The Otto thermodynamic cycle using the magnetic molecule Ni$_2$

In order to design realistic molecular heat engines, the study of quantum thermodynamics is essential since classical thermodynamics does not apply in this extreme miniaturization limit [1,2]. Realizing a thermodynamic cycle on an existing magnetic molecule embodies a novel and unique approach to understand and exploit the thermodynamic properties of spin at the molecular level.\\ Here we propose an Otto cycle in the Ni$_2$ dimer based on a fully ab-initio calculation of the electronic states and the perturbative inclusion of spin-orbit coupling. A laser pulse, described by the time-dependent Schr\"{o}dinger equation, is used to heat the Ni$_2$ dimer. The pulse not only excites the electrons to higher, many-body electronic states, but also influences the spin of the system due to spin-orbit coupling. Using a low-temperature thermal bath the system is cooled back to the ground state. The adiabatic work exchange between the Ni$_2$ and the environment is described by the quasi-static expansion or compression of the bond length of the dimer. The calculated efficiency of the cycle is up to 34\%.\\ $[1]$ T. D. Kieu, Phys. Rev. Lett. {\bf 93 } 140403 (2004)\\ $[2]$ H. T. Quan, Phys. Rev. E {\bf 79} 041129 (2009)\\ $[3]$ T. Zhang \emph{et al.}, Phys. Rev. A {\bf 75} 062102 (2007)