulated both in frequency and in magnitude. Its role is to drive the magnetization from the metastable equilibrium position towards the saddle point and then damping induces the relaxation to the stable equilibrium position. For the pumping to be efficient, the microwave field frequency must match at the early stage of the switching process the proper precession frequency of the magnetization, which depends on the magnitude and direction of the static field. We investigate the effect of the static field (in amplitude and direction) and of damping on the characteristics of the microwave field. We have computed the switching curves in the presence of the optimal microwave field. The results are in qualitative agreement with micro-SQUID experiments on isolated nanoclusters. The strong dependence of the microwave field and that of the switching curve on the damping parameter may be useful in probing damping in various nanoclusters.
We consider a current-biased dc SQUID in the presence of an applied time-dependent bias current or magnetic flux. The phase dynamics of such a Josephson device is equivalent to that of a quantum particle trapped in a $1-$D anharmonic potential, subje
ct to external time-dependent control fields, {it i.e.} a driven multilevel quantum system. The problem of finding the required time-dependent control field that will steer the system from a given initial state to a desired final state at a specified final time is formulated in the framework of optimal control theory. Using the spectral filter technique, we show that the selected optimal field which induces a coherent population transfer between quantum states is represented by a carrier signal having a constant frequency but which is time-varied both in amplitude and phase. The sensitivity of the optimal solution to parameter perturbations is also addressed.
