Entropy and canonical ensemble of hybrid quantum classical systems

In this work we generalize and combine Gibbs and von Neumann approaches to build, for the first time, a rigorous definition of entropy for hybrid quantum-classical systems. The resulting function coincides with the two cases above when the suitable limits are considered. Then, we apply the MaxEnt principle for this hybrid entropy function and obtain the natural candidate for the hybrid canonical ensemble (HCE). We prove that the suitable classical and quantum limits of the HCE coincide with the usual classical and quantum canonical ensembles since the whole scheme admits both limits, thus showing that the MaxEnt principle is applicable and consistent for hybrid systems

Spin-orbit torque from the introduction of Cu interlayers in Pt/Cu/Co/Pt nanolayered structures for spintronic devices

Spin currents can modify the magnetic state of ferromagnetic ultrathin films through spin-orbit torque. They may be generated by means of spin-orbit interactions by either bulk or interfacial phenomena. Electrical transport measurements reveal a 6-fold increase of the spin-orbit torque accompanied by a drastic reduction of the spin Hall magnetoresistance upon the introduction of an ultrathin Cu interlayer in a Pt/Cu/Co/Pt structure with perpendicular magnetic anisotropy. We analyze the dependence of the spin Hall magnetoresistance with the thickness of the interlayer, ranging from 0.5 to 15 nm, in the frame of a drift diffusion model that provides information on the expected spin currents and spin accumulations in the system. The results demonstrate that the major responsibility of both effects is spin memory loss at the interface. The enhancement of the spin-orbit torque when introducing an interlayer opens the possibility to design more efficient spintronic devices based on materials that are cheap and abundant such as copper. More specifically, spin-orbit torque magnetic random access memories and spin logic devices could benefit from the spin-orbit torque enhancement and cheaper material usage presented in this study