Spin-lattice dynamics simulation of the Einstein–de Haas effect

The spin and lattice dynamics of a ferromagnetic nanoparticle are studied via molecular dynamics and with semi-classical spin dynamics simulations where spin and lattice degrees of freedom are coupled via a dynamic uniaxial anisotropy term. We show that this model conserves total angular momentum, whereas spin and lattice angular momentum are not conserved. We carry out simulations of the Einstein–de Haas effect for a Fe nanocluster with more than 500 atoms that is free to rotate, using a modified version of the open-source spin-lattice dynamics code (SPILADY). We show that the rate of angular momentum transfer between spin and lattice is proportional to the strength of the magnetic anisotropy interaction. The addition of the anisotropy allows full spin-lattice relaxation to be achieved on previously reported timescales of ∼ 100 ps and for tight-binding magnetic anisotropy energies comparable to those of small Fe nanoclusters. We acknowledge financial support from the Ministry of Science and Innovation of Spain (grant No. PID2019-109539GB-4). This work was supported by the Generalitat Valenciana, Spain through PROMETEO2017/139 and PROMETEO/2021/017. C. S. gratefully acknowledges financial supports from Generalitat Valenciana with (CDEIGENT2018/028). JFR acknowledges funding from FCT, Portugal grant PTDC/FIS-MAC/2045/2021. The SLD calculations in this paper were performed on the high-performance computing facilities of the University of South Africa.